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For moir\'e bilayer TMD superlattices, full-configuration-interaction (FCI) calculations are presented that take into account both the intra-moir\'e-quantum-dot (MQD) charge-carrier Coulombic interactions, as well as the crystal-field effect from the surrounding moir\'e pockets (inter-moir\'e-QD interactions). Such FCI calculations enable an effective computational embedding strategy and allow for a complete interpretation of the counterintuitive experimental observations reported recently in the context of moir\'e TMD superlattices at integer fillings $\nu=2$ and 4. Two novel states of matter are reported: (i) a genuinely quantum-mechanical supercrystal of {\it sliding\/} Wigner molecules (WMs) for unstrained moir\'e TMD materials (when the crystal field is commensurate with the trilobal symmetry of the confining potential in each embedded MQD) and (ii) a supercrystal of {\it pinned\/} Wigner molecules when strain is involved and the crystal field is incommensurate with the trilobal symmetry of the confining potential in each embedded MQD. The case of $\nu=3$ is an exception, in that both unstrained and strained cases produce a supercrystal of pinned WMs, which is due to the congruence of intrinsic (that of the WM) and external (that of the confining potential of the MQD) $C_3$ point-group symmetries. Furthermore, it is shown that the unrestricted Hartree-Fock approach fails to describe the supercrystal of sliding WMs in the unstrained case, providing a qualitative agreement only in the case of a supercrystal of pinned WMs, Comment: 7 pages, 4 color figures. For similar papers, see https://sites.gatech.edu/cyannouleas/. arXiv admin note: text overlap with arXiv:2403.12262

The spectral properties of electrons confined in a wire-like quasi-one-dimensional (1D) elongated quantum dot (EQD) coupler between silicon qubits, are investigated with a newly developed valley-augmented unrestricted Hartree-Fock (va-UHF) method, generalized to include the valley degree of freedom treated as an isospin, allowing calculations for a large number of electrons. The lower energy symmetry-broken solutions of the self-consistent generalized Pople-Nesbet equations exhibit, for a confinement that has been modeled after an experimentally fabricated one in silicon, formation of Wigner-molecular polymeric (longitudinal) chains, initiating through charge accumulation at the edges of the finite-length quasi-1D wire. An increasing number of parallel zig-zag chains form as the number of electrons loaded into the confinement is increased, with the formation of newly added chains determined by the strength of the transverse harmonic confinement. The broken-symmetry va-UHF solutions, subsequently augmented by the quantum-mechanically required parity-restoration, go beyond the va-UHF single-determinant solution, predicting formation of entangled Wigner-molecular chains whose charge distributions obliterate the zig-zag organization of the broken-symmetry solutions. The symmetry-restored va-UHF methodology enables systematic investigations of multi-electron complex nano-scale confined structures that could be targeted for future imaging microscopy experiments in silicon and other materials (e.g., 1D domain walls in TMD materials), and quantum information utilization., Comment: 10 pages, 10 color figures. Accepted for publication in Physical Review Applied. For related papers, see https://sites.gatech.edu/cyannouleas/

The few-body problem for $N=4$ fermionic charge carriers in a double-well moir\'{e} quantum dot (MQD), representing the first step in a bottom-up strategy to investigate formation of molecular supercrystals in transition metal dichalcogenide (TMD) moir\'e superlattices with integral fillings, $\nu > 1$, is solved exactly by employing large-scale exact-diagonalization via full configuration interaction (FCI) computations. A comparative analysis with the mean-field solutions of the often used spin-and-space unrestricted Hartree Fock (sS-UHF) demonstrates the limitations of the UHF method (by itself) to provide a proper description of the influence of the interdot Coulomb interaction. In particular, it is explicitly shown for $\nu=2$ that the exact charge densities (CDs) within each MQD retain the ring-like shape characteristic (for a wide range of relevant parameters) of a fully isolated MQD, as was found for sliding Wigner molecules (WMs). This deeply quantum-mechanical behavior contrasts sharply with the UHF CDs that portray solely orientationally pinned and well localized dumbbell dimers. An improved CD, which agrees with the FCI-calculated one, derived from the restoration of the sS-UHF broken parity symmetries is further introduced, suggesting a beyond-mean-field methodological roadmap for correcting the sS-UHF results. It is conjectured that the conclusions for the $\nu=2$ moir\'e TMD superlattice case extend to all cases with integral fillings that are associated with sliding WMs in isolated MQDs. The case of $\nu=3$, associated with a pinned WM in isolated MQDs, is an exception., Comment: 9-page Letter with 5 color figures. For related papers, see https://sites.gatech.edu/cyannouleas/

The few-body problem (with $N \leq 6$ fermionic charge carriers) in isolated moir\'{e} quantum dots (MQDs) in transition metal dichalcogenide (TMD) bilayer materials with integer fillings, $\nu \geq 2$, is investigated by employing large-scale full configuration interaction (FCI, also termed exact-diagonalization) computations, and by performing a comparative analysis of the ensuing first-order (charge densities, CDs) and second-order (conditional probability distributions, CPDs) correlation functions. With parameters representative of bilayer experimental TMD setups, our investigations reveal the determining role of the strong inter-particle Coulombic repulsion in bringing about Wigner molecularization, which is associated with many-body physics beyond both that described by the Aufbau principle of natural atoms, as well as by the widely used Hubbard model for strongly-interacting condensed-matter systems. In particular, for weak and moderate trilobal crystal-field deformations of the MQDs, the imperative employment of the CPDs brings to light the geometrical polygonal-ring configurations underlying the Wigner molecules (WMs) that remain hidden at the level of a charge-density analysis, apart from the case of $N=3$ when a pinned WM emerges in the charge density due to the coincidence of the $C_3$ symmetries associated with both the intrinsic geometry of the $N=3$ WM and the TMD trilobal crystal-field of the confining pocket potential. The FCI numerically exact-diagonalization results provide critical benchmarks for assessing and guiding the development of future computational methodologies of interacting strongly-correlated fermions in isolated MQDs and their superlattices in TMD materials., Comment: Published version (Editors' Suggestion). 11 pages. 7 color figures. For related papers, see https://sites.gatech.edu/cyannouleas/

The influence of strong electron-electron interactions and Wigner-molecule (WM) formation on the spectra of $2e$ singlet-triplet double-dot Si qubits is presented based on a full configuration interaction (FCI) approach that incorporates the valley degree of freedom (VDOF) in the context of the continuous (effective mass) description of semiconductor materials. Our FCI treats the VDOF as an isospin in addition to the regular spin. Our treatment is able to assign to each energy curve in the qubit's spectrum a complete set of good quantum numbers for both the spin and the valley isospin. This reveals an underlying SU(4) $\supset$ SU(2) $\times$ SU(2) group-chain organization in the Si double-dot spectra. With parameters in the range of actual experimental situations, we demonstrate in a double-dot qubit that, in the (2,0) charge configuration and compared to the expected large, and dot-size determined, single-particle (orbital) energy gap, the strong $e-e$ interactions drastically quench the spin-singlet$-$spin-triplet energy gap, $E_{\rm ST}$, within the same valley, making it competitive to the small energy gap, $E_V$, between the two valleys. We present results for both the $E_{\rm ST} < E_V$ and $E_{\rm ST} > E_V$ cases. We investigate the spectra as a function of detuning and demonstrate the strengthening of the avoided crossings due to a lowering of the interdot barrier and/or the influence of valley-orbit coupling. We further demonstrate, as a function of an applied magnetic field, the emergence of avoided crossings in the (1,1) charge configuration due to the spin-valley coupling. The valleytronic FCI formulated here, and implementeded for two electrons confined in a tunable double quantum dot, offers also a most effective tool for analyzing the spectra of Si qubits with more than two wells and/or more than two electrons., Comment: 19 pages with 6 color figures. A longer and more complete abstract can be found in the PDF file of the manuscript. For related papers, see https://sites.gatech.edu/cyannouleas/

It is demonstrated that exact diagonalization of the microscopic many-body Hamiltonian via systematic full configuration-interaction (FCI) calculations is able to predict the spectra as a function of detuning of three-electron hybrid qubits based on GaAs asymmetric double quantum dots. It is further shown that, as a result of strong inter-electron correlations, these spectroscopic patterns, including avoided crossings between states associated with different electron occupancies of the left and right wells, are inextricably related to the formation of Wigner molecules. These physical entities cannot be captured by the previously employed independent-particle or Hubbard-type theoretical modeling of the hybrid qubit. We report remarkable agreement with recent experimental results. Moreover, the present FCI methodology for multi-well quantum dots can be straightforwardly extended to treat Si/SiGe hybrid qubits, where the central role of Wigner molecules was recently experimentally confirmed as well., Comment: Letter, 10 pages, 2 color figures. For the related in-depth study, see arXiv:2204.02243. For other related papers, see https://sites.gatech.edu/cyannouleas/about. arXiv admin note: substantial text overlap with arXiv:2204.02243

We show that systematic full configuration-interaction (FCI) calculations enable prediction of the energy spectra and the intrinsic spatial and spin structures of the many-body wave functions as a function of the detuning parameter for the case of three-electron hybrid qubits based on GaAs asymmetric double quantum dots. Specifically, in comparison with the case of weak interactions and treating the entire three-electron double-dot hybrid qubit as an integral unit, it is shown that the predicted spectroscopic patterns, originating from strong electron correlations, manifest the formation of Wigner molecules (WMs). Signatures of WM formation include: (1) a strong suppression of the energy gaps relative to the non-interacting-electrons modeling, and (2) the appearance of a pair of avoided crossings arising between states associated with two-electron occupancies in the left and right wells. The Wigner molecule is a physical entity associated with electron localization within each well and it cannot be captured by the previously employed independent-particle or two-site-Hubbard theoretical modeling of the hybrid qubits. The emergence of strong WMs is investigated in depth through the concerted use of FCI-adapted diagnostic tools like charge and spin densities, as well as conditional probability distributions. Furthermore, the energy spectrum as a function of the strength of the Coulomb repulsion (at constant detuning) is calculated in order to complement the thorough analysis of the factors contributing to WM emergence. We report remarkable agreement with recent experimental measurements. The present FCI methodology for multi-well quantum dots can be straightforwardly extended to treat valleytronic two-band Si/SiGe hybrid qubits, where the central role of the WMs was confirmed recently., Comment: Published version. 16 pages with 9 color figures. For related publications, see https://sites.gatech.edu/cyannouleas/about/

Measurements and a theoretical interpretation of the excitation spectrum of a two-electron quantum dot fabricated on a parabolic Ga[Al]As quantum well are reported. Experimentally, excited states are found beyond the well-known lowest singlet- and triplet states. These states can be reproduced in an exact diagonalization calculation of a parabolic dot with moderate in-plane anisotropy. The calculated spectra are in reasonable quantitative agreement with the measurement, and suggest that correlations between the electrons play a significant role in this system. Comparison of the exact results with the restricted Hartree-Fock and the generalized Heitler-London approach shows that the latter is more appropriate for this system because it can account for the spatial correlation of the electron states., Comment: ICPS28 (Vienna 2006) conference paper announcing early experimental results in semiconductor quantum dots that were successfully interpreted as a signature (strong suppression of the singlet-triplet gap) of Wigner-molecule formation, in accordance with previous theoretical work and predictions; see Ref. [7] in this paper

Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin $0 \leq S \leq N/2$ in the neighborhood of the $\nu=1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical predictions for higher-order spatial and momentum correlations reveal intrinsic polygonal, multi-ring crystalline-type structures, which can be tested with ultracold-atom experiments in rapidly rotating traps, simulating quantum Hall physics (including quantum LLL skyrmions)., Comment: Accepted for publication as a letter in Phys. Rev. Research. 12 pages with 3 color figures, including the Supplemental Material. For related papers, see https://sites.gatech.edu/cyannouleas/about/

Realizing high-performance nanoelectronics requires control of materials at the nanoscale. Methods to produce high quality epitaxial graphene (EG) nanostructures on silicon carbide are known. The next step is to grow Van der Waals semiconductors on top of EG nanostructures. Hexagonal boron nitride (h-BN) is a wide bandgap semiconductor with a honeycomb lattice structure that matches that of graphene, making it ideally suited for graphene-based nanoelectronics. Here, we describe the preparation and characterization of multilayer h-BN grown epitaxially on EG using a migration-enhanced metalorganic vapor phase epitaxy process. As a result of the lateral epitaxial deposition (LED) mechanism, the grown h-BN/EG heterostructures have highly ordered epitaxial interfaces, as desired in order to preserve the transport properties of pristine graphene. Atomic scale structural and energetic details of the observed row-by-row, growth mechanism of the 2D epitaxial h-BN film are analyzed through first-principles simulations, demonstrating one-dimensional nucleation-free-energy-barrierless growth. This industrially relevant LED process can be applied to a wide variety of van der Waals materials.

The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in a single rapidly rotating two-dimensional harmonic trap. Going beyond the commonly used second-order correlations in the real configuration space, the methodology in this paper will assist the analysis of experimental observations by providing benchmark results for $N$-body spin-unresolved, as well as spin-resolved, momentum correlations measurable in time-of-flight experiments with individual particle detection. Our analysis shows that the few-body lowest-Landau-level (LLL) states with good magic angular momenta exhibit inherent ordered quantum structures in the $N$-body correlations, similar to those associated with rotating Wigner molecules (WMs), familiar from the field of semiconductor quantum dots under high magnetic fields. The application of a small perturbing stirring potential induces, at the ensuing avoided crossings, formation of symmetry broken states exhibiting ordered polygonal-ring structures, explicitly manifest in the single-particle density profile of the trapped particles. Away from the crossings, an LLL state obtained from exact diagonalization of the microscopic Hamiltonian, found to be well-described by a (1,1,1) Halperin two-component variational wavefunction, represents also a spinful rotating WM. Analysis of the calculated LLL wavefunction enables a two-dimensional generalization of the Girardeau one-dimensional 'fermionization' scheme, originally invoked for mapping of bosonic-type wave functions to those of spinless fermions., Comment: 33 pages with 12 color figures (includes Supplemental Material and MATHEMATICA scripts). Extensive clarifications and additions. Accepted for publication in Physical Review A. For related papers, see https://sites.gatech.edu/cyannouleas

All-order momentum correlation functions associated with the time-of-flight spectroscopy of three spinless ultracold bosonic interacting neutral atoms confined in a linear three-well optical trap are presented. The underlying Hamiltonian employed for the interacting atoms is an augmented three-site Hubbard model. Our investigations target matter-wave interference of massive particles, aiming at the establishment of experimental protocols for characterizing the quantum states of trapped attractively or repulsively interacting ultracold particles, with variable interaction strength. The manifested advantages and deep physical insights that can be gained through the employment of the results of our study for a comprehensive understanding of the nature of the quantum states of interacting many-particle systems, via analysis of the all-order (that is 1st, 2nd and 3rd) momentum correlation functions for three bosonic atoms in a three well confinement, are illustrated and discussed in the context of time-of-flight inteferometric interrogations of the interaction-strength-induced emergent quantum phase transition from the Mott insulating phase to the superfluid one. Furthermore, we discuss that our inteferometric interrogations establish strong analogies with the quantum-optics interference of three photons, including the aspects of genuine three-photon interference, which are focal to explorations targeting the development and implementation of quantum information applications and quantum computing., Comment: Accepted for publication in Physical Review A. Extensive clarifications and explanations added. 34 pages, 14 color figures. For similar papers, see http://www.prism.gatech.edu/~ph274cy/

Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W- and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order and second-order spin-resolved and spin-unresolved momentum correlations, aiming at matter-wave interference investigations with trapped massive particles in analogy with, and having the potential for expanding the scope of, recent three-photon quantum-optics interferometry., Comment: Accepted for publication in Physical Review A. Extensive explanations added. 7 pages, 2 figures, 3 tables. For related papers, see http://www.prism.gatech.edu/~ph274cy/

The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic, as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space, our findings provide impetus for time-of-flight experimental protocols for detecting anyonic statistics via interferometry measurements of massive particles that broaden the scope of the biphoton interferometry of quantum optics., Comment: Published version. Typos corrected. 10 pages with 3 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically-trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton joint-coincidence spectral correlations, studied with massless non-interacting biphotons emanating from EPR-Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total second-order momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON, component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. This partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science., Comment: Published version. 31 pages, 10 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the second-order density matrix constructed via exact diagonalization of the microscopic Hamiltonian, and an analytic Hubbard-type model, we explore here the systematic evolution of characteristic interference patterns in the two-body momentum and spatial correlation maps of two entangled ultracold fermionic atoms in a double well, for the entire attractive- and repulsive-interaction range. We uncover statistics-governed bunching and antibunching, as well as interaction-dependent interference patterns, in the ground and excited states, and interpret our results in light of the Hong-Ou-Mandel interference physics, widely exploited in photon indistinguishability testing and quantum information science., Comment: 18 pages, 8 color figures. A new section V was added; it describes entanglement aspects and the connection to the Hong-Ou-Mandel interference physics. Also the whole range for both repulsive and attractive interparticle interaction is now investigated. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of spin-resolved patterns exhibited in two-point correlations, accessible directly by experiments, are key for uncovering the symmetry and structure of the many-body wave functions of the trapped system. Using the configuration interaction method for exact diagonalization of the many-body Hamiltonian of $N=2-4$ fermionic atoms trapped in single, double, triple, and quadruple wells, we analyze both two-point momentum and space correlations, as well as associated noise distributions, for a broad range of interparticle contact repulsion strengths and interwell separations, unveiling characteristics allowing insights into the transition, via an intermediate phase, from the non-interacting Bose-Einstein condensate to the weakly interacting quasi-Bose-Einstein regime, and from the latter to the strong-repulsion Tonks-Girardeau (TG) one. The ab-initio numerical predictions are shown to agree well with the results of a constructed analytical model employing localized displaced Gaussian functions to represent the $N$ fermions. The two-point momentum correlations are found to exhibit damped oscillatory diffraction behavior. This diffraction behavior develops fully for atoms trapped in a single well with strong interatomic repulsion in the TG regime, or for atoms in well-separated multi-well traps. Additionally, the two-body momentum correlation and noise distributions are found to exhibit "shortsightedness", with the main contribution coming from nearest-neighboring particles., Comment: Published extended version. 19 pages, 14 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

A constructive theoretical platform for the description of quantum space-time crystals uncovers for $N$ interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta $L_m$. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond mean field can be induced by superpositions of such good-$L_m$ many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons., Comment: 14 pages, 3 color figures. Accepted for publication in Phys. Rev. A. This version incorporates extensive explanations, clarifications, and commentary concerning the connection of the present manuscript to previous literature. For related publications, see http://www.prism.gatech.edu/~ph274cy/

A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schroedinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of Lithium-6 atoms in a single square plaquette in the hole-pairing regime, and by analyzing the entanglement (symmetry-preserving) and disentanglement physics (via symmetry-breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy RVB states contribute only partially to the exact many-body solutions, and the CI results map onto a Hubbard Hamiltonian, but not onto the double-occupancy-excluding t-J one. For the double-plaquette case, effects brought about by breaking the symmetry between two weakly-interacting plaquettes, either by distorting, or by tilting and detuning, one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored., Comment: 14 pages with 9 color figures. Physical Review A (2017, in press)

Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly-correlated behavior of ultracold strongly-repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric double wells reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T$_c$ superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, double wells suggest three-cold-atom DW quantum computing qubits., Comment: 35 pages, 10 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Strong repelling interactions between a few fermions or bosons confined in two-dimensional circular traps lead to particle localization and formation of quantum Wigner molecules (QWMs) possessing definite point-group space symmetries. These point-group symmetries are "hidden" (or emergent), namely they cannot be traced in the circular single-particle densities (SPDs) associated with the exact many-body wave functions, but they are manifested as characteristic signatures in the ro-vibrational spectra. An example, among many, are the few-body QWM states under a high magnetic field or at fast rotation, which are precursor states for the fractional quantum Hall effect. The hidden geometric symmetries can be directly revealed by using spin-resolved conditional probability distributions, which are extracted from configuration-interaction (CI), exact-diagonalization wave functions. The hidden symmetries can also be revealed in the CI SPDs by reducing the symmetry of the trap (from circular to elliptic to quasi-linear). In addition the hidden symmetries are directly connected to the explicitly broken-symmetry (BS) solutions of mean-field approaches, such as unrestricted Hartree-Fock (UHF). A companion step of restoration of the broken symmetries via projection operators applied on the BS-UHF solutions produces wave functions directly comparable to the CI ones, and sheds further light into the role played by the emergence of hidden symmetries in the exact many-body wave functions. Illustrative examples of the importance of hidden symmetries in the many-body problem of few electrons in semiconductor quantum dots and of few ultracold atoms in optical traps (where unprecedented control of the interparticle interaction has been experimentally achieved recently) will be presented., Comment: 11 pages with 4 color figures. Invited extended abstract for the Proceedings of the 16th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016, Rota, Cadiz, Spain, 4-8 July, 2016

"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynman's vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational microscopy solutions of the hamiltonian, uncovering the spectral evolution, wave-function anatomy, and entanglement properties of the interacting fermions in the entire parameter range, including crossover from a SW to a DW confinement and a controllable energy imbalance between the wells. We demonstrate attractive pairing and formation of repulsive, highly-correlated, ultracold Wigner molecules, well-described in the natural orbital representation. The agreement with the measurements affirms the henceforth gained deep insights into ultracold molecules and opens access to the size-dependent evolution of nano-clustered and condensed-matter phases and ultracold-atoms quantum information., Comment: 32 pages, 6 color figures. In addition to the previously considered case of a linear double-well arrangement, new results for a parallel arrangement of the two quasi-1D traps are reported. One new figure added. One previous figure modified

The unique ultra-relativistic, massless, nature of electron states in two-dimensional extended graphene sheets, brought about by the honeycomb lattice arrangement of carbon atoms in two-dimensions, provides ingress to explorations of fundamental physical phenomena in graphene nanostructures. Here we explore the emergence of new behavior of electrons in atomically precise segmented graphene nanoribbons (GNRs) and graphene rings with the use of tight-binding calculations, non-equilibrium Green's function transport theory, and a newly developed Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. Through transport investigations in variable-width segmented GNRs with armchair, zigzag, and mixed edge terminations we uncover development of new Fabry-Perot-like interference patterns in segmented GNRs, a crossover from the ultra-relativistic massless regime, characteristic of extended graphene systems, to a massive relativistic behavior in narrow armchair GNRs, and the emergence of nonrelativistic behavior in zigzag-terminated GNRs. Evaluation of the electronic states in a polygonal graphene nanoring under the influence of an applied magnetic field in the Aharonov-Bohm regime, and their analysis with the use of a relativistic quantum-field theoretical model, unveils development of a topological-in-origin zero-energy soliton state and charge fractionization. These results provide a unifying framework for analysis of electronic states, coherent transport phenomena, and the interpretation of forthcoming experiments in segmented graphene nanoribbons and polygonal rings., Comment: 5 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/. in J. Phys. Chem. C (2015), article ASAP. arXiv admin note: substantial text overlap with arXiv:1502.00205

Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces the NEGF results, including optical Dirac Fabry-Perot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs., Comment: 12 pages, 6 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

The doubly-connected polygonal geometry of planar graphene rings is found to bring forth topological configurations for accessing nontrivial relativistic quantum field (RQF) theory models that carry beyond the constant-mass Dirac-fermion theory. These include generation of sign-alternating masses, solitonic excitations, and charge fractionization. The work integrates a RQF Lagrangian formulation with numerical tight-binding Aharonov-Bohm electronic spectra and the generalized position-dependent-mass Dirac equation. In contrast to armchair graphene rings (aGRGs) with pure metallic arms, certain classes of aGRGs with semiconducting arms, as well as with mixed metallic-semiconducting ones, are shown to exhibit properties of one-dimensional nontrivial topological insulators. This further reveals an alternative direction for realizing a graphene-based nontrivial topological insulator through the manipulation of the honeycomb lattice geometry, without a spin-orbit contribution., Comment: 6 pages with 3 color figures. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Spin-density-functional calculations of tip-suspended gold chains, with molecular oxygen, or dissociated oxygen atoms, incorporated in them, reveal structural transitions for varying lengths. The nanowires exhibit enhanced strength for both oxygen incorporation modes, and upon stretching tip atoms join the wire. With incorporated molecular oxygen the wire conductance is about 1(2e2/h), transforming to an insulating state beyond a critical length. The nanowire conductance with embedded oxygen atoms is low, 0.2 (2e2/h), and it develops magnetic moments localized on the oxygens and the neighboring Au atoms., Comment: 16 pages, 4 figures

Armchair and zigzag edge terminations in planar hexagonal and trigonal graphene nanorings are shown to underlie one-dimensional topological states associated with distinctive energy gaps and patterns (e.g., linear dispersion of the energy of an hexagonal ring with an armchair termination versus parabolic dispersion for a zigzag terminated one) in the bands of the tight-binding spectra as a function of the magnetic field. A relativistic Dirac-Kronig-Penney model analysis of the tight-binding Aharonov-Bohm behavior reveals that the graphene quasiparticle in an armchair hexagonal ring is a condensed-matter realization of an ultrarelativistic fermion with a position-dependent mass term, akin to the zero-energy fermionic solitons with fractional charge familiar from quantum field theory and from the theory of polyacetylene. The topological origins of the above behavior are highlighted by contrasting it with the case of a trigonal armchair ring, where we find that the quasiparticle excitations behave as familiar Dirac fermions with a constant mass. Furthermore, the spectra of a zigzag hexagonal ring correspond to the low-kinetic-energy nonrelativistic regime of a leptonlike massive fermion. A onedimensional relativistic Lagrangian formalism coupling a fermionic and a scalar bosonic field via a Yukawa interaction, in conjunction with the breaking of the Z2 reflectional symmetry of the scalar field, is shown to unify the above dissimilar behaviors., Comment: 12 pages with 10 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/ For a version with high-quality figures, see http://www.prism.gatech.edu/~ph274cy/

Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakes with such reczag defective edges, emphasis is placed on topological aspects and connections underlying the patterns dominating these spectra. The electronic spectra of trigonal graphene nanoflakes with reczag edge terminations exhibit certain unique features, in addition to those that are well known to appear for graphene dots with zigzag edge termination. These unique features include breaking of the particle-hole symmetry, and they are associated with nonlinear dispersion of the energy as a function of momentum, which may be interpreted as nonrelativistic behavior. The general topological features shared with the zigzag flakes include the appearance of energy gaps at zero and low magnetic fields due to finite size, the formation of relativistic Landau levels at high magnetic fields, and the presence between the Landau levels of edge states (the socalled Halperin states) associated with the integer quantum Hall effect. Topological regimes, unique to the reczag nanoflakes, appear within a stripe of negative energies E_b < E < 0, and along a separate feature forming a constant-energy line outside this stripe. The lower bound (E_b) specifying the energy stripe is independent of size. A main finding concerns the limited applicability of the continuous Dirac-Weyl equation, since the latter does not reproduce the special reczag features. (See also the extended abstract in the paper.), Comment: Physical Review B (2012), in press. 17 pages with 15 color figures. For related papers see http://www.prism.gatech.edu/~ph274cy/. For a version with high quality figures, click on http://www.prism.gatech.edu/~ph274cy/Reczag_flake_prb_r.pdf

Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary conditions. Unlike the previous literature, we demonstrate the universality of integer (hc/e) and half-integer (hc/2e) values for the period of the AB oscillations as a function of the magnetic flux, in consonance with the case of mesoscopic metal rings. Odd-even (in the number of Dirac electrons, N) sawtooth-type patterns relating to the halving of the period have also been found; they are more numerous for a monolayer hexagonal ring, compared to the cases of a trigonal and a bilayer hexagonal ring. Additional more complicated patterns are also present, depending on the shape of the graphene ring. Overall, the AB patterns repeat themselves as a function of N with periods proportional to the number of the sides of the rings., Comment: REVTEX 4-1, 6 pages with 7 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Motivated by recent experiments, and using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjunction with exact diagonalization, we develop a unified microscopic approach for the interplay between liquid fractional-quantum-Hall-effect (FQHE) states and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of nu=1/3. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the conditional probability distributions and the emergence of cusp yrast states in the LLL spectra. It is shown that away from the exact fractional fillings, weak pinning perturbations (due to weak disorder) may overcome the energy gaps between adjacent global states and generate pinned broken symmetry ground states as a superposition of symmetry-conserving LLL states with different total angular momenta. The electron densities of such mixed states (without good angular momentum quantum numbers) exhibit oscillating patterns that correspond to molecular crystallites. These pinned Wigner crystallites represent finite-size precursors of the bulk Wigner-solid state. It is further shown that the emergence of these molecular crystallites is a consequence of the presence of RVEM components in the symmetry-conserving LLL states. In addition, it is shown that the RVEM approach accounts for the Wigner-solid state in the neighborhood of nu=1, which was also found in the experiments. We utilize results for sizes in a wide range from N=6 to N=29 electrons, and we address the extrapolation to the thermodynamic limit., Comment: 19 pages, 17 figures, 4 tables. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Here we show results of first-principles investigations aiming at tuning and controlling the catalytic activity of gold nanoclusters through the design of the underlying support. We show that gold clusters adsorbed on a very thin (2 layers) defect-free MgO film which is itself supported on Mo(100), may serve as model catalysts for the low-barrier oxidation of CO. The origin of the emergent activity of the nanoclusters is a dimensionality crossover of the adsorbed gold clusters, from inactive three-dimensional (3D) optimal structures on thick MgO films, to catalytically active 2D ones for sufficiently thin MgO films (less then 1nm in thickness) supported on Mo(100)., Comment: 2 pages, 2 figures

Dirac electrons in finite graphene samples with zigzag edges under high magnetic fields (in the regime of Landau-level formation) are investigated with regard to their bulk-type and edge-type character. We employ tight-binding calculations on finite graphene flakes (with various shapes) to determine the sublattice components of the electron density in conjunction with analytic expressions (via the parabolic cylinder functions) of the relativistic-electron spinors that solve the continuous Dirac-Weyl equation for a semi-infinite graphene plane. Away from the sample edge, the higher Landau levels are found to comprise exclusively electrons of bulk-type character (for both sublattices); near the sample edge, these electrons are described by edge-type states similar to those familiar from the theory of the integer quantum Hall effect for nonrelativistic electrons. In contrast, the lowest (zero) Landau level contains relativistic Dirac electrons of a mixed bulk-edge character without an analog in the nonrelativistic case. It is shown that such mixed bulk-edge states maintain also in the case of a square flake with combined zigzag and armchair edges. Implications for the many-body correlated-electron behavior (relating to the fractional quantum Hall effect) in finite graphene samples are discussed., Comment: Physical Review B, in press. Revtex4-1. 12 pages with 14 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

A recent letter [H. Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)] reports the first measurements of a pinned mode in a Wigner solid at the (electronic) nu = 1/3 fractional quantum Hall effect (FQHE) filling. The authors suggest that an interpretation of their findings may be found within the interacting composite fermion (ICF) theory. However, to date there is no record reporting crystalline correlations for nu ~ 1/3 obtained from ICF theory, or related theories. We argue that an appropriate interpretation of these findings follows naturally from the rotating-Wigner-molecule approach, which (with inclusion of the rovibrational spectrum of the molecule) encompasses both the crystalline and liquid aspects in the FQHE regime (in particular for nu=1/3, as well as in its neighborhood created by deviations of nu from 1/3, as revealed experimentally)., Comment: Clarifications added (footnote [9]). Short comment; 1 page with 1 figure. For related papers, see http://www.prism.gatech.edu/~ph274cy

Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (nu=1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing, at all sizes, mixed equal-weight bulk and edge components. The consequent depletion of the bulk electron density attenuates the fractional-quantum-Hall-effect excitation energies and the edge charge accumulation results in a gap in the many-body spectrum., Comment: 8 pages with 7 figures. REVTEX4. For related publications, see http://www.prism.gatech.edu/~ph274cy

Orbital-free (OF) methods promise significant speed-up of computations based on density functional theory (DFT). In this field, the development of accurate kinetic-energy density functionals remains an open question. In this chapter we review the shell-correction method (SCM, commonly known as Strutinsky's averaging method) applied originally in nuclear physics and its more recent formulation in the context of DFT [Yannouleas and Landman, Phys. Rev. B 48, 8376 (1993)]. We demonstrate the DFT-SCM method through its earlier applications to condensed-matter finite systems, including metal clusters, fullerenes, and metal nanowires. The DFT-SCM incorporates quantum mechanical interference effects and thus offers an improvement compared to the use of Thomas-Fermi-type kinetic energy density functionals in OF-DFT., Comment: LATEX, 47 pages with 17 figures. For related publications, see http://www.prism.gatech.edu/~ph274cy/

Through the introduction of a class of trial wave functions portraying combined rotations and vibrations of molecules formed through particle localization in concentric polygonal rings, a correlated basis is constructed that spans the translationally invariant part of the lower-Landau-level (LLL) spectra. These trial functions, referred to as rovibrational molecular (RVM) functions, generalize our previous work which focused exclusively on electronic cusp states, describing them as pure vibrationless rotations. From a computational viewpoint, the RVM correlated basis enables controlled and systematic improvements of the original strongly-correlated variational wave function. Conceptually, it provides the basis for the development of a quantal molecular description for the full LLL spectra. This quantal molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. Furthermore, it follows that all other translationally invariant trial functions (e.g., the Jastrow-Laughlin, compact composite-fermion, or Moore-Read functions) are reducible to a description in terms of an excited rotating/vibrating quantal molecule., Comment: Revtex4. 17 pages with 4 figures and 8 Tables. To appear in Physical Review A. For related papers, see http://www.prism.gatech.edu/~ph274cy/

This paper (concerning the infinite-mass boundary condition) has been withdrawn by the author. Another, independent study regarding the zigzag boundary condition has appeared in Phys. Rev. B 82, 125419 (2010)., Comment: This paper has been withdrawn by the author [instead, see C. Yannouleas et al., Phys. Rev. B 82, 125419 (2010)]

A description of neutral and multiply charged fullerenes is proposed based on a stabilized jellium (structureless pseudopotential) approximation for the ionic background and the local density approximation for the sigma and pi valence electrons. A recently developed shell-correction method is used to calculate total energies and properties of both the neutral and multiply charged anionic and cationic fullerenes. The effect of the icosahedral symmetry is included perturbatively. The calculated single-particle energy level spectrum of C_60 is in good correspondence with experimentally measured ones and previous self-consistent local-density-approximation calculations. For the multiply charged fullerenes, we calculate microscopically the charging energies for up to 12 excess charges. A semiclassical interpretation of these results is developed, which views the fullerenes as Coulomb islands possessing a classical capacitance. The calculated values for the first ionization potential and the first electron affinity agree well with the experimental ones. Our calculations support the results from charge transfer bracketing experiments and from direct ionization experiments through electron impact. The doubly charged negative ion is found to be a very long-lived metastable species, in agreement with observations., Comment: In addition to the zero-node (sigma) and one-node (pi) orbitals, this early (1994) jellium study described three two-node (delta) orbitals that are delocalized within the fullerene-cage cavity. Such superatom/central-potential two-node orbitals have been recently observed experimentally

Energy spectra and spin configurations of a system of N=4 electrons in lateral double quantum dots (quantum dot Helium molecules) are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field (B), and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin and the ensuing spin degeneracies for four electrons. The energies of the six states appear to cross at a single value of the magnetic field, and with increasing Coulomb repulsion they tend to become degenerate, with a well defined energy gap separating them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangle. Using spin-resolved pair-correlation distributions, a method for mapping the complicated EXD many-body wave functions onto simpler spin functions associated with a system of four localized spins is introduced. Detailed interpretation of the EXD spin functions and EXD spectra associated with the low-energy band via a 4-site Heisenberg cluster (with B-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well known N-qubit Dicke states, are also discussed., Comment: REVTEX 4. 18 pages with 10 figures. Accepted for publication in Physical Review B. This paper incorporates material from arXiv:0902.0839. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Through the introduction of a class of appropriate translationally invariant trial wave functions, we show that the strong correlations in the lowest Landau level (LLL) reflect in finite systems the emergence of intrinsic point-group symmetries associated with rotations and vibrations of molecules formed through particle localization. This quantal molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. "Quantum-fluid" physical pictures associated with Jastrow-type trial functions are shown to be reducible to the molecular description introduced in this paper., Comment: REVTEX 4. 6 pages with 1 color figure and 3 Tables. An extended version [15 pages] was published as Phys. Rev. A 81, 023609 (2010); see http://arxiv.org/abs/1001.1090. For other related papers, see http://www.prism.gatech.edu/~ph274cy/

Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field, and strength of interelectron repulsion. A distinctly different quantum behavior is found compared to that of circular single quantum dots. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin of the four electrons and the ensuing spin degeneracies. These six states appear to cross at a single value of the magnetic field, with the crossing point becoming sharper for larger interdot distances. As the strength of the Coulomb repulsion increases, the six states tend to become degenerate and a well defined energy gap separates them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangular parallelogram. Using the spin-resolved pair-correlation functions, one can map the EXD many-body wave functions onto the spin functions associated with the four localized electrons. Analogies with nanomagnets, such as finite Heisenberg clusters, are discussed. The ability to determine associated spin functions enables investigations concerning entanglement properties of the system of four electrons. In particular, the formation of Wigner supermolecules generates EXD solutions belonging to the class of strongly entangled states referred to as N-qubit Dicke states in the quantum-information literature., Comment: Revtex 4. 15 pages with 13 figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons., Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Low frequency plasma oscillations in superconducting tubes are considered. The emergence of two different dimensionality regimes of plasma oscillations in tubes, exhibiting a crossover from one-dimensional to two-dimensional behavior, depending on whether $k R\ll 1$ or $k R\gg 1$, where $k$ is the plasmon wave vector and $R$ is the radius of the tube, is discussed. The Aharonov-Bohm effect pertaining to plasma oscillations in superconducting tubes and rings, resulting in an oscillatory behavior of the plasmon frequency as a function of the magnetic flux, with a flux quantum period $hc/2e$ (analog of the Little-Parks effect), is studied. The amplitude of the oscillations is proportional to $(\xi/R)^2$, where $\xi$ is the superconducting coherence length., Comment: 18 pages, 4 figures

Through the introduction of a class of appropriate translationally invariant trial wave functions, we show that the strong correlations in the lowest Landau level (LLL) reflect in finite systems the emergence of intrinsic point-group symmetries associated with rotations and vibrations of molecules formed through particle localization. This molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. This physical picture is fundamentally different from the "quantum-fluid" one associated with Jastrow-type trial functions., Comment: 5 pages with two tables. Revtex

The properties of a special class of correlated many-body wave functions, named rotating vortex clusters (RVCs), that preserve the total angular momentum of a small cloud of trapped rotating bosons are investigated. They have lower energy and provide a superior description for the formation of vortices compared to the mean-field Gross-Pitaevskii (GP) states that break the rotational symmetry. The GP vortex states are shown to be wave packets composed of such RVC states. Our results suggest that, for a small number of bosons, the physics is different from that of ideal Bose-Einstein condensates which characterize larger assemblies, Comment: Revtex 4 with 4 color figures. Published version. Ref. [25] (experimental) was added. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Systematic trends of nonuniversal behavior of electron transmission phases through a quantum dot, with no phase lapse for the transition N=1 -> N=2 and a lapse of pi for the N=2 -> N=3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels., Comment: Published version. REVTEX4. 4 pages with 3 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semicoductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include: (I) Chemical bonding, dissociation, and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot. (II) Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. (III) At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs)., Comment: Due to renewed interest in Wigner (or electron) molecules in the context of quantum-computer qubits (see, e.g., arXiv:2009.13572), updated links to this review, which describes earlier theoretical work and predictions, are provided. For the published version click-on https://cpb-us-w2.wpmucdn.com/sites.gatech.edu/dist/8/1647/files/2021/02/ROP_published_2007.pdf

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy., Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color figures. To download a copy with higher-quality figures, go to publication #78 in http://www.prism.gatech.edu/~ph274cy/