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The α-T3 model is characterized by a variable Berry phase that changes continuously from π to 0. We take advantage of this property to highlight the effects of this underlying geometrical phase on a number of physical quantities. The Hall quantization of the two limiting cases is dramatically different: a relativistic series is associated with a Berry phase of it, and a nonrelativistic series is associated with the other limit. We study the quantization of the Hall plateaus as they continuously evolve from a relativistic to a nonrelativistic regime. Additionally, we describe two physical quantities that retain knowledge of the Berry phase in the absence of a motion-inducing magnetic field. The variable Berry phase of the α-T3 model allows us to explicitly describe the Berry phase dependence of the dynamical longitudinal optical conductivity and of the angular scattering probability. [ABSTRACT FROM AUTHOR]

A two-dimensional network model representing an array of coupled orbitals of nonzero orbital momenta has been used to illustrate the origin of the topological phase transformation between insulators of different Chern number. The model is based on the standard tight-binding approach, improved by inclusion of wave-function phases of orbital states. For a coupling stronger than a critical value the existence of chiral edge states has been observed. The corresponding anomalous Hall conductivity becomes quantized, as experimentally observed in magnetic topological insulators. [ABSTRACT FROM AUTHOR]

We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantize the vortices and, by relating their dynamics to a matrix model, show that their ground state wave function is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasiholes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin. [ABSTRACT FROM AUTHOR]

In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without timereversal symmetry and the isotropic magnetoelectric response function of time-reversal-symmetric insulators are known to be topological invariants displaying an exact Z2 quantization. This quantization is stabilized by the symmetries. In the present work, we investigate the fate of such symmetry-stabilized topological invariants in the presence of a disorder which breaks the symmetries but restores them on average. Using a rigorous analysis, we conclude that the strict quantization still holds in these conditions. Numerical calculations confirm this prediction. [ABSTRACT FROM AUTHOR]

Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry protected topological phase supported by the spatial inversion symmetry. The Z2 Berry phase associated with a symmetry respecting boundary and quantized into 0 and π is used as a symmetry protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry breaking boundary is considered. Then, we observe a unique type of quantization of the Berry phase, a quantization into ±π/2 of the Berry phase. In this case, the bulk-edge correspondence is also unique, namely, there emerge "polarized" edge states for the case with ±π/2 quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry phase based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD. [ABSTRACT FROM AUTHOR]

Electronic properties of surface areas decoupled from graphite are studied using scanning tunneling microscopy and spectroscopy. We show that it is possible to identify the decoupled graphene monolayer, the Bernal bilayer, and the Bernal trilayer on a graphite substrate according to their tunneling spectra in a high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap ~35 meV in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split into two valley-polarized quartets polarized on each layer. In the decoupled Bernal trilayer, we find that both massless and massive Dirac fermions coexist and its low-energy band structure can be described quite well by taking into account only the nearest-neighbor intra- and interlayer hopping parameters. A strong correlation between the Fermi velocity of the massless Dirac fermions and the effective mass of the massive Dirac fermions is observed in the graphene trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers. [ABSTRACT FROM AUTHOR]

We introduce a "second-quantized" representation of the ring of symmetric functions tofurther develop a purely second-quantized, or "lattice," approach to the study of zero modes of frustration-free Haldane-pseudopotentialtype Hamiltonians, which in particular stabilize Laughlin ground states. We present three applications of this formalism. We start demonstrating how to systematically construct ah zero modes of Laughlin-type parent Hamiltonians in a framework that is free of first-quantized polynomial wave functions, and show that they are in one-to-one correspondence with dominance patterns. The starting point here is the pseudopotential Hamiltonian in "lattice form," stripped of all information about the analytic structure of Landau levels (dynamical momenta). Second, as a by-product, we make contact with the bosonization method, and obtain an alternative proof for the equivalence between bosonic and fermionic Fock spaces. Finally, we explicitly derive the second-quantized version of Read's nonlocal (string) order parameter for the Laughlin state, extending an earlier description by Stone. Commutation relations between the local quasihole operator and the local electron operator are generalized to various geometries. [ABSTRACT FROM AUTHOR]

We note an implication of the chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with reverse flux attached or edge reconstruction, we show that nonuniversality of the edge exponent implies nonuniversality of the Hall conductance, as measured in the two-terminal conductance. [ABSTRACT FROM AUTHOR]

A numerically exact solution to the many emitter-cavity problem as an open many body system is presented. The solution gives access to the full, nonperturbative density matrix and thus the full quantum statistics and quantum correlations. The numerical effort scales with the third power in the number of emitters. Notably the solution requires none of the common approximations such as good/bad cavity limit. As a first application the recently discussed concept of coherent surface plasmon amplification--spaser--is addressed: A spaser consists of a plasmonic nanostructure that is driven by a set of quantum emitters. In the context of laser theory it is a laser in the (very) bad cavity limit with an extremely high light matter interaction strength. The method allows us to answer the question of spasing with a fully quantized theory. [ABSTRACT FROM AUTHOR]

We propose a new quantization method for superconducting electronic circuits involving a Joseph son-junction device coupled to a linear microwave environment. The method is based on an exact impedance synthesis of the microwave environment considered as a black box with impedance function Z(s). The synthesized circuit captures dissipative dynamics of the system with resistors coupled to the reactive part of the circuit in a nontrivial way. We quantile the circuit and compute relaxation rates following previous formalisms for lumped element circuit quantisation. Up to the errors in the fit our method gives an exact description of the system and its losses. [ABSTRACT FROM AUTHOR]

We review the concept of superfluidity and, based on real and thought experiments, we use the formalism of second quantization to derive expressions that allow the calculation of the superfluid density for general Hamiltonians with path-integral methods. It is well known that the superfluid density can be related to the response of the free energy to a boundary phase twist, or to the fluctuations of the winding number. However, we show that this is true only for a particular class of Hamiltonians. In order to treat other classes, we derive general expressions of the superfluid density that are valid for various Hamiltonians. While the winding number is undefined when the number of particles is not conserved, our general expressions allow us to calculate the superfluid density in all cases. We also provide expressions of the superfluid densities associated to the individual components of multispecies Hamiltonians, which remain valid when interspecies conversions occur. The cases of continuous and discrete spaces are discussed, and we emphasize common mistakes that occur when considering lattices with nonorthonormal primitive vectors. [ABSTRACT FROM AUTHOR]

The effects of size quantization on the nonlinear optical response of Ag nanoparticles are experimentally studied by spectroscopic ellipsometry and femtosecond spectroscopic pump-and-probe techniques. In the vicinity of a localized surface-plasmon resonance (2.0-3.5 eV), we have investigated the optical nonlinearity of Ag particles embedded in silica glass for particle diameters ranging from 3.0 to 16 nm. The intrinsic third-order optical susceptibility xm(3) of Ag particles exhibited significant spectral and size dependences. These results are explained as quantum and dielectric confinements and are compared to the results of theoretical quantum finite-size effects calculation for metallic particles. In light of these results, we discuss the contribution of interband transitions to the size dependence of xm(3). Quantum size effects lead to an increase in nonlinearity in small Ag particles. [ABSTRACT FROM AUTHOR]

We theoretically investigate magnetic properties in the low-temperature phase with the formation of eight-site clusters, octamers, in the spinel compound CuIr2S4. The octamer state was considered to be a spin-singlet state induced by a Peierls instability through the strong anisotropy of d orbitals, the so-called orbital Peierls state. We reexamine this picture by taking into account the spin-orbit coupling, which was ignored in the previous study. We derive a low-energy effective model between Jeff=1/2 quasispins on Ir4+ cations in an octamer from the multiorbital Hubbard model with the strong spin-orbit coupling by performing the perturbation expansion from the strong correlation limit. The effective Hamiltonian is in the form of the Kitaev-Heisenberg model but with an additional interaction, a symmetric off-diagonal exchange interaction originating from the perturbation process including both d-d and d-p-d hoppings. Analyzing the effective Hamiltonian on two sites and the octamer by the exact diagonalization, we find that there is competition between a spin-singlet state and a quadrupolar state. The former singlet state is a conventional one, adiabatically connected to the orbital Peierls state. On the other hand, the latter quadrupolar state is stabilized by the additional interaction, which consists of a linear combination of different total spin momenta along the spin quantization axis. In the competing region, the model exhibits paramagnetic behavior with a renormalized small effective moment at low temperature. This peculiar remnant paramagnetism is not obtained in the Kitaev-Heisenberg model without the additional interaction. Our results renew the picture of the octamer state and provide a scenario for the intrinsic paramagnetic behavior recently observed in a muon spin rotation experiment [K. M. Kojima et al., Phys. Rev. Lett. 112, 087203 (2014)]. [ABSTRACT FROM AUTHOR]

In the recently discovered topological crystalline insulators SnTe and Pb1-xSnx (Te. Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz transition, Van-Hove singularity, and fermion mass generation. These surface states are protected by mirror symmetry with respect to the (110) plane. In this work we present a comprehensive study of the effects of different mirror-symmetry-breaking perturbations on the (001) surface band structure. Pristine (001) surface states have four branches of Dirac fermions at low energy. We show that ferroelectric-type structural distortion generates a mass and gaps out some or all of these Dirac points, while strain shifts Dirac points in the Brillouin zone. An in-plane magnetic field leaves the surface state gapless, but introduces asymmetry between Dirac points. Finally, an out-of-plane magnetic field leads to discrete Landau levels. We show that the Landau level spectrum has an unusual pattern of degeneracy and interesting features due to the unique underlying band structure. This suggests that Landau level spectroscopy can detect and distinguish between different mechanisms of symmetry breaking in topological crystalline insulators. [ABSTRACT FROM AUTHOR]

We study a superconducting quantum point contact made of a narrow In0.75Ga0.25 As channel with Nb proximity electrodes. The narrow channel is formed in a gate-fitted constriction of InGaAs/InAlAs/InP heterostructure hosting a two-dimensional electron gas. When the channel opening is varied with the gate, the Josephson critical current exhibits a discretized variation that arises from the quantization of the transverse momentum in the channel. The quantization of Josephson critical current persists down to the single-channel regime, providing an unambiguous demonstration of a semiconductor-superconductor hybrid Josephson junction involving only a .single ballistic channel. [ABSTRACT FROM AUTHOR]

The envelope function method is applied to hole and exciton states in wurtzite and zinc-blende structure cylindrical nanowires using the axial Kohn-Luttinger Hamiltonian including a crystal-field splitting for the wurtzite case. The quantized states are found to be mixtures of heavy- and light-hole band derived states. Explicit expressions for the mixing coefficients and the conditions giving the quantized energy states are derived. These are then applied to obtain the relative intensity of light emitted polarized parallel and perpendicular to the nanowire for the lowest-energy excitons. Slightly different expressions are obtained in the weak quantization and strong quantization limits. In the latter case, an overlap integral of the hole and electron envelope function is involved, while in the former case only an integral over the hole envelope function is required. An expression for the degree of polarization of the spectrally integrated photoluminescence as a function of temperature is obtained by summing over the excitons within the integration range. The degree of polarization as a function of temperature is explored numerically as a function of nanowire radius and crystal-field splitting for GaAs and GaN nanowires. Examples of complete reversal of the polarization are illustrated. [ABSTRACT FROM AUTHOR]

We demonstrate that a finite-size chiral soliton lattice formed in a chiral helimagnet with fixed boundary conditions exhibits magnetization jumps in a response to the magnetic field applied perpendicular to the chiral axis. The imposed boundary conditions lead to confinement of topological charges and quantized spatial periods of the soliton lattice. Building an envelope of the ground-state energies belonging to different topological sectors, we find the magnetization jumps related with the level crossing. After numerically establishing the quantization condition, we also develop a field-theoretical model to support the numerical results. [ABSTRACT FROM AUTHOR]

Berry phases defined by the one-dimensional momentum as a parameter show Z2 quantization due to the inversion symmetry combined with the time reversal, or existence of the reflection plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. These ideas are applied in the fermionic Shastry-Sutherland model, which has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Wey 1 fermion. We also demonstrate that the Z2 Berry phases determine the existence of edge states as the bulk-edge correspondence of the massless Dirac fermion systems. [ABSTRACT FROM AUTHOR]

A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px + ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px + ipy)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a "squeezing principle" that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) "incompressible filling factors" for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems precise. [ABSTRACT FROM AUTHOR]

Low-temperature scanning tunneling microscopy has been employed to analyze the formation of quantum well states (QWS) in two-dimensional gold islands, containing between 50 and 200 atoms, on MgO thin films. The energy position and symmetry of the eigenstates are revealed from conductance spectroscopy and imaging. The majority of the QWS originates from overlapping Au 6p orbitals in the individual atoms and is unoccupied. Their characteristic is already reproduced with simple particle-in-a-box models that account for the symmetry of the islands (rectangular, triangular, or linear). However, better agreement is achieved when considering the true atomic structure of the aggregates via a density functional tight-binding approach. Based on a statistically relevant number of single-island data, we have established a correlation between the island geometry and the gap between the highest-occupied and the lowest-unoccupied molecular orbital in the finite-sized islands. The linear eccentricity is identified as a suitable descriptor for this relationship, as it combines information on both island size and island shape. Finally, the depth of the confinement potential is determined from the spatial extension of QWS beyond the physical boundaries of the Au islands. Our paper demonstrates how electron quantization effects can be analyzed in detail in metal nanostructures. The results may help elucidating the interplay between electronic and chemical properties of oxide-supported clusters as used in heterogeneous catalysis. [ABSTRACT FROM AUTHOR]

The surface of a 3+1d-topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here, we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional space-time. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect. [ABSTRACT FROM AUTHOR]

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, Δ1 and Δ2. We consider two main situations, Δ1=0Δ2≠0, and Δ1=-Δ2. They are different in a fundamental aspect: only the latter features kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two-terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal boron-nitride, as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall. [ABSTRACT FROM AUTHOR]

A systematic theory of the conductance measurements of noninvasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first- and second-order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first-order correction dominates at the conductance steps and vanishes on the plateaux where the second-order term dominates. Both corrections are nonlocal for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second-order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact, we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections. [ABSTRACT FROM AUTHOR]

Inspired by a recent experimental observation of the zero-bias tunneling conductance in superconductor- semiconductor nanowire devices [V. Mourik et al., Science 336, 1003 (2012)], we consider here transport properties of the junctions consisting of a nanowire (Luttinger liquid) coupled to a topological superconductor characterized by the presence of Majorana zero-energy end states. The presence of the Majorana modes leads to a quantization of the zero-bias tunneling conductance at zero temperature. In order to understand this phenomenon, we have developed a framework, based on real-time Keldysh technique, which allows one to compute tunneling conductance at finite temperature and voltage in a realistic experimental setup. Our approach allows one to understand this transport phenomenon from a more general perspective by including the effect of interactions in the nanowire, which sometimes results in a drastic departure from the noninteracting predictions. Thus, our results provide a key insight for the tunneling experiments aiming at detecting Majorana particles in one-dimensional nanowire devices. [ABSTRACT FROM AUTHOR]

Transport in InAs/GaSb heterostructures with different InAs layer thicknesses is studied using a six-terminal Hall bar geometry with a 2-μm edge channel length. For a sample with a 12-nm-thick InAs layer, nonlocal resistance measurements with various current/voltage contact configurations reveal that the transport is dominated by edge channels with a negligible bulk contribution. Systematic nonlocal measurements allow us to extract the resistance of individual edge channels, revealing sharp resistance fluctuations indicative of inelastic scattering. Our results show that the InAs/GaSb system can be tailored to have conducting edge channels while keeping a gap in the bulk region and provide a way of studying two-dimensional topological insulators even when quantized transport is absent. [ABSTRACT FROM AUTHOR]

By discussing field-induced quantum interference effects due to monopole moments and those due to dipole moments on equal footing, their similarities and differences are clarified. First, we demonstrate the general principle for flux quantization. For particles carrying a monopole moment, the interference causes the monopole current to oscillate periodically, with the flux defined as the inner product of the field and area, whereas for particles carrying a fixed dipole moment the dipole current oscillates periodically, with the flux vector defined as the cross product of the field and trajectory. Our analysis unifies the oscillation of monopole or dipole currents in various devices, such as the superconducting quantum interference device and spin field-effect transistor, into the same physical picture. Second, we show that interference effects can also happen in open trajectory devices that transport dipole currents, such as the spin Josephson effect, based on the non-gauge-field nature of the interference effects of dipole moments. In addition, we propose that the interference effect of electric dipoles, known as the He-McKellar-Wilkens effect, can be realized by the bilayer exciton condensates observed in semiconductor heterostructures and bilayer graphene. [ABSTRACT FROM AUTHOR]

We report a detailed investigation of the interplay between size quantization and local scattering centers in graphene nanoribbons, as seen in the local density of states. The spectral signatures, obtained after Fourier transformation of the local density of states, include characteristic peaks that can be related to the transverse modes of the nanoribbon. In armchair ribbons, the Fourier transformed density of states of one of the two inequivalent sublattices takes a form similar to that of a quantum channel in a two-dimensional electron gas, modified according to the differences in band structure. After addition of the second sublattice contribution, a characteristic modulation of the pattern due to superposition is obtained, similar to what has been obtained in spectra due to single impurity scattering in large-area graphene. We present analytic results for the electron propagator in armchair nanoribbons in the Dirac approximation, including a single scattering center within a T-matrix formulation. For comparison, we have extended the investigation with numerics obtained with an atomistic recursive Green's function approach. The spectral signatures of the atomistic approach include the effects of trigonal warping. The impurity induced oscillations in the local density of states are not decaying at large distance in few-mode nanoribbons. [ABSTRACT FROM AUTHOR]

Theoretical research has predicted that a ripple of graphene generates an effective gauge field on its low-energy electronic structure and could lead to Landau quantization. Here, we demonstrate using a combination of an experimental method (scanning tunneling microscopy) and a theoretical approach (tight-binding approximation) that Landau levels will form when the effective pseudomagnetic flux per ripple Φ~(h²/la)Φ0 is larger than the flux quantum Φ0 (here, h is the height, l is the width of the ripple, and a is the nearest C-C bond length). The strain-induced gauge field in the ripple only results in one-dimensional (1D) Landau-level quantization along the ripple. Such 1D Landau quantization does not exist in two-dimensional systems in an external magnetic field. Its existence offers a unique opportunity to realize interesting electronic properties in strained graphene. [ABSTRACT FROM AUTHOR]

We predict a tunable and nonadiabatic Berry phase effect of Dirac fermions, which is an electronic analog of the Pancharatnam phase of polarized light. The Berry phase occurs as a scattering phase shift in a single scattering event of transmission or reflection of Dirac fermions at a junction with a spatially nonuniform mass gap, unveiling the topological aspects of scattering of chiral Dirac fermions. This geometric phase plays different roles in solids as compared with the Pancharatnam phase in optics. It provides a unique approach of detecting the Chern number of the insulator side in a metal-insulator junction of Dirac fermions, implying a different type of bulk-edge correspondence at the boundary between a metal and an insulator. This phase also modifies the quantization rule of Dirac fermions, suggesting geometric-phase devices with nontrivial charge and spin transport such as a topological waveguide and a topological transistor. [ABSTRACT FROM AUTHOR]

We show that in the regime when strong disorder is more relevant than field quantization, the superfluid-to-Bose-glass criticality of one-dimensional bosons is preceded by the prolonged logarithmically slow classical-field renormalization flow of the superfluid stiffness at mesoscopic scales. With the system compressibility remaining constant, the quantum nature of the system manifests itself only in the renormalization of dilute weak links. On the insulating side, the flow ultimately reaches a value of the Luttinger parameter at which the instanton-anti-instanton pairs start to proliferate, in accordance with the universal quantum scenario. This happens first at astronomical system sizes because of the suppressed instanton fugacity. We illustrate our result by first-principles simulations. [ABSTRACT FROM AUTHOR]

The electronic spectrum on the spherical surface of a topological insulator reflects an active property of the helical surface state that stems from a constraint on its spin on a curved surface. The induced spin connection can be interpreted as an effective vector potential associated with a fictitious magnetic monopole induced at the center of the sphere. The strength of the induced magnetic monopole is found to be g = ±2π, being the smallest finite (absolute) value compatible with the Dirac quantization condition. We have established an explicit correspondence between the bulk Hamiltonian and the effective Dirac operator on the curved spherical surface. An explicit construction of the surface spinor wave functions implies a rich spin texture possibly realized on the surface of topological insulator nanoparticles. The electronic spectrum inferred by the obtained effective surface Dirac theory, confirmed also by the bulk tight-binding calculation, suggests a specific photoabsorption/emission spectrum of such nanoparticles. [ABSTRACT FROM AUTHOR]

Dynamics of quantized Auger recombination in Si1-xGex nanocrystals (NCs) embedded in SiO2 films was studied by femtosecond intraband pump-probe spectroscopy. The temporal change of the electron-hole pair number under strong photoexcitation was well explained by the quantized Auger recombination model that considered the size distribution of NCs. On the basis of the dependence of the Auger decay rate on temperature and Ge composition, we confirmed the occurrence of breakdown of the k-conservation rule in quantized Auger recombination in Si and Si1-xGex NCs. [ABSTRACT FROM AUTHOR]

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semiquantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a θ term in the action for the electromagnetic field, where θ is not a constant parameter, like, for example, in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the θ term and the corresponding topological response survive for sufficiently weak translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes. [ABSTRACT FROM AUTHOR]

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number of a Cn-invariant insulator can be determined, up to a multiple of n, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a Cn-invariant insulator is also determined, up to a multiple of n, by the Cn eigenvalue of the Slater determinant of a noninteracting many-body system; and (iii) the Chern number vanishes in insulators with dihedral point groups Dn, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that (i) only insulators with point groups Cn, Cnh, and Sn PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization P3 in the term P3E · B, the axion term in the electrodynamics of the insulator (medium). [ABSTRACT FROM AUTHOR]

We present a description of photon-plasmon interactions in metal nanoparticles based on the second quantization of electromagnetic fields and collective electron excitations. The quantum optical properties of nanostructured systems sustaining resonant charge oscillations will be derived by applying perturbation theory. The linear optical properties can be completely derived from the plasmon-photon coupling coefficients that apply to the particular particle material, environment, and geometry. Nonlinear electromagnetic phenomena such as second harmonic generation need instead to be described by explicidy accounting for the nonlinear corrections of the plasmon-photon interaction Hamiltonian. [ABSTRACT FROM AUTHOR]

Quantized vortices are phase singularities in complex fields. In superfluids, they appear as mobile interacting defects that may cross and reconnect by exchanging tails. Reconnection is a topology-changing event that allows vortex tangles to decay; it is a defining signature of quantum turbulence. We report a family of fixed points (i.e., stationary solutions), including planar forms, that capture reconnection in the Gross-Pitaevskii model in contrast to previous suggestions of pyramidal structures. These are obtained using a well known, systematic method for generating low-energy relaxed initial conditions for Gross-Pitaevskii simulations. [ABSTRACT FROM AUTHOR]

We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick Nig0Fe2o film. The 250-nm-wide circular holes are arranged in a rhombic unit cell with a lattice constant of 400 nm. By Brillouin light scattering, we find that quantized spin wave modes transform to propagating ones and vice versa by changing the in-plane orientation of the applied magnetic field H by 30°. Spin waves of either negative or positive group velocity are found. In the latter case, they propagate in narrow channels exhibiting a width of below 100 nm. We use the plane wave method to calculate the spin wave dispersions for the two relevant orientations of H. The theory allows us to explain the wave-vector-dependent characteristics of the prominent modes. Allowed minibands are formed for selected modes only for specific orientations of H and wave vector. The results are important for applications such as spin wave filters and interconnected waveguides in the emerging field of magnonics where the control of spin wave propagation on the nanoscale is key. [ABSTRACT FROM AUTHOR]

The dynamics of quantized vortices is studied in superfluid 3He-B after a rapid stop of rotation. We use Andreev reflection of thermal excitations to monitor vortex motion with quartz tuning-fork oscillators in two different experimental setups at temperatures below 0.2Tc. Deviations from ideal cylindrical symmetry in the flow environment cause the early decay to become turbulent. This is identified from a rapid initial overshoot in the vortex density above the value before the spin-down and its subsequent decay with a t-3/2 time dependence. The high polarization of the vortices along the rotation axis significantly suppresses the effective turbulent kinematic viscosity &ngr;′ below the values reported for more homogeneous turbulence and leads to a laminar late-time response. The laminar dissipation down to T &alt; 0A5TC is determined from the precession frequency of the polarized vortex configuration. In the limit of vanishing normal-component density, it is found to approach a temperature-independent value, whose origin is currently under discussion. [ABSTRACT FROM AUTHOR]

We study numerically the behavior of a single quantized vortex in a rotating cylinder. We study in particular the spiraling motion of a vortex in a cylinder that is parallel to the rotation axis. We determine the asymptotic form of the vortex and its axial and azimuthal propagation velocities under a wide range of parameters. We also study the stability of the vortex line and the effect of tilting the cylinder from the rotation axis. [ABSTRACT FROM AUTHOR]

Superconducting quantum coherent circuits have opened up a novel area of fundamental low-temperature science since they could potentially be the element base for future quantum computers. Here we report a quasi-three-level coherent system, the so-called superconducting qutrit, which has some advantages over a two-level information cell (qubit) and is based on the qutrit readout circuit intended to measure individually the states of each qubit in a quantum computer. The designed and implemented radio-frequency superconducting qutrit detector (rf SQUTRID) with atomic-size ScS-type contact utilizes the coherent-state superposition in the three-well potential with energy splitting ΔE01/kB ≈ 1.5 K at the 30th quantized energy level with good isolation from the electromagnetic environment. The reason why large values of ΔE01 (and thus using atomic-size Nb-Nb contact) are required is to ensure an adiabatic limit for the quantum dynamics of magnetic flux in the rf SQUTRID. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate theoretically that an electric-field-dependent multimode quantized thermal conductance can be achieved in a composite polymer in the frame of ballistic phonon transport. The composite polymer consists of three segments, where an ionic polymer is introduced as its central part and the nonpolar polymers are designed on the left and right parts, respectively. By increasing the applied electric field, the dispersion relation of phononic torsion mode is tuned, hence multiple phononic channels are adjusted one by one in the composite polymer. As a result, multiple-step quantized thermal conductance can be manipulated by external electric field. The analysis based on Landauer formula is in good agreement with both the numerical calculations with transfer-matrix method and molecular dynamics simulations. By designing such a three-segment composite polymer, multimode quantized thermal conductance tuned by external electric field becomes an exact analog to multistep quantized electrical conductance tuned by external magnetic field in the quantum Hall effect. The investigations may have potential applications in thermal manipulation and information transfer in mesoscopic phonon systems. [ABSTRACT FROM AUTHOR]

We study the disordered topological Anderson insulator in a two-dimensional (square not strip) geometry. We first report the phase diagram of finite systems and then study the evolution of phase boundaries when the system size is increased to a very large 1120 x 1120 area. We establish that conductance quantization can occur without a bulk band gap, and that there are two distinct scaling regions with quantized conductance: TAI-I with a bulk band gap, and TAI-II with localized bulk states. We show that there is no intervening insulating phase between the bulk conduction phase and the TAI-I and TAI-II scaling regions, and that there is no metallic phase at the transition between the quantized and insulating phases. Centered near the quantized-insulating transition there are very broad peaks in the eigenstate size and fractal dimension d2; in a large portion of the conductance plateau eigenstates grow when the disorder strength is increased. The fractal dimension at the peak maximum isd2=1 -5. Effective-medium theory (Coherent Potential Approximation, self-consistent Born approximation) predicts well the boundaries and interior of the gapped TAI-I scaling region, but fails to predict all boundaries save one of the ungapped TAI-II scaling region. We report conductance distributions near several phase transitions and compare them with critical conductance distributions for well-known models. [ABSTRACT FROM AUTHOR]

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field. [ABSTRACT FROM AUTHOR]

We studied numerically the Andreev scattering cross-sections of three-dimensional isolated quantized vortex rings in superfluid 3He-B at ultralow temperatures. We calculated the dependence of the cross-section on the ring's size and on the angle between the beam of incident thermal quasiparticle excitations and the direction of the ring's motion. We also introduced, and investigated numerically, the cross-section averaged over all possible orientations of the vortex ring; such a cross-section may be particularly relevant for the analysis of experimental data. We also analyzed the rôle of screening effects for Andreev reflection of quasiparticles by systems of vortex rings. Using the results obtained for isolated rings we found that the screening factor for a system of unlinked rings depends strongly on the average radius of the vortex ring, and that the screening effects increase with decreasing the rings' size. [ABSTRACT FROM AUTHOR]

The effective Hamiltonian for an electron in a quasi-one-dimensional quantum ring in the presence of spin-orbit interactions is derived. We demonstrate that, when both coupling types are simultaneously present, the effective Hamiltonian derived by the lowest-radial-state approximation produces energy spectra and charge densities which deviate strongly from the exact ones. For equal Rashba and Dresselhaus coupling constants the lowest-radial-state approximation opens artifactal avoided crossings in the energy spectra and deforms the circular symmetry of the confined charge densities. In this case, there does not exist a ring thin enough to justify the restriction to the lowest radially quantized energy state. We derive the effective Hamiltonian accounting for both the lowest and the first excited radial states, and show that the inclusion of the latter restores the correct features of the exact solution. Relation of this result to the states of a quantum wire is also discussed. [ABSTRACT FROM AUTHOR]

We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such materials' behavior is determined by just the eigenvalues under inversion symmetry of occupied states at time reversal invariant momenta (TRIM parities). In particular, if the total number of --1 eigenvalues at all TRDVIs is odd then the material cannot be an insulator. A likely possibility is that it is then a "Weyl" semimetal. Additionally if the material is an insulator and has vanishing Hall conductivity, then a magnetoelectric response, parameterized by θ, can be defined, and is quantized to θ = 0, π. The value is π if the total number of TRIM parities equal to -- 1 is twice an odd number. This generalizes the rule of Fu and Kane that applies to materials in which time reversal is unbroken. This result may be useful in the search for magnetic insulators with large θ. These two results are obtained as part of a classification of the band topology of inversion-symmetric insulators. Such band structures can be classified by two sets of numbers: the TRIM parities and three Chern numbers. The TRIM parities have the physical implications just described, and additionally they constrain the values of the Chern numbers modulo 2. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground-state wave function. [ABSTRACT FROM AUTHOR]

Here we demonstrate a simple and reconfigurable way to create a polariton condensate in well defined discrete momentum states, allowing us to manipulate the local polariton flow. To this end, we created a spatially varying potential formed in the presence of noncondensed carriers by subjecting a microcavity to spatially modulated nonresonant optical excitation. The choice of the spatial shape of this potential allows us to tailor the properties of the polariton condensate in momentum space. Our results demonstrate a way to prepare a polariton condensate in an adjustable momentum state and provide a first step toward the creation of functional all-optical elements for polaritonic logic circuits on demand by projecting circuits onto an unprocessed planar sample. [ABSTRACT FROM AUTHOR]

We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level-like quantization appear with the full two- and three-dimensional rotational symmetry and time-reversal symmetry. Inside each band, states are labeled by their angular momenta over which energy dispersions are strongly suppressed by spin-orbit coupling, to being nearly flat. The radial quantization generates energy gaps between neighboring bands at the order of the harmonic frequency. Helical edge or surface states appear on open boundaries characterized by the Z2 index. These Hamiltonians can be viewed from the dimensional reduction of the high-dimensional quantum Hall states in three- and four-dimensional flat spaces. These states can be realized with ultracold fermions inside harmonic traps with synthetic gauge fields. [ABSTRACT FROM AUTHOR]

We present the results of million-atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic-scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ∼0.5 x 2e2/h as in recent experiments [N. Tombros et al, Nat. Phys. 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/ h occur even for strongly nonadiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also show that conductance plateaus near 0.5 x 2e2/ h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions. [ABSTRACT FROM AUTHOR]

We present a microscopic theory to give a physical picture of the formation of the quantum anomalous Hall (QAH) effect in magnetized graphene coupled with Rashba spin-orbit coupling. Based on a continuum model at valley K or K', we show that there exist two distinct physical origins of the QAH effect at two different limits. For large exchange field M, the quantization of Hall conductance in the absence of Landau-level quantization can be regarded as a summation of the topological charges carried by skyrmions from real-spin textures and merons from AB sublattice pseudospin textures, while for strong Rashba spin-orbit coupling λR, the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane model, giving rise to a nonzero Chern number C=1 at either K or K'. In the presence of staggered AB sublattice potential U, a topological phase transition occurs at U=M from a QAH phase to a quantum valley Hall phase. We further find that the band gap responses at K and K' are different when λR, M, and U are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling λSo, and it transitions to a trivial phase when λSO > (√M2 + λR2 + M)/2. Moreover, we use a tight-binding model to reproduce the ab initio method obtained band structures through doping magnetic atoms on 3×3 and 4×4 supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene. [ABSTRACT FROM AUTHOR]