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The interplay between disorder and interactions can dramatically influence the physical properties of thin-film superconductors. In the most extreme case, strong disorder is able to suppress superconductivity as an insulating phase emerges. Due to the known pair-breaking potential of magnetic disorder on superconductors, the research focus is on the influence of non-magnetic disorder. Here we provide direct evidence that magnetic disorder is also present at the surface of amorphous superconducting films. This magnetic disorder is present even in the absence of magnetic impurity atoms and is intimately related to the surface termination itself. While bulk superconductivity survives in sufficiently thick films, we suggest that magnetic disorder may crucially affect the superconductor-to-insulator transition in the thin-film limit.

Characterizing the many-body localization (MBL) transition in strongly disordered and interacting quantum systems is an important issue in the field of condensed matter physics. We study the single particle Green's functions for a disordered interacting system in one dimension using exact diagnonalization in the infinite temperature limit and provide strong evidence that single particle excitations carry signatures of delocalization to MBL transition. In the delocalized phase, the typical values of the local density of states and the scattering rate are finite while in the MBL phase, the typical values for both the quantities become vanishingly small. The probability distribution functions of the local density of states and the scattering rate are broad log-normal distributions in the delocalized phase while the distributions become very narrow and sharply peaked close to zero in the MBL phase. We also study the eigenstate Green's function for all the many-body eigenstates and demonstrate that both, the energy resolved typical scattering rate and the typical local density of states, can track the many-body mobility edges., Comment: A few changes to the text to improve clarity. No change in results. Close to the published version

The properties of semiconductors can be crucially impacted by midgap states induced by dopants, which can be native or intentionally incorporated in the crystal lattice. For Bernal-stacked bilayer graphene (BLG), which has a tunable bandgap, the existence of midgap states induced by dopants has been conjectured, but never confirmed experimentally. Here, we report scanning tunneling microscopy and spectroscopy results, supported by tight-binding calculations, that demonstrate the existence of midgap states in BLG. We show that the midgap state in BLG -- for which we demonstrate gate-tunability -- appears when the dopant is hosted on the non-dimer sublattice sites. We further evidence the presence of narrow resonances at the onset of the high energy bands (valence or conduction, depending on the dopant type) when the dopants lie on the dimer sublattice sites. These results suggest that dopants/defects can play an important role in the transport and optical properties of multilayer graphene samples, especially at energies close to the band extrema., Includes supplementary material

The Hamiltonian size reduction method or the mode space method applicable to general heterogeneous structures is developed in this work. The effectiveness and accuracy of the method are demonstrated for four example devices, such as GaSb/InAs tunnel field effect transistors (FETs), MoTe 2/SnS 2 bilayer vertical FETs, InAs nanowire FETs with a defect, and Si nanowire FETs with rough surfaces. The Hamiltonian size is reduced to around 5% of the original full-Hamiltonian size without losing the accuracy of the calculated transmission and local density of states in a practical sense. The method developed in this work can be used with any type of Hamiltonian and can be applied virtually to any hetero-structure, and so it has the potential to become an enabling technology for efficient simulations of hetero-structures.

We use scanning gate microscopy to study electron transport through an open, gate-defined resonator in a Ga(Al)As heterostructure. Raster-scanning the voltage-biased metallic tip above the resonator, we observe distinct conductance modulations as a function of the tip position and voltage. Quantum-mechanical simulations reproduce these conductance modulations and reveal their relation to the partial local density of states in the resonator. Our measurements illustrate the current frontier between possibilities and limitations in imaging the local density of states in buried electron systems using scanning gate microscopy., Physical Review Research, 3 (3), ISSN:2643-1564

Iterative Green's function, based on cyclic reduction of block tridiagonal matrices, has been the ideal algorithm, through tight-binding models, to compute the surface density-of-states of semi-infinite topological electronic materials. In this paper, we apply this method to photonic and acoustic crystals, using finite-element discretizations and a generalized eigenvalue formulation, to calculate the local density-of-states on a single surface of semi-infinite lattices. The three-dimensional (3D) examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence and accuracy are analyzed., 7 pages, 4 figures

In a Type II superconductor, the vortex core behaves like a normal metal. Consequently, the single-particle density of states in the vortex core of a conventional Type II superconductor remains either flat or (for very clean single crystals) exhibits a peak at zero bias due to the formation of Caroli-de Gennes-Matricon bound state inside the core. Here we report an unusual observation from scanning tunneling spectroscopy measurements in a weakly pinned thin film of the conventional s-wave superconductor a-MoGe, namely, that a soft gap in the local density of states continues to exist even at the center of the vortex core. We ascribe this observation to rapid fluctuation of vortices about their mean position that blurs the boundary between the gapless normal core and the gapped superconducting region outside. Analyzing the data as a function of magnetic field we show that the variation of fluctuation amplitude as a function of magnetic field is consistent with quantum zero-point motion of vortices., arXiv admin note: substantial text overlap with arXiv:1905.01045

Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of wave functions are also at the heart of the topological classification of the gapped phases of matter. Despite identical singular features, topological insulators and topological defects in waves remain two distinct fields. Realising 1D microwave insulators, we experimentally observe a wavefront dislocation – a 2D phase singularity – in the local density of states when the systems undergo a topological phase transition. We show theoretically that the change in the number of interference fringes at the transition reveals the topological index that characterises the band topology in the insulator., Topological properties are defined from singularities of the wave functions delocalised in the bulk of the material, but most experimental manifestations remain indirect. Here, the authors observe a wavefront dislocation as a direct evidence of the phase singularity of the delocalised wave functions in 1D microwave photonic insulators.

Silicon (Si) donors in GaAs have been the topic of extensive studies since Si is the most common and well understood n-type dopant in III-V semiconductor devices and substrates. The indirect bandgap of AlAs compared to the direct one of GaAs leads to interesting effects when introducing Si dopants. Here we present a study of cross-sectional scanning tunneling microscopy (X-STM) and density functional theory (DFT) calculations to study Si donors in AlAs at the atomic scale. Based on their crystal symmetry and contrast strengths, we identify Si donors up to four layers below the (110) surface of AlAs. Interestingly, their short-range local density of states (LDOS) is very similar to Si atoms in the (110) surface of GaAs. Additionally we show high-resolution images of Si donors in all these layers. For empty state imaging, the experimental and simulated STM images based on DFT show excellent agreement for Si donor up to two layers below the surface.

Spectromicroscopy techniques with fast electrons can quantitatively measure the optical response of excitations with unrivalled spatial resolution. However, owing to their inherently scalar nature, electron waves cannot access the polarization-related quantities. Despite promising attempts based on the conversion of concepts originating from singular optics (such as vortex beams), the definition of an optical polarization analogue for fast electrons has remained an open question. Here we establish such an analogue using the dipole transition vector of the electron between two well-chosen singular wave states. We show that electron energy loss spectroscopy allows the direct measurement of the polarized electromagnetic local density of states. In particular, in the case of circular polarization, it directly measures the local optical spin density. This work establishes electron energy loss spectroscopy as a quantitative technique to tackle fundamental issues in nano-optics, such as super-chirality, local polarization of dark excitations or polarization singularities at the nanoscale. The functionality of electron energy loss spectroscopy can be extended to include a polarization analogue constructed via the dipole transition vector between two electronic states, bringing it closer to its optical counterpart.

The discovery of interaction-driven insulating and superconducting phases in moir\'e van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moir\'e unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moir\'e systems., Comment: 24 pages, 5 figures

Infinite quasiperiodic arrangements in space, such as quasicrystals, are typically described as projections of higher-dimensional periodic lattices onto the physical dimension. The concept of a reference higher-dimensional space, called a superspace, has proved useful in relation to quasiperiodic systems. Although some quantum-mechanical systems in quasiperiodic media have been shown to admit quasiperiodic states, any sort of general Hamiltonian formalism in superspace is lacking to this date. Here, we show how to extend generic quantum-mechanical Hamiltonians to higher dimensions in such a way that eigenstates of the original Hamiltonian are obtained as projections of the Hamiltonian in superspace, which we call the super Hamiltonian. We apply the super Hamiltonian formalism to a simple, yet realistic one-dimensional quantum particle in a quasiperiodic potential without the tight-binding approximation, and obtain continuously labelled eigenstates of the system corresponding to a continuous spectrum. All states corresponding to the continuum are quasiperiodic. We also obtain the Green's functions for continuum states in closed form and, from them, the density of states and local density of states, and scattering states off defects and impurities. The closed form of this one-dimensional Green's function is equally valid for any continuum state in any one-dimensional single-particle quantum system admitting continuous spectrum. With the basis set we use, which is periodic in superspace, and therefore quasiperiodic in physical space, we find that Anderson-localised states are also quasiperiodic if distributional solutions are admitted, but circumvent this difficulty by generalising the superspace method to open boundary conditions (cont'd)., 11 pages, 6 figures. See article for full abstract

We propose a mechanism to substantially rectify radiative heat flow by having one side of the thermal diode offering a large contrast in the local density of electromagnetic states, while the opposite side serving as a narrow bandpass filter that limits the transport to a desired spectral range. To demonstrate, we realize such a scenario by matching thin films of metal-to-insulator transition materials and polar dielectrics in the near field. By leveraging the distinct scaling behaviors of the local density of states with film thickness for metals and insulators, we theoretically achieve rectification ratios over 140, a 10-fold improvement over the state of the art, with nanofilms of vanadium dioxide and cubic boron nitride in the parallel-plane geometry at experimentally feasible gap sizes (\ensuremath{\sim}100 nm). Our rational design offers relative ease of fabrication, flexible choice of materials, and robustness against deviations from optimal film thicknesses. We expect this work to facilitate the application of thermal diodes in solid-state thermal circuits and energy-conversion devices.

Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $\pm 1$ are found in a wide range of parameter space when the moire bands are isolated through gaps, while the local density of states associated to the flat bands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moire period ratios indicate it is possible to achieve narrow width $W \lesssim 30$ meV isolated folded band bundles for tBG angles $\theta \lesssim 1^{\circ}$., Comment: 17 pages, 9 figures

Metal-to-insulator transitions (MIT) can be driven by a number of different mechanisms, each resulting in a different type of insulator—Change in chemical potential can induce a transition from a metal to a band insulator; strong correlations can drive a metal into a Mott insulator with an energy gap; an Anderson transition, on the other hand, due to disorder leads to a localized insulator without a gap in the spectrum. Here, we report the discovery of an alternative route for MIT driven by the creation of a network of narrow channels. Transport data on Pt substituted for Ti in 1T-TiSe2 shows a dramatic increase of resistivity by five orders of magnitude for few % of Pt substitution, with a power-law dependence of the temperature-dependent resistivity ρ(T). Our scanning tunneling microscopy data show that Pt induces an irregular network of nanometer-thick domain walls (DWs) of charge density wave (CDW) order, which pull charge carriers out of the bulk and into the DWs. While the CDW domains are gapped, the charges confined to the narrow DWs interact strongly, with pseudogap-like suppression in the local density of states, even when they were weakly interacting in the bulk, and scatter at the DW network interconnects thereby generating the highly resistive state. Angle-resolved photoemission spectroscopy spectra exhibit pseudogap behavior corroborating the spatial coexistence of gapped domains and narrow domain walls with excess charge carriers.

We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. The dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [$1\overline{1}0$] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state., Comment: 13 pages, 6 figures, 5 tables

Slow light in topological valley photonic crystal structures offers new possibilities to enhance light-matter interaction. We report a topological cavity based on slow light topological edge mode for broadband Purcell enhancement. The topological edge modes with large group indices over 100 can be realized with a bearded interface between two topologically distinct valley photonic crystals, featuring the greatly enhanced Purcell factor because of the increased local density of states. In the slow light regime, the topological cavity supports much more cavity modes with higher quality factor than that in the fast light regime, which is both demonstrated theoretically and experimentally. We demonstrate the cavity enables the broadband Purcell enhancement together with substantial Purcell factor, benefiting from dense cavity modes with high quality factor in a wide spectral range. It has great benefit to the realization of high-efficiency quantum-dot-based single-photon sources and entangled-photon sources with less restriction on spectral match. Such topological cavity could serve as a significant building block toward the development of photonic integrated circuits with embedded quantum emitters., Comment: 16 pages, 4 figures

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

We have implemented the Bogoliubov-de Gennes equation in a screened Korringa-Kohn-Rostoker method for solving, self-consistently, the superconducting state for three-dimensional (3D) crystals including substitutional impurities. In this paper we extend this theoretical framework to allow for collinear magnetism and apply it to fcc Pb with 3D magnetic impurities. In the presence of magnetic impurities, there is a pair-breaking effect that results in in-gap Yu-Shiba-Rusinov (YSR) states which we decompose into contributions from the individual orbital character. We determine the spatial extent of these impurity states, showing how the different orbital character affects the details of the YSR states within the superconducting gap. Our work highlights the importance of a first-principles-based description which captures the quantitative details, making direct comparisons with experimental findings possible., The above work was supported by the Centre for Doctoral Training in Condensed Matter Physics, funded by EPSRC Grant No. EP/L015544/1. T.G.S. gratefully acknowledges support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Grant No. TRR 173/2 - 268565370 Spin+X (project A11). G.C. gratefully acknowledges support from the European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 754510. This work was supported by Spanish MINECO (the Severo Ochoa Centers of Excellence Program under Grant No. SEV- 2017-0706), Spanish MICIU, AEI and EU FEDER (Grant No. PGC2018-096955-B-C43), and Generalitat de Catalunya (Grant No. 2017SGR1506 and the CERCA program). The work was also supported by the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143). M.G. thanks the visiting professorship program of the Centre for Dynamics and Topology at Johannes Gutenberg University Mainz.

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity., Comment: 30 pages, 3 figures, accepted to Localisation 2020 volume of Annals of Physics

For the pristine phosphorene nanoribbons (PNRs) with edge states, there exist two categories of edge bands near the Fermi energy (${E}_{F}$), i.e., the shuttle-shaped twofold-degenerate and the near-flat simple degenerate edge bands. However, the usual experimental measurement may not distinguish the difference between the two categories of edge bands. Here we study the varying rule for the edge bands of PNRs under an external electrostatic field. By using the KWANT code based on the tight-binding approach, we find that the twofold-degenerate edge bands can be divided into two separated shuttles until the degeneracy is completely removed and a gap near ${E}_{F}$ is opened under a sufficiently strong in-plane electric field. Importantly, each shuttle from the ribbon upper or lower edge outmost atoms is identified according to the local density of states. However, under a small off-plane field the shuttle-shaped bands are easily induced into two near-flat bands contributed from the edge atoms of the top and bottom sublayers, respectively. The evidence provides the edge and sublayer degrees of freedom (DOF) for the PNRs with shuttle-shaped edge bands, which is obviously different from another category of PNRs intrinsically with near-flat edge bands. This is because the former category of ribbons solely have four zigzaglike atomic configurations at the edges in each unit cell, which also results in that the property is robust against the point defect in the ribbon center area. As an application, furthermore, based on this issue we propose a homogenous junction of a shuttle-edge-band PNR attached by two electric gates. Interestingly, the transport property of the junction with field manipulation well reflects the characteristics of the two DOFs. These findings may provide a further understanding on PNRs and initiate new developments in PNR-based electronics.

Angle disorder is an intrinsic feature of twisted bilayer graphene and other moir\'e materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-B\"uttiker transmission through an angle disorder barrier of width comparable to the moir\'e period, using a decimation technique based on a real space description. We find that barriers which separate regions where the width of the bands differ by 50% or more lead to a minor suppression of the transmission, and that the transmission is close to one for normal incidence, which is reminiscent of Klein tunneling. These results suggest that transport in twisted bilayer graphene is weakly affected by twist angle disorder., Comment: 5 pages, 4 figures and supplementary material

The signatures of Majorana zero-energy mode leaking into a spin-charge entangled double quantum dot are investigated theoretically in the strong electron correlation regime. The considered setup consists of two capacitively coupled quantum dots attached to external contacts and side-attached to topological superconducting wire hosting Majorana quasiparticles. We show that the presence of Majorana mode gives rise to unique features in the local density of states in the $SU(4)$ Kondo regime. Moreover, it greatly modifies the gate voltage dependence of the linear conductance, leading to fractional values of the conductance. We also analyze the effect of a finite length of topological wire and demonstrate that non-zero overlap of Majorana modes at the ends of the wire is revealed in local extrema present in the local density of states of the dot coupled directly to the wire. The calculations are performed with the aid of the numerical renormalization group method., Comment: 12 pages, 10 figures

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states., Comment: 6 pages, 3 figures

We present a fully relativistic first-principles-based theoretical approach for the calculation of the spectral properties of magnetic impurities on the surface of a superconducting substrate, providing a material specific framework for the investigation of the Yu-Shiba-Rusinov (YSR) states. By using a suitable orbital decomposition of the local densities of states we discuss in great detail the formation of the YSR states for an Mn adatom and for two kinds of Mn dimers placed on the Nb(110) surface and compare our results to recent experimental findings. In the case of the adatom we find that the spin-orbit coupling slightly shifts some of the YSR peaks and also the local spin polarization on the Nb atoms has marginal effects on their positions. Moreover, by scaling the exchange field on the Mn site we could explain the lack of the dx2−y2-like YSR state in the spectrum. While our results for a close packed ferromagnetic dimer are in satisfactory agreement with the experimentally observed splitting of the YSR states, in the case of an antiferromagnetic dimer we find that the spin-orbit coupling is not sufficiently large to explain the splitting of the YSR states seen in the experiment. Changing the relative orientation of the magnetic moments in this dimer induces splitting of the YSR states and also shifts their energy, leading even to the formation of a zero bias peak in the case of the deepest YSR state., Among the authors B.N., A.L., L.S., and B.U. are grateful for the financial support by the Ministry for Innovation and Technology and the National Research, Development and Innovation Office under Project No. K131938 and within the Quantum Information National Laboratory of Hungary. B.N. is also grateful for the support of ÚNKP-20-3-II-BME-249 New National Excellence Program of the Ministry for Innovation and Technology of Hungary. G.C. gratefully acknowledges support from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 754510. This work was supported by Spanish MINECO (the Severo Ochoa Centers of Excellence Program under Grant No. SEV- 2017-0706), Spanish MICIU, AEI and EU FEDER (Grant No. PGC2018-096955-B-C43), and Generalitat de Catalunya (Grant No. 2017SGR1506 and the CERCA Program). The work was also supported by the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143).

We present an exhaustive study of Andreev crystals (ACs)—quasi-one-dimensional superconducting wires with a periodic distribution of magnetic regions. The exchange field in these regions is assumed to be much smaller than the Fermi energy. Hence, the transport through the magnetic region can be described within the quasiclassical approximation. In the first part of the paper, by assuming that the separation between the magnetic regions is larger than the coherence length, we derive the effective nearest-neighbor tight-binding equations for ACs with a helical magnetic configuration. The spectrum within the gap of the host superconductor shows a pair of energy-symmetric bands. By increasing the strength of the magnetic impurities in ferromagnetic ACs, these bands cross without interacting. However, in any other helical configuration, there is a value of the magnetic strength at which the bands touch each other, forming a Dirac point. Further increase of the magnetic strength leads to a system with an inverted gap. We study junctions between ACs with inverted spectrum and show that junctions between (anti)ferromagnetic ACs (always) never exhibit bound states at the interface. In the second part, we extend our analysis beyond the nearest-neighbor approximation by solving the Eilenberger equation for infinite ACs and junctions between semi-infinite ACs with collinear magnetization. From the obtained quasiclassical Green functions, we compute the local density of states and the local spin polarization in anti- and ferromagnetic ACs. We show that these junctions may exhibit bound states at the interface and fractionalization of the surface spin polarization., M.R. and F.S.B. acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Project FIS2017-82804-P), and EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19)

The ab initio simulation of charged interfaces in the framework of density functional theory (DFT) is heavily employed for the study of electrochemical energy conversion processes. The capacitance is the primary descriptor for the response of the electrochemical interface. It is essentially equal to the inverse of the energy curvature as a function of electron number, and as such there appears a conflict with the fundamental principle of piecewise linearity in DFT that requires the energy curvature to be zero at fractional electron numbers, i.e., almost everywhere. To resolve this conflict, we derive an exact expression between the energy curvature and the Kohn-Sham density of states, the local density of states, and the Fukui potential. We find that the piecewise linearity requirement does not hold for the volume- or area-specific energy of extended systems and surfaces. Applied to the joint density functional theory of an electrode-electrolyte interface, including the ionic and dielectric response of the electrolyte, the same expression represents a rigorous basis for the partitioning of the total interfacial capacitance into contributions of the quantum capacitance, space-charge capacitance, and electrochemical double-layer capacitance. It provides insight into the influence of the electrode material, thickness, and temperature on the charging characteristics, as demonstrated by results for a bulk gold electrode, a single-layer gold electrode, and a single-layer graphene electrode.

Trilayer graphene with a twisted middle layer has recently emerged as a new platform exhibiting correlated phases and superconductivity near its magic angle. A detailed characterization of its electronic structure in the parameter space of twist angle $\theta$, interlayer potential difference $\Delta$, and top-bottom layer stacking $\tau$ reveals that flat bands with large Coulomb energy vs bandwidth $U/W > 1$ are expected within a range of $\pm 0.2^{\circ}$ near $\theta \simeq1.5^{\circ}$ and $\theta \simeq1.2^{\circ}$ for $\tau_{\rm AA}$ top-bottom layer stacking, between a wider $1^{\circ} \sim 1.7^{\circ}$ range for $\tau_{\rm AB}$ stacking, whose bands often have finite valley Chern numbers thanks to the opening of primary and secondary band gaps in the presence of a finite $\Delta$, and below $\theta \lesssim 0.6^{\circ}$ for all $\tau$ considered. The largest $U/W$ ratios are expected at the magic angle $\sim 1.5^{\circ}$ when $|\Delta| \sim 0$~meV for AA, and slightly below near $\sim 1.4^{\circ}$ for finite $|\Delta| \sim 25$~meV for AB stackings, and near $\theta \sim 0.4^{\circ}$ for both stackings. When ${\tau}$ is the saddle point stacking vector between AB and BA we observe pronounced anisotropic local density of states (LDOS) strip patterns with broken triangular rotational symmetry. We present optical conductivity calculations that reflect the changes in the electronic structure introduced by the stacking and gate tunable system parameters., Comment: 13 pages 8 figures

The photonic local density of states (PLDOS) determines the light matter interaction strength in nanophotonic devices. For standard dielectric devices, the PLDOS is fundamentally limited by diffraction, but its precise dependence on the size parameter $s$ of a device can be non-trivial. Here, we measure the PLDOS dependence on the size parameter in a waveguide using a new technique - nanowaveguide coupled cathode luminescence (CL). We observe that depending on the position within the waveguide cross-section, the effective diffraction limit of the PLDOS varies, and the PLDOS peak shape changes. Our results are of fundamental importance for optimizing coupling to nanophotonic devices, and also open new avenues for spectroscopy based on evanescently coupled CL., Comment: Comments welcome

In this paper we propose a novel approach to enhance the efficiency of the two-photon spontaneous emission process that is driven by the multifractal optical mode density of photonic structures based on the aperiodic distributions of Eisenstein and Gaussian primes. In particular, using the accurate Mie-Lorenz multipolar theory in combination with multifractal detrended fluctuation analysis, we compute the local density of states of periodic and aperiodic systems and demonstrate the formation of complete bandgaps with distinctive fractal scaling behavior for scattering arrays of dielectric nanocylinders. Moreover, we systematically study the Purcell enhancement and the most localized optical mode resonances in these novel aperiodic photonic systems and compute their two-photon spontaneous emission rates based on the general Green's tensor approach. Our results demonstrate that the excitation of the highly-resonant critical states of Eisenstein and Gaussian photonic arrays across broadband multifractal spectra gives rise to significantly enhanced emission rates compared to what is possible at the band-edges of periodic structures with comparable size. Besides defining a novel approach for enhanced quantum two-photon sources on the chip, the engineering of aperiodic bandgap structures with multifractal mode density may provide access to novel electromagnetic resonant phenomena in a multiscale-invariant vacuum for quantum nanophotonics applications., Comment: 14 pages, 9 Figures

In quantum dot (QD) electron transport experiments additional features can appear in the differential conductance $dI/dV$ that do not originate from discrete states in the QD, but rather from a modulation of the density-of-states (DOS) in the leads. These features are particularly pronounced when the leads are strongly confined low dimensional systems, such as in a nanowire (NW) where transport is one-dimensional and quasi-zero dimensional lead-states can emerge. In this paper we study such lead-states in InAs NWs. We use a QD integrated directly into the NW during the epitaxial growth as an energetically and spatially well-defined tunnel probe to perform $dI/dV$ spectroscopy of discrete bound states in the `left' and `right' NW lead segments. By tuning a sidegate in close proximity of one lead segment, we can distinguish transport features related to the modulation in the lead DOS and to excited states in the QD. We implement a non-interacting capacitance model and derive expressions for the slopes of QD and lead resonances that appear in two-dimensional plots of $dI/dV$ as a function of source-drain bias and gate voltage in terms of the different lever arms determined by the capacitive couplings. We discuss how the interplay between the lever arms affect the slopes. We verify our model by numerically calculating the $dI/dV$ using a resonant tunneling model with three non-interacting quantum dots in series. Finally, we used the model to describe the measured $dI/dV$ spectra and extract quantitatively the tunnel couplings of the lead segments. Our results constitute an important step towards a quantitative understanding of normal and superconducting subgap states in hybrid NW devices., Comment: 11 pages, 4 figures

We describe the formation of charge- and spin-density patterns induced by spin-selective photoexcitations of interacting fermionic systems in the presence of a microstructure. As an example, we consider a one-dimensional Hubbard-like system with a periodic magnetic microstructure, which has a uniform charge distribution in its ground state, and in which a long-lived charge-density pattern is induced by the spin-selective photoexcitation. Using tensor-network methods, we study the full quantum dynamics in the presence of electron-electron interactions and identify doublons as the main decay channel for the induced charge pattern. Our setup is compared to the optically induced spin transfer (OISTR) mechanism, in which ultrafast optically induced spin transfer in Heusler and magnetic compounds is associated to the difference of the local density of states of the different elements in the alloys. We find that applying a spin-selective excitation there induces spatially periodic patterns in local observables. Implications for pump-probe experiments on correlated materials and experiments with ultracold gases on optical lattices are discussed.

We calculate and resolve with unprecedented detail the local density of states (DOS) and momentum-dependent spectral functions at zero temperature of one of the key models for strongly correlated electron materials, the degenerate two-orbital Kanamori-Hubbard model, by means of a highly optimized Dynamical Mean Field Theory which uses the Density Matrix Renormalization Group as the impurity solver. When the system is hole doped, and in the presence of a finite interorbital Coulomb interaction we find the emergence of a novel holon-doublon in-gap subband which is split by the Hund's coupling. We also observe new interesting features in the DOS like the splitting of the lower Hubbard band into a coherent narrowly dispersing peak around the Fermi energy, and another subband which evolves with the chemical potential. We characterize the main transitions giving rise to each subband by calculating the response functions of specific projected operators and comparing with the energies in the atomic limit, obtaining excellent agreement. The detailed results for the spectral functions found in this work pave the way to study with great precision the microscopic quantum behavior in correlated materials., Replaced with updated results

The functional renormalization group (FRG) provides a flexible tool to study correlations in low-dimensional electronic systems. In this paper, we present a novel FRG approach to the steady-state of quantum wires out of thermal equilibrium. Our method is correct up to second order in the two-particle interaction and accounts for inelastic scattering. We combine semi-analytic solutions of the flow equations with MPI parallelization techniques, which allows us to treat systems of up to 60 lattice sites. The equilibrium limit is well-understood and serves as a benchmark. We compute effective distribution functions, the local density of states, and the steady-state current and demonstrate that all of these quantities depend strongly on the choice of the cutoff employed within the FRG. Non-equilibrium is plagued by the lack of physical arguments in favor of a certain cutoff as well as by the appearance of secular higher-order terms which are only partly included in our approach. This demonstrates the inadequacy of a straightforward second-order FRG scheme to study interacting quantum wires out of equilibrium in the absence of a natural cutoff choice.

In this work, we investigate models for bulk, bi- and multilayers containing half-metallic ferromagnets (HMFs), at zero and at finite temperature, in order to elucidate the effects of strong electronic correlations on the spectral properties (density of states). Our focus is on the evolution of the finite-temperature many-body induced tails in the half-metallic gap. To this end, the dynamical mean-field theory (DMFT) is employed. For the bulk, a Bethe lattice model is solved using a matrix product states based impurity solver at zero temperature and a continuous-time quantum Monte Carlo (CT-QMC) solver at finite temperature. We demonstrate numerically, in agreement with the analytical result, that the tails vanish at the Fermi level at zero temperature. In order to study multilayers, taken to be square lattices within the layers, we use the real-space DMFT extension with the CT-QMC impurity solver. For bilayers formed by the HMF with a band or correlated insulator, we find that charge fluctuations between the layers enhance the finite temperature tails. In addition, in the presence of inter-layer hopping, a coherent quasiparticle peak forms in the otherwise correlated insulator. In the multilayer heterostructure setup, we find that by suitably choosing the model parameters, the tails at the HMF/Mott insulator interface can be reduced significantly, and that a high spin polarization is conceivable, even in the presence of long-ranged electrostatic interactions., Comment: to be published in Physical Review Research

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states., 20 pages, 4 figures

Metalated phthalocyanines (Pc's) are robust and versatile molecular complexes, whose properties can be tuned by changing their functional groups and central metal atom. The electronic structure of magnesium Pc (MgPc) - structurally and electronically similar to chlorophyll - adsorbed on the Ag(100) surface is investigated by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), non-contact atomic force microscopy (ncAFM) and density functional theory (DFT). Single, isolated MgPc's exhibit a flat, four-fold rotationally symmetric morphology, with doubly degenerate, partially populated (due to surface-to-molecule electron transfer) lowest unoccupied molecular orbitals (LUMOs). In contrast, MgPc's with neighbouring molecules in proximity undergo a lift of LUMOs degeneracy, with a near-Fermi local density of states with reduced two-fold rotational symmetry, indicative of a long-range attractive intermolecular interaction. The latter is assigned to a surface-mediated two-step electronic hybridization process. First, LUMOs interact with Ag(100) conduction electrons, forming hybrid molecule-surface orbitals with enhanced spatial extension. Then, these delocalized molecule-surface states further hybridize with those of neighbouring molecules. This work highlights how the electronic structure of molecular adsorbates - including orbital degeneracies and symmetries - can be significantly altered via surface-mediated intermolecular hybridization, over extended distances (beyond 3 nm), having important implications for prospects of molecule-based solid-state technologies., Comment: 28 pages, 4 figures; supplementary 35 pages, 19 figures

Using scanning tunneling microscopy and spectroscopy, we visualized the native defects in antiferromagnetic topological insulator $\mathrm{MnBi_2Te_4}$. Two native defects $\mathrm{Mn_{Bi}}$ and $\mathrm{Bi_{Te}}$ antisites can be well resolved in the topographic images. $\mathrm{Mn_{Bi}}$ tend to suppress the density of states at conduction band edge. Spectroscopy imaging reveals a localized peak-like local density of state at $\sim80$~meV below the Fermi energy. A careful inspection of topographic and spectroscopic images, combined with density functional theory calculation, suggests this results from $\mathrm{Bi_{Mn}}$ antisites at Mn sites. The random distribution of $\mathrm{Mn_{Bi}}$ and $\mathrm{Bi_{Mn}}$ antisites results in spatial fluctuation of local density of states near the Fermi level in $\mathrm{MnBi_2Te_4}$., 6 pages, 4 figures

We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells simulates an axial twist that enables us, in principle, to probe a wide variety of systems ranging from a ribbon Hofstadter geometry to helical DNA chains. We perform an in-depth numerical analysis, using a direct diagonalization of the lattice Hamiltonian to study the electronic spectra and transport properties of the model. We show that such a geometry creates a self-similar multifractal pattern in the energy landscape. The spectral properties are analyzed using the local density of states and a Green's function formalism is employed to obtain the two-terminal transmission probability. With the standard multifractal analysis and the evaluation of inverse participation ratio we show that, the system hosts both critical and extended phase for a slowly varying aperiodic sequence of flux indicating a possible mobility edge. Finally, we report signatures of topological edge modes that are found to be robust against a correlated perturbation given to the nearest neighbor hopping integrals. Our results can be of importance in experiments involving ladder-like quantum networks, realized with cold atoms in an optical trap setup., Comment: 12 pages, 21 figures

We propose a new preconditioner based on the local density of states for computing the self-consistent problem in Kohn–Sham density functional theory. This preconditioner is inexpensive and able to cure the long-range charge sloshing known to hamper convergence in large, inhomogeneous systems such as clusters and surfaces. It is based on a parameter-free and physically motivated approximation to the independent-particle susceptibility operator, appropriate for both metals and insulators. It can be extended to semiconductors by using the macroscopic electronic dielectric constant as a parameter in the model. We test our preconditioner successfully on inhomogeneous systems containing metals, insulators, semiconductors and vacuum.

We theoretically investigate the application of topological plasmon polaritons (TPPs) to temperature sensing for the first time. Based on an analogy of the topological edge states in the Su-Schrieffer-Heeger model, TPPs are realized in a one-dimensional intrinsic indium antimonide (InSb) microsphere chain. The existence of TPPs is demonstrated by analyzing the topology of the photonic band structures and the eigenmode distribution. By exploiting the temperature dependence of the permittivity of InSb in the terahertz range, the resonance frequency of the TPPs can be largely tuned by the temperature. Moreover, it is shown that the temperature sensitivity of the TPP resonance frequency can be as high as $0.0264~\mathrm{THz/K}$ at room temperature, leading to a figure of merit over 150. By calculating the LDOS near the chain, we further demonstrate that the temperature sensitivity of TPPs is experimentally detectable via near-field probing techniques. This sensitivity is robust since TPPs are highly protected modes immune to disorder and can achieve a strong confinement of radiation. We envisage these TPPs can be utilized as promising candidates for robust and enhanced temperature sensing., 6 pages, 4 figures. comments are welcome

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap $\Delta$ and of the critical temperature $T_c$, the ratio $\Delta$/$k_BT_c$ remaining roughly constant. In addition, in most films an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature $T_c$ and the energy gap $\Delta$ starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of a NbN film with scanning tunneling spectroscopy (STS) we show that the inhomogeneous spatial distribution of $\Delta$ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modelling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of $\Delta$ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now., Comment: 11 pages, 4 figures

We identify quantum many-body scars in the transverse field quantum Ising model on a ladder. We make explicit how the corresponding (mid spectrum, low entanglement) many-body eigenstates can be approximated by injecting quasiparticle excitations into an exact, zero-energy eigenstate, which is of valence bond solid type. Next, we present a systematic construction of product states characterized, in the limit of a weak transverse field, by a sharply peaked local density of states. We describe how the construction of these 'peak states' generalizes to arbitrary dimension and we show that on the ladder their number scales with system size as the square of the golden ratio.

Stacking layered materials revealed to be a very powerful method to tailor their electronic properties. It has indeed been theoretically and experimentally shown that twisted bilayers of graphene (tBLG) with a rotation angle $\ensuremath{\theta}$, forming a Moir\'e pattern, confine electrons in a tunable way as a function of $\ensuremath{\theta}$. Here, we study electronic structure and transport in tBLG using tight-binding numerical calculations in commensurate twisted bilayer structures and a pertubative continuous theory, which is valid for not-too-small angles ($\ensuremath{\theta}g\ensuremath{\sim}{2}^{\ensuremath{\circ}}$). These two approaches allow us to understand the effect of $\ensuremath{\theta}$ on the local density of states, the electron lifetime due to disorder, the DC conductivity, and the conductivity quantum correction due to multiple scattering effects. We distinguish the cases where disorder is equally distributed over two layers or only one layer. When only one layer is disordered, diffusion properties depend strongly on $\ensuremath{\theta}$, thus showing the effect of Moir\'e electronic localization at intermediate angles $\ensuremath{\theta}, \ensuremath{\sim}{2}^{\ensuremath{\circ}}l\ensuremath{\theta}l\ensuremath{\sim}{20}^{\ensuremath{\circ}}$.

The boundary Green's function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial superconducting phases with Majorana bound states at their boundaries. We introduce a general method for computing the bGF of spinful multi-channel lattice models for such Majorana nanowires, where the bGF is expressed in terms of the roots of a secular polynomial evaluated in complex momentum space. In many cases, those roots, and thus the bGF, can be accurately described by simple analytical expressions, while otherwise our approach allows for the numerically efficient evaluation of bGFs. We show that from the behavior of the roots, many physical quantities of key interest can be inferred, e.g., the value of bulk topological invariants, the energy dependence of the local density of states, or the spatial decay of subgap excitations. We apply the method to single- and two-channel nanowires of symmetry class D or DIII. In addition, we study the spectral properties of multi-terminal Josephson junctions made out of such Majorana nanowires., Comment: 16 pages, 11 figures

Superconductor-ferromagnetic heterostructures have been suggested as one of the most promising alternatives of realizing odd-frequency superconductivity. In this work we consider the limit of shrinking the ferromagnetic region to the limit of a single impurity embedded in a conventional superconductor, which gives raise to localized Yu-Shiba-Rusinov (YSR) bound states with energies inside the superconducting gap. We demonstrate that all the sufficient ingredients for generating odd-frequency pairing are present at the vicinity of these impurities. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii $SP^{\ast}OT^{\ast} = -1$ rule, being the symmetry under the exchange of spin, spatial, orbital (in our case $O=+1$) and time index, respectively. We study the spatial and frequency dependence of of the possible pairing amplitudes, analyzing their evolution with impurity strength and identifying a reciprocity between different symmetries related through impurity scattering. We show that the odd-frequency spin-triplet pairing amplitude dominates at the critical impurity strength, where the YSR states merge at the middle of the gap, while the even components cancel out close to the impurity. We also show that the spin-polarized local density of states exhibits the same spatial and frequency behavior as the odd-$\omega$ spin-triplet component at the critical impurity strength., Comment: 13 pages, 10 figures

The topological properties of a material's electronic structure are encoded in its Berry curvature, a quantity which is intimately related to the transverse electrical conductivity. In transition metal dichalcogenides with broken inversion symmetry, the nonzero Berry curvature results in a valley Hall effect. In this paper we identify a previously unrecognized consequence of Berry curvature in these materials: an electric field-induced change in the electrons' charge density orientation. We use first principles calculations to show that measurements of the electric field-induced change in the charge density or local density of states in MoS$_2$ can be used to measure its energy-dependent valley and orbital Hall conductivity., Main text: 5 pages, 4 figures. Supp. Info: 10 pages, 7 figures

We study the rectification of near-field radiative heat transfer between two InSb nano-particles due to the presence of non-reciprocal surface modes in a nearby InSb sample when an external magnetic field is applied and its dependence on the magnetic field strength. We reveal the spin-spin coupling mechanism of the localized particle resonances and the surface mode resonances which is substantiated by the directional heat flux in the given setup. We discuss further the interplay of the frequency shift, the propagation length, and local density of states on the strength and directionality of the rectification as well as the non-reciprocal heating effect of the nanoparticles.

Previous works on deformed graphene predict the existence of valley-polarized states, however, optimal conditions for their detection remain challenging. We show that in the quantum Hall regime, edgelike states in strained regions can be isolated in energy within Landau gaps. We identify precise conditions for conducting edgelike states to be valley polarized. By the appropriate design of strain profiles these states can be positioned at chosen locations in the sample. A map of the local density of states as a function of energy and position reveals a unique braid pattern that serves as a fingerprint to identify valley polarization.

As the surface Andreev bound state (ABS) forms at the open ($1,1$) edge of a $d_{x^2-y^2}$-wave superconductor, the local density of states (LDOS) increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study large cluster Hubbard model with an open ($1,1$) edge in the presence of a bulk $d$-wave gap. We calculate the site-dependent spin susceptibility by performing random-phase-approximation (RPA) and modified fluctuation-exchange (FLEX) approximation in the real space. We find that near the ($1,1$) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk $d$-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena., 9 pages, 15 figures