Local Density Of States Research Articles

TBPLaS: A tight-binding package for large-scale simulation

TBPLaS is an open-source software package for the accurate simulation of physical systems with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an intuitive object-oriented Python application interface (API) and Cython/Fortran extensions for the performance-critical parts, ensuring both flexibility and efficiency. Under the hood, numerical calculations are mainly performed by both exact diagonalization and the tight-binding propagation method (TBPM) without diagonalization. Especially, the TBPM is based on the numerical solution of the time-dependent Schrödinger equation, achieving linear scaling with system size in both memory and CPU costs. Consequently, TBPLaS provides a numerically cheap approach to calculate the electronic, optical, plasmon and transport properties of large tight-binding models with billions of atomic orbitals. Current capabilities of TBPLaS include the calculations of band structure, density of states, local density of states, quasi-eigenstates, optical conductivity, electrical conductivity, Hall conductivity, polarization function, dielectric function, plasmon dispersion, carrier mobility and velocity, localization length and free path, Z2 topological invariant, wave-packet propagation, etc. All the properties can be obtained with only a few lines of code. Other algorithms involving tight-binding Hamiltonians can be implemented easily due to the extensible and modular nature of the code. In this paper, we discuss the theoretical framework, implementation details and common workflow of TBPLaS, and give a few demonstrations of its applications. Program summaryProgram Title:TBPLaSCPC Library link to program files:https://doi.org/10.17632/5cjmzj9jwm.1Code Ocean capsule:https://codeocean.com/capsule/8296734Licensing provisions: BSD 3-clauseProgramming language: Python, Cython, FortranNature of problem: The TB method is a powerful tool for investigating the electronic structures and many other properties in condensed matter physics. However, the costs of memory and CPU time using standard diagonalization-based TB techniques scale as O(N2) and O(N3) with the model size N, severely limiting their applications in large complex systems. The development of numerical methods to solve TB problems without any diagonalization, as well as the implementation of these techniques in software packages, are urgently needed to promote the capability of TB methods to large systems with billions of atoms.Solution method: We proposed the TBPM and implemented it in the TBPLaS package. In TBPM, the electronic properties of a TB model are calculated numerically by solving the time-dependent Schrödinger equation without any diagonalization, which ensures a linear scaling of both memory and CPU costs with the system size. Models with billions of atoms (orbitals) can be easily handled, with many properties available from the evolution of time-dependent correlation functions. The TBPLaS package features an intuitive object-oriented Python API and Cython/Fortran extensions for performance-critical parts, ensuring both flexibility and efficiency. Moreover, TBPLaS implements hybrid MPI+OpenMP parallelism, which can exploit the modern hardware of high-performance computers.

Efficient Spin‐Direction Coupling between Circular Polarized Electric and Magnetic Dipoles and Photonic Modes

AbstractIntegrated single photon sources are essential elements in quantum computing, simulation, communication, and photonic neural networks. The directional radiation and scattering of single‐photon sources play a crucial role in light manipulation and rely on electric and magnetic dipole moments. Although clever physical insights and designer intuition strategies have been successfully applied in the development of integrated sources, inverse strategies could enhance and maximize its performance. Recently, topology‐optimized couplers for on‐chip single‐photon sources are designed to efficiently couple a guided mode and an electric dipole. However, the superposition of orthogonal electric and magnetic dipoles can also be harnessed due to the additional degrees of freedom via their interference. Here, the authors have extended the strategy to couplers that enhance spin‐direction coupling of circularly polarized, Huygens, and Janus dipoles. The authors demonstrate that optimization not only increases the coupling to a desire mode but also enhances the electric and magnetic local density of states (LDOS) while maintaining the amplitude and phase relation between the orthogonal dipoles for unidirectional coupling. Currently, coupling efficiency and enhanced LDOS of up to 88%, 94%, and 93% and up to 9.4, 18.6, and 14.9 are obtained for these dipoles. The topology optimization improves the performances of 3D integrated photonic devices.

Tomographic Reconstruction of Quasistatic Surface Polariton Fields.

We theoretically investigate the tomographic reconstruction of the three-dimensional photonic environment of nanoparticles. As input for our reconstruction we use electron energy loss spectroscopy (EELS) maps for different rotation angles. We perform the tomographic reconstruction of surface polariton fields for smooth and rough nanorods and compare the reconstructed and simulated photonic local density of states, which are shown to be in very good agreement. Using these results, we critically examine the potential of our tomography scheme and discuss limitations and directions for future developments.

On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement.

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.

Tunable valley filtering in dynamically strained α−T3 lattices

Mechanical deformations in $\alpha$-$\mathcal{T}_3$ lattices induce local pseudomagnetic fields of opposite directionality for different valleys. When this strain is equipped with a dynamical drive, it generates a complementary valley-asymmetric pseudoelectric field which is expected to accelerate electrons. We propose that by combining these effects by a time-dependent nonuniform strain, tunable valley filtering devices can be engineered that extend beyond the static capabilities. We demonstrate this by implementing an oscillating Gaussian bump centered in a four-terminal Hall bar $\alpha$-$\mathcal{T}_3$ setup and calculating the induced pseudoelectromagnetic fields analytically. Within a recursive Floquet Green-function scheme, we determine the time-averaged transmission and valley polarization, as well as the spatial distributions of the local density of states and current density. As a result of the periodic drive, we detect novel energy regimes with highly valley-polarized transmission, depending on $\alpha$. Analyzing the spatial profiles of the time-averaged local density of states and current density we can relate these regimes to the pseudoelectromagnetic fields in the setup.By means of the driving frequency, we can manipulate the valley-polarized states, which might be advantageous for future device applications.

Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties

The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random graphs with an arbitrary degree distribution in the high-connectivity limit, from which we perform a thorough analysis of the impact of degree fluctuations on the spectral density, the inverse participation ratio, and the distribution of the local density of states (LDOSs). For random graphs with a negative binomial degree distribution, we show that all eigenvectors are extended and that the spectral density exhibits a logarithmic or a power-law divergence when the variance of the degree distribution is large enough. We elucidate this singular behaviour by showing that the distribution of the LDOSs at the centre of the spectrum displays a power-law tail controlled by the variance of the degree distribution. In the regime of weak degree fluctuations the spectral density has a finite support, which promotes the stability of large complex systems on random graphs.

Modeling of Gold Adsorption by the Surface of Defect Graphene

The results of the theoretical investigation of the local structural changes and adsorption characteristics of the graphene (GP) surface in the presence of a vacancy + Auads adatom complex are presented. Based on the density functional theory (DFT), the adsorption properties of Auads at the surface of GP supercells containing 50 carbon atoms with vacancies ({text{GP}}leftlangle {{text{A}}{{{text{u}}}_{{{text{ads}}}}}} rightrangle ,{text{ G}}{{{text{P}}}_{{text{V}}}}leftlangle {{text{A}}{{{text{u}}}_{{{text{ads}}}}}} rightrangle ) are calculated. The most stable configuration of {text{G}}{{{text{P}}}_{{text{V}}}}leftlangle {{text{A}}{{{text{u}}}_{{{text{ads}}}}}} rightrangle supercells with a vacancy + Auads adatom complex is determined. The effect that an Auads adatom has on the band structure and local magnetic moment in {text{G}}{{{text{P}}}_{{text{V}}}}leftlangle {{text{A}}{{{text{u}}}_{{{text{ads}}}}}} rightrangle is calculated. The data are analyzed based on the equilibrium atomic configuration {text{G}}{{{text{P}}}_{{text{V}}}}leftlangle {{text{A}}{{{text{u}}}_{{{text{ads}}}}}} rightrangle , local density of electronic states, and spin polarization. The calculations are made using the exchange-correlation functional in a local electron-spin density approximation (LSDA).

Nitrogen tuned crystal structure, optical band gap, localized states on amorphous and crystalline GeTe films

The nitrogen (N) doping effect on crystal structure, optical band gap, and localized states for amorphous/crystalline GeTe films was studied. The crystallization temperature and sheet resistance were improved by N doping. The local bonding structure of amorphous and crystalline N x ( GeTe ) 1 - x was elucidated by Raman spectra. The changes in optical band gap and localized states density for the films were evaluated by transmittance spectra. The band gap broadening after N doping is crucial to reducing the threshold current for phase change memory.

RKKY interaction on curved surfaces: Different behavior of Dirac and Schrödinger carriers as interaction-mediating particles

The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved systems and for two types of Schr\"{o}dinger and Dirac carriers, the RKKY interaction and local density of states (LDOS) are calculated. Results show that the strength of the RKKY interaction on a curved surface depends significantly on the nature of particles embedded on this surface, indicating that the geometry has a different effect on the dynamics of Schr\"{o}dinger and Dirac carriers. While the curved surface increases the RKKY interaction strength for Schr\"{o}dinger-type carriers in comparison with the flat sample, RKKY interaction decreases in the curved surface for Dirac-type particles. This can be understood regrading the effective magnetic field experienced by the Dirac particles as a result of the curved surface. There is also a correlation between LDOS and the RKKY interaction, which could be explained by the effect of conducting electrons density on the exchange interaction mediated by these carriers.

Bamboo-like Vortex Chains Confined in Canals with Suppressed Superconductivity and Standing Waves of Quasiparticles.

The vortex core can be regarded as a nanoscale confined system for quasiparticles in a type-II superconductor. It is very interesting to investigate the interplay between the vortex core and other microscopic quantum confined systems. We observe band-like canals with the width of about 15 nm on the surface of KCa2(Fe1-xNix)4As4F2 (x = 0.05) by scanning tunneling microscopy. Some canals suppress superconductivity and confine parallel standing waves due to the quasiparticle interference. Upon magnetic fields being applied, some elongated vortices are formed within canals showing bamboo-like one-dimensional vortex chains. Interestingly, the confined vortex cores are elongated roughly along the perpendicular direction of canals, and the local density of states at positive and negative energies shows an in-phase oscillation at zero field; but, it becomes out-of-phase crossing the vortex cores. Our work reveals a new type of vortex patterns in confined canals and its interplay with the quasiparticle interference.

Unravelling Disorder Effects on Thermoelectric Properties of Semicrystalline Polymers in a Wide Range of Doping Levels.

Thermoelectric (TE) performance of a specific semicrystalline polymer is studied experimentally only in a limited range of doping levels with molecular doping methods. The doping level is finely controlled via in situ electrochemical doping in a wide range of carrier concentrations with an electrolyte ([PMIM]+ [TFSI]- )-gated organic electrochemical transistor system. Then, the charge generation/transport and TE properties of four p-type semicrystalline polymers are analyzed and their dynamic changes of crystalline morphologies and local density of states (DOS) during electrochemical doping are compared. These polymers are synthesized based on poly[(2,5-bis(2-alkyloxy)phenylene)-alt-(5,6-difluoro-4,7-di(thiophene-2-yl)benzo[c][1,2,5]thiadiazole)] by varying side chains: With oligoethylene glycol (OEG) substituents, facile p-doping is achieved because of easy penetration of TFSI- ions into the polymer matrix. However, the charge transport is hindered with longer OEG chains length because of the enhanced insulation. Therefore, with the shortest OEG substituents the electrical conductivity (30.1 S cm-1 ) and power factor (2.88 µW m-1 K-2 ) are optimized. It is observed that all polymers exhibit p- to n-type transition in Seebeck coefficients in heavily doped states, which can be achieved by electrochemical doping. These TE behaviors are interpreted based on the relation between the localized DOS band structure and molecular packing structure during electrochemical doping.

Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands

We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors.

Maximum electromagnetic local density of states via material structuring

Abstract The electromagnetic local density of states (LDOS) is crucial to many aspects of photonics engineering, from enhancing emission of photon sources to radiative heat transfer and photovoltaics. We present a framework for evaluating upper bounds on the LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects. The bounds are solely determined by the bandwidth, material susceptibility, and device footprint, with no assumptions on geometry. We derive an analytical expression for the maximum LDOS consistent with the conservation of energy across the entire design domain, which upon benchmarking with topology-optimized structures is shown to be nearly tight for large devices. Novel scaling laws for maximum LDOS enhancement are found: the bounds saturate to a finite value with increasing susceptibility and scale as the quartic root of the bandwidth for semi-infinite structures made of lossy materials, with direct implications on material selection and design applications.

Andreev reflection mediated by Majorana zero modes in T-shaped double quantum dots

We theoretically study the Andreev reflection processes in T-shaped double quantum dots (TDQDs) in terms of the nonequilibrium Green’s function technique. It is considered that one of the TDQDs is coupled to the Majorana zero modes (MZMs) prepared at the ends of a topological superconductor nanowire and simultaneously to one metallic and one superconductor lead. Our numerical results show that the in-gap state originated from the proximity effect due to the superconductor lead being sensitive to the existence of MZMs. The local density of states (LDOS) of the spin-up electrons, which are directly coupled to the MZMs, has a Fano antiresonance at the in-gap state. Meanwhile, the local density of the spin-down electrons, which are free from hybridization to the MZMs due to the helical property of the latter, has a Lorentzian resonance at the same state. The differential Andreev conductance of both the spin directions exhibits Fano-type resonance but with different tails’ directions. The in-gap state is also significantly influenced by the energy level and coupling strength of the other side-coupled dot, as well as the MZM–MZM interaction.

Emergence and manipulation of non-equilibrium Yu-Shiba-Rusinov states

The experimental advances in the study of time-dependent phenomena has opened a new path to investigating the complex electronic structure of strongly correlated and topological materials. Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities in s-wave superconductors provide an ideal candidate system to study the response of a system to time-dependent manipulations of the magnetic environment. Here, we show that by imposing a time-dependent change in the magnetic exchange coupling, by changing the relative alignment of magnetic moments in an impurity dimer, or through a periodic drive of the impurity moment, one can tune the system through a time-dependent quantum phase transition, in which the system undergoes a transition from a singlet to a doublet ground state. We show that the electronic response of the system to external perturbations can be imaged through the time-dependent differential conductance, dI(t)/dV, which, in analogy to the equilibrium case, is proportional to a non-equilibrium local density of states. Our results open the path to visualizing the response of complex quantum systems to time-dependent external perturbations.

Resonance energy transfer near higher-order exceptional points of non-Hermitian Hamiltonians

Exceptional points (EPs) of both eigenvalue and eigenvector degeneracy offer remarkable properties of the non-Hermitian systems based on the Jordanian form of Hamiltonians at EPs. Here we propose the perturbation theory able to underpin the physics in the vicinity of the higher-order EPs. The perturbation theory unveils lifting of degeneracy and origin of the different phases merging at the EP. It allows us to analyze the photonic local density of states and resonance energy transfer, determining their spectral behaviors in a general form. Resonant energy transfer is investigated in analytical and numerical examples. We analytically find the resonance energy transfer rate near the third-order EP occurring in the system of three coupled cavities and reveal singularities caused by the interplay of the perturbation and frequency detuning from degenerate eigenfrequency. Numerical simulation of the coupled-resonator system reveals the vital role of a mirror for switching to the EP of the doubled order and corresponding enhancement of the resonance energy transfer rate. Our investigation sheds light on the behavior of nanophotonic systems in non-Hermitian environments.

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation

We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a 1D bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the non-interacting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spin-like for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection we find that these edge excitations are quasiparticle-like as long as they remain within the bulk gap. Above a critical interaction strength of $U_c\approx 5 t$ these quasiparticles on the boundary loose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the non-trivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

Rotationally Symmetrical Spoof-Plasmon Antenna for Polarization-Independent Radiation Enhancement

Plasmon antennas allow subwavelength confinement and enhancement of electromagnetic fields at the ``hotspot'' where the radiation efficiency of emitters can be substantially enhanced. Such enhancement, however, is often polarization dependent. Consequently, the radiation behaviors (e.g., radiation pattern and polarization states) of the emitter placed at the hotspot are also modified significantly. Enhancing the radiation efficiency without altering the original radiation pattern and polarization state of the emitter is highly desired for many sought-after applications involving chiral emitters but remains a challenging task, especially at low frequencies. To this end, spoof-plasmon antennas with fourfold and sixfold rotational symmetries are designed and realized experimentally. These plasmon antennas support polarization-independent localized plasmon resonances, which can significantly enhance the local density of photonic states at the structural center without changing the polarization state of the emitter. As a typical example, the structure with sixfold rotational symmetry is coupled with a half-wave dipole antenna. The measurement results show that the far-field radiation pattern of the dipole antenna is maintained with the radiation efficiency enhanced by more than 2 orders of magnitude, irrespective of the dipole orientation.

Multifunctional 2D g-C4N3/MoS2 vdW Heterostructure-Based Nanodevices: Spin Filtering and Gas Sensing Properties.

Two-dimensional (2D) magnetic materials are the key to the development of the new generation in spintronics technology and engineering multifunctional devices. Herein, the electronic, spin-resolved transmission, and gas sensing properties of the 2D g-C4N3/MoS2 van der Waals (vdW) heterostructure have been investigated by using density functional theory with non-equilibrium Green's function method. First, the g-C4N3/MoS2 vdW heterostructure demonstrates ferromagnetic half-metallicity and superior adsorption capacity for gas molecules. The spin-dependent electronic transport of the g-C4N3/MoS2-based nanodevice is obviously regulated by parallel or anti-parallel spin configuration in electrodes, leading to perfect single-spin conduction behavior with a nearly 100% spin filtering efficiency, a negative differential resistance effect, and other interesting electrical transport phenomena. Moreover, g-C4N3/MoS2 exhibits directional dependency and strong transport anisotropic behavior under bias windows, indicating that the electric current propagates more easily through the vertical direction than the horizontal direction. The physical mechanisms are revealed and analyzed by presenting the bias-dependent transmission spectra in combination with the projected local device density of states. Finally, the g-C4N3/MoS2-based gas sensor is more sensitive to CO, NO, NO2, and NH3 molecules with the chemisorption type. The strong chemical adsorption leads to the formation of electrons on the local scattering center and ultimately affects the transport properties, resulting in the maximum gas sensitivity reaching 6.45 for NO at the bias of 0.8 V. This work not only reveals that the g-C4N3/MoS2 vdW heterostructure with high anisotropy, perfect spin filtering, and outstanding gas sensitivity is a promising 2D material but also provides an insight into the further application in futuristic electronic nanodevices.

Anomalous spontaneous emission dynamics at chiral exceptional points.

An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.