Model Of Noninteracting Electrons Research Articles

Physical entanglement between localized orbitals

The goal of the present work is to guide the development of quantum technologies in the context of fermionic systems. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This demonstrates the significance of the number-parity superselection rule and highlights the relevance of localized few-orbital subsystems for quantum information processing tasks. Then, we explore and quantify the entanglement between localized orbitals in two systems, a tight-binding model of non-interacting electrons and the hydrogen ring. For this, we apply the first closed formula of a faithful entanglement measure, derived in (arXiv:2207.03377) as an extension of the von Neumann entropy to genuinely correlated many-orbital systems. For both systems, long-distance entanglement is found at low and high densities η, whereas for medium densities, , practically only neighboring orbitals are entangled. The Coulomb interaction does not change the entanglement pattern qualitatively except for low and high densities where the entanglement increases as function of the distance between both orbitals.

Nonadiabatic Correction and Adiabatic Criteria of Noninteracting Quantum Dot Systems

We theoretically study nonadiabatic corrections for charge pumping in a noninteracting electron model of a single-level quantum dot. We derive a formula for the velocity limit of parameter driving to realize adiabatic pumping and illustrate its features in the wide-band limit. We discuss the effect of the nonadiabatic corrections in terms of a typical velocity limit, which is defined by averaging the velocity limits on the parameter contour. We also show that the typical velocity limit vanishes when the adiabaticity breakdown occurs in a quantum dot coupled to reservoirs with a band edge.

Extrinsic thermoelectric response of coherent conductors

We investigate the thermoelectric response of a coherent conductor in contact with a scanning probe. Coupling to the probe has the dual effect of allowing for the controlled local injection of heat currents into the system and of inducing interference patterns in the transport coefficients. This is sufficient to generate a multiterminal thermoelectric effect even if the conductor does not effectively break electron-hole symmetry and the tip injects no charge. Considering a simple model for noninteracting electrons, we find a nonlocal thermoelectric response which is modulated by the position of the hot probe tip, and a nonreciprocal longitudinal response which leads to a thermoelectric diode effect. A separate investigation of the effects of dephasing and of quasielastic scattering gives further insights into the different mechanisms involved.

Impurity bound states as detectors of topological band structures revisited

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126 (2015)] has argued, based on theoretical results for a particular class of models, that insulators with topologically trivial and non-trivial band structures in two space dimensions display a qualitatively different response to point-like impurities. Here we present a comprehensive investigation of the impurity response of a large set of models of non-interacting electrons on the honeycomb lattice, driven insulating by either broken inversion, broken time reversal, broken $C_3$, or broken translation symmetry. These cases include Hofstadter bands, strain-induced pseudo-Landau levels and higher-order topological insulators. Our results confirm that for hopping models respecting the lattice symmetries, the response to a single impurity can indeed distinguish between trivial and non-trivial band topology. However, for modulated or inhomogeneous host systems we find that trivial states of matter can display an impurity response akin to that of topologically non-trivial states, and thus the diagnostic fails.

Mobility Edges in One-dimensional Disordered Aharonov-Bohm Rings

We study numerically the localization properties of the eigenstates of a tight-binding Hamiltonian model for noninteracting electrons moving in a one-dimensional disordered ring pierced by an Aharonov-Bohm flux. By analyzing the dependence of the inverse participation ratio on Aharonov-Bohm flux, energy, disorder strength and system size, we find that all states in the ring are delocalized in the weak disorder limit. The states lying deeply in the band tails will undergo a continuous delocalization-localization transition as the disorder strength in the ring sweeps from the weak to the strong disorder regime.

Consistency of local density approximations and quantum corrections for time-dependent quantum systems

ABSTRACT Time-dependent quantum systems are the subject of intense inquiry, in mathematics, science, and engineering, particularly at the atomic and molecular levels. In 1984, Runge and Gross introduced time-dependent density functional theory, a non-interacting electron model, which predicts charge exactly. An exchange-correlation potential is included in the Hamiltonian to enforce this property. We have previously investigated such systems on bounded domains for Kohn–Sham potentials by use of evolution operators and fixed point theorems. In this article, motivated by usage in the physics community, we consider local density approximations (LDA) for building the exchange-correlation potential, as part of a set of quantum corrections. Existence and uniqueness of solutions are established separately within a framework for general quantum corrections, including time-history corrections and ionic Coulomb potentials, in addition to LDA potentials. In summary, we are able to demonstrate a unique weak solution, on an arbitrary time interval, for a general class of quantum corrections, including those typically used in numerical simulations of the model.

The chemical potential and the work function of a metal film on a dielectric substrate

ABSTRACTThe chemical potential and the work function of an aluminium metal film which is in the vacuum (1) and on a dielectric substrate (2) are obtained using the model of non-interacting electrons confined by an asymmetric rectangular potential well. For the first time, these two characteristics are calculated with correct taking into account the electroneutrality condition. As a result, the values of the chemical potential and the work function tend to their bulk values upon increasing the film thickness. The presence of a dielectric substrate leads to a small shift in the values of these characteristics.

Electronic correlation effects on the neutralization of Ga+ scattered by a gold surface

The monotonous increasing with temperature behavior of the neutralization of $\mathrm{Ga}{}^{+}$ scattered by a gold surface plus the nonmagnetic character of the ion induced to disregard the important electronic correlation effects. In this work, we show that contrary to this assumption, the electron-electron interaction in the Ga site is crucial for describing the experimental results. We extend the formalism previously used in the $\mathrm{Sr}{}^{+}$/Au system to include more than one valence orbital in the projectile, which is the case of $\mathrm{Ga}{}^{+}$, where the neutralization occurs to a $p$-type shell. We consider the six possible orbital-spin neutral configurations in a correlated way within the Anderson model. The comparison with the results obtained from a noninteracting electron model allows one to infer how important the many-body effects in the charge exchange between $\mathrm{Ga}{}^{+}$ and the gold surface are. We also found that the proximity of the projectile one-electron energy levels to the substrate Fermi level determines the influence of electronic correlation effects on the neutral fraction and its temperature and velocity dependences.

Spin resonance and spin fluctuations in a quantum wire

This is a review of theoretical works on spin resonance in a quantum wire associated with the spin-orbit interaction. We demonstrate that the spin-orbit induced internal “magnetic field” leads to a narrow spin-flip resonance at low temperatures in the absence of an applied magnetic field. An applied dc magnetic field perpendicular to and small compared with the spin-orbit field enhances the resonance absorption by several orders of magnitude. The component of applied field parallel to the spin-orbit field separates the resonance frequencies of right and left movers and enables a linearly polarized ac electric field to produce a dynamic magnetization as well as electric and spin currents. We start with a simple model of noninteracting electrons and then consider the interaction that is not weak in 1d electron system. We show that electron spin resonance in the spin-orbit field persists in the Luttinger liquid. The interaction produces an additional singularity (cusp) in the spin-flip channel associated with the plasma oscillation. As it was shown earlier by Starykh and his coworkers, the interacting 1d electron system in the external field with sufficiently large parallel component becomes unstable with respect to the appearance of a spin-density wave. This instability suppresses the spin resonance. The observation of the electron spin resonance in a thin wires requires low temperature and high intensity of electromagnetic field in the terahertz diapason. The experiment satisfying these two requirements is possible but rather difficult. An alternative approach that does not require strong ac field is to study two-time correlations of the total spin of the wire with an optical method developed by Crooker and coworkers. We developed theory of such correlations. We prove that the correlation of the total spin component parallel to the internal magnetic field is dominant in systems with the developed spin-density waves but it vanishes in Luttinger liquid. Thus, the measurement of spin correlations is a diagnostic tool to distinguish between the two states of electronic liquid in the quantum wire.

Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in $1/\omega$, with $\omega$ being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.

Quantum theory of electroabsorption in semiconductor nanocrystals.

We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.

Correction to kinetic energy density functional using exactly solvable model

Herein we present an accurate correction to the Thomas–Fermi (TF) approximation for the non-interacting kinetic energy. The correction is derived from an entirely solvable model and not through the application of the truncated gradient expansion. The used approach exploits the comparable nature of the difference between the TF approximation and the non-interacting kinetic energy and its analogue within a model of non-interacting electrons that resembles the actually studied problem. For the atom, the used model is a system of N non-interacting electrons moving independently in the Coulomb field of the nuclear charge. It is shown numerically that this correction enhances the accuracy of the TF approximation for atoms by an order of magnitude.

Resonant scattering induced thermopower in one-dimensional disordered systems

This study analyzes thermoelectric properties of a one-dimensional random conductor which shows localization effects and simultaneously includes resonant scatterers yielding sharp conductance resonances. These sharp features give rise to a distinct behavior of the Seebeck coefficient in finite systems and incorporate the degree of localization as a means to enhance thermoelectric performance, in principle. The model for noninteracting electrons is discussed within the Landauer-B\"uttiker formalism such that analytical treatment is possible for a wide range of properties, if a special averaging scheme is applied. The approximations in the averaging procedure are tested with numerical evaluations showing good qualitative agreement, with some limited quantitative disagreement. The validity of low-temperature Mott's formula is determined and a good approximation is developed for the intermediate temperature range. In both regimes the intricate interplay between Anderson localization due to disorder and conductance resonances of the disorder potential is analyzed.

Surface corrugations influence monolayer graphene electromagnetic response

We consider the corrugated monolayer graphene membrane electromagnetic response in terahertz range. We study the generated in irradiated graphene total current (from both valleys) taking into account for the first time both the synthetic electric fields arising due to the (inevitable) presence in graphene of inherent out-of-plane nanodeformations and the double-valleys energy spectrum of Dirac charge particles. Our approach is based on atomistic quantum mechanics used for the description of (1) the valence π−σ bonds changes generated by activating external periodic electric field and also (2) the mechanism of Dirac electron interaction with this time-dependent perturbation. We consider the problem in the framework of the model of noninteracting Dirac electrons. Assuming surface corrugations not to be very rough we obtain for weak fields the formula for the total current induced in graphene membrane. Our formula describes the curved current paths in the linear in E→ext(t) approximation for the given graphene surface form. We show that the local direction of current paths is determined by the synthetic electric field whose direction may essentially differ from the one of the external field and depends on the local curvature of the graphene membrane. We also demonstrate that valley currents generated by a linearly external field have nonzero elliptic polarization angles depending on the point (x,y). Valley currents are shown to rotate in opposite directions in different valleys. The results obtained below can be applied to the analysis of different devices in terahertz optics and optoelectronics and the imaging experiments at the Dirac point.

Calculation of spectral and Rosseland paths in a plasma with multiply charged ions based on a statistical approach

The semiclassical approach to determine the Fourier components of the electron dipole moment disregarding polarization (noninteracting electron model) is used for analyzing ion oscillator strengths and determining the radiation properties of plasmas consisting of multiply charged ions of heavy elements. The oscillator strength distribution df/dω (proportional to the photoabsorption cross section) is calculated as a function of the degree of ionization and self-similar frequency Ω = ω/Z. It is found that for low degrees of ionization, function df/dω for an ion is close to function df/dω for a neutral atom; upon an increase in the degree of ionization, regions are formed in which df/dω = 0 (transparency windows) and the photoabsorption cross section for high degrees of ionization differs from zero only in small frequency ranges. The resultant distribution of the ion oscillator strengths is used for calculating the polarizability of ions as a function of frequency and the cross section of radiation scattering on ions. For a gold plasma, the absorbance and opacity (both spectral and averaged according to Rosseland and Planck) are calculated. The results of computing the paths and absorption coefficients coincide in order of magnitude with the available data. The effect of scattering on the Rosseland path is estimated.

Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

We study some stationary, dynamical, and spectral properties of a tight-binding Hamiltonian model for noninteracting electrons in a random two-channels ladder with correlated disorder that presents superposed bands of localized and extended states. We compute the participation number, Kubo-Greenwood conductance, Lyapunov exponent, the spread of an initially localized wave packet, as well as the level-spacing statistics in the band of coexisting localized and extended states. All stationary quantities show a metallic character at the coexistence energy band, such as a finite conductance and vanishing Lyapunov exponent. The wave packet exhibits a ballistic spread due to the Bloch-type nature of the extended states. On the other hand, the level-spacing statistics is characterized by a new distribution function which accounts for the superposition of uniformly distributed Bloch-type states and Poissonian-distributed localized states.

Full counting statistics for noninteracting fermions: exact finite-temperature results andgeneralized long-time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensionaltight-binding model of noninteracting electrons are presented at finite temperatures usingan identity recently published by Abanov and Ivanov. A similar idea is used to derive anexplicit expression for the cumulant generating function for a system consisting of twoquasi-one-dimensional leads connected by a quantum dot in the long-time limit,generalizing the Levitov–Lesovik formula for two single-channel leads to systems with anarbitrary number of transverse channels.

Critical exponent for the quantum Hall transition

We report an estimate $\ensuremath{\nu}=2.593$ [2.587,2.598] of the critical exponent of the Chalker-Coddington model of the integer quantum Hall effect that is significantly larger than previous numerical estimates and in disagreement with experiment. This suggests that models of noninteracting electrons cannot explain the critical phenomena of the integer quantum Hall effect.

On the dimensional properties of electron gas

A statistical model of noninteracting electrons is considered. It is assumed that free electrons can possess fractal properties in phase space and form electron gas with an arbitrary degree of degeneracy. Within the framework of the model suggested, expressions for the Fermi energy, concentration, heat capacity, and elec- trical conductivity of the electron gas have been obtained. It has been shown also that a dimensional dependence of the Lorentz number is possible. An expression for the electronic component of the surface tension has been derived.

Statistical, collective, and critical phenomena of classical one-dimensional disordered Wigner lattices

We explore various properties of classical one-dimensional Wigner solids in the presence of weak disorder at $T=0$ in the context of a recently discovered Anderson transition of plasma modes in a random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. Regarding the plasma oscillations, the exact plasmon dispersion relations for the ordered Wigner crystal is derived analytically from the real space equations of motion. The methods introduced for performing the necessary lattice sums can be extended to tight-binding models of noninteracting electrons with power law hopping. We also discuss other quantities that follow from plasma oscillations such as the multifractal eigenfunctions, the compressibility of the electrons, and the ac conductivity.