Noninteracting Electrons Research Articles

Supersymmetry with self-consistent Schrödinger–Poisson equations: finding partner potentials and breaking symmetry

It is shown that isospectral Hamiltonians and partner potentials can be found for self-consistent solutions of the Schrödinger and Poisson equations in the presence of identical non-interacting electrons. Perturbation of these systems by an external electric field can be used to break symmetry and spectrally distinguish between states. For a given pair of partner potentials, symmetry may also be broken by a change of electron density or temperature.

The influence of corrugations on spin polarization in magnetic field

Noninteracting electrons confined to a corrugated surface are considered in the presence of magnetic field, and the effective Pauli equation is given in the thin-layer quantization formalism. We find that the Zeeman splitting gaps are considerably affected by the corrugations. Furthermore, the spin transport on the corrugated surface is numerically calculated for GaAs material by transfer matrix method. And we find that the spin polarization is substantially influenced by the corrugations when the incident energy takes small values. As a potential application, the corrugations can be used to design a spin transistor with small incident energy.

Gutzwiller hybrid quantum-classical computing approach for correlated materials

Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chemistry, physics and material science. Proof-of-principle quantum chemistry simulations for small molecules have been demonstrated on NISQ devices. While several approaches have been theoretically proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with non-interacting conduction electrons. Our simulation results quantitatively reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.

Bound states and energy shifts resulting from corrugations

In the thin-layer quantization formalism, we give the effective Hamiltonian describing the noninteracting electron confined to the corrugated torus. In the presence of the geometric potential, we find that the low-energy part of the electron energy spectrum strongly depends on the corrugations of torus. Specifically, the bound states and the energy shifts both result from the geometry of the corrugated torus. Moreover, the eigenstates probability density distributions can be reconstructed by designing the corrugations, to predominantly localize the electron at the peaks and valleys of corrugations on the torus.

Analytical approximations of single-electron device current through non-interacting quantum dot

Abstract The electron transport through single electron transistor (SET) consisting of quantum dot (QD) coupled to two metallic electrodes has been studied by employing the non-equilibrium Green function (NEGF) technique. The QD considered in this study has a single energy level and non-interacting electrons. The current-voltage characteristics of QD has been studied by using Meir-Wingreen expression. In this paper, an analytical approximation of Meir-Wingreen formula has been presented with respect to the following conditions: (1) low-temperature limit, (2) finite temperature limit with finite energy | e − e d | k T , (3) finite temperature limit with finite bias Γ e | V | / 2 K T e d , and at high temperatures. Furthermore, the derived analytical formulae are employed to investigate the effect of device parameters (energy level, tunneling rate “level width”, gate voltage, and temperature) on the current-voltage characteristic of SET.

Noninteracting electrons in a prototypical one-dimensional sinusoidal potential

A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy, periodic with the lattice, contains the first reciprocal lattice vector G1=2π/a, where a is the lattice constant. The time-independent Schrödinger equation can be written in reduced variables as a Mathieu equation for which numerically exact solutions for the band structure and wave functions are obtained. The band structure has band gaps that increase with increasing amplitude q of the cosine potential. In the extended-zone scheme, the energy gaps decrease with increasing index n of the Brillouin-zone boundary ka=nπ, where k is the crystal momentum of the electron. The wave functions of the band electron are derived for various combinations of k and q as complex combinations of the real Mathieu functions with even and odd parity, and the normalization factor is discussed. The wave functions at the bottoms and tops of the bands are found to be real or imaginary, respectively, corresponding to standing waves at these energies. Irrespective of the wave vector k within the first Brillouin zone, the electron probability density is found to be periodic with the lattice. The Fourier components of the wave functions are derived versus q, which reveal multiple reciprocal-lattice-vector components with variable amplitudes in the wave functions unless q = 0. The magnitudes of the Fourier components are found to decrease exponentially as a power of n for n∼3 to 45 for ka=π/2 and q = 2, and a precise fit is obtained to the data. The probability densities and probability currents obtained from the wave functions are also discussed. The probability currents are found to be zero for crystal momenta at the tops and bottoms of the energy bands, because the wave functions for these crystal momenta are standing waves. Finally, the band structure is calculated from the central equation and compared to the numerically exact band structure.

Ionized impurity scattering in quantum wells and quantum wires

Low-field mobility for scattering of electrons by ionized impurities is calculated in quantum wells and quantum wires. Analytical expressions for mobility are obtained on the basis of the quantum-kinetic approach using the quantum mechanical formalism of the dielectric function for non-interacting and interacting electrons. If the kinetic energy of electrons is much higher than their inter-particle potential energy, the electron system remains qualitatively similar to a non-interacting electron gas. The Lindhard dielectric function is used to calculate the mobility and screening factor of non-interacting electrons. If the potential energy of electrons is close to or prevails over their kinetic energy, the electron system displays a collective behavior similar to an electron liquid. In this case, electrons are considered interacting. To calculate the mobility of the interacting electrons, we have used the static local-field correction factor to the electron dielectric function. Analytical dependences of the electron mobility on dimensionality of the electron system, sizes of the quantum structures in the confining directions, temperature, forms of confining potential, electron density, and material parameters are obtained. The quantum confinement is modeled by triangular and rectangular confining potentials. The results of calculations are compared with the known experimental data.

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for non-interacting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topologicalinsulators (3DFOTIs), DMs and AIs. At a weak disorder when the on-site random potential of strength $W$ is below a low critical value $W_{c1}$ at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of $e^2/h$ through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder $W_{c2}$, and the system is a disordered 3DFOTI in a lower intermediate disorder between $W_{c1}$ and $W_{c2}$ in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between $W_{c2}$ and $W_{c3}$ above which the states at the Fermi level are localized. It undergoes a normal three-dimension metal-to-insulator transition at $W_{c3}$ and becomes the conventional AI for $W>W_{c3}$. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.

Driven-dissipative quantum mechanics on a lattice: Simulating a fermionic reservoir on a quantum computer

The driven-dissipative many-body problem remains one of the most challenging unsolved problems in quantum mechanics. The advent of quantum computers may provide a unique platform for efficiently simulating such driven-dissipative systems. But, there are many choices for how one can engineer the reservoir. One can simply employ ancilla qubits to act as a reservoir and then digitally simulate them via algorithmic cooling. A more attractive approach, which allows one to simulate an infinite reservoir, is to integrate out the bath degrees of freedom and describe the driven-dissipative system via a master equation, that can also be simulated on a quantum computer. In this work, we consider the particular case of noninteracting electrons on a lattice driven by an electric field and coupled to a fermionic thermostat. Then, we provide two different quantum circuits: the first one reconstructs the full dynamics of the system using Trotter steps, while the second one dissipatively prepares the final nonequilibrium steady state in a single step. We run both circuits on the IBM quantum experience. For circuit (i), we achieved up to five Trotter steps. When partial resets become available on quantum computers, we expect that the maximum simulation time can be significantly increased. The methods developed here suggest generalizations that can be applied to simulating interacting driven-dissipative systems.

Self-equilibration theorem in quantum-point contacts of interacting electrons: Time-dependent quantum fluctuations of tunnel transport beyond the Levitov–Lesovik scattering approach

Equilibration to the steady state for a wide class of Luttinger liquid ballistic weakly linked tunnel contacts is extensively studied. Quantum fluctuations of tunnel current are considered in all orders in tunnel coupling and out of the equilibrium in the time domain. Especially, two important mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration (SE-)lemma on the exact re-exponentiation of thermal average from the Keldysh-contour-ordered evolution operator for arbitrary weakly linked Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem and SE-lemma represents first evidence of a novel emergent phenomenon of ”self-equilibration” in the dynamics of quantum fluctuations of electron transport through ballistic tunnel junctions. This phenomenon and all related real-time full counting statistics are shown to be much more general as compared to the usual Levitov–Lesovik scattering approach for the non-interacting electrons, though SE-theorem also contains known results obtained within the Levitov–Lesovik scattering approach as corresponding limiting case for lowest order cumulants at g=1. As the result, corresponding differential equation of ”self-equilibration” for time-dependent Keldysh partition function of tunnel contact is derived and explained. It is shown that proven SE-theorem can be considered also as the dynamical version of well-known Jarzynski equality for the tunnel electron transport out of the equilibrium. As the result, for arbitrary weakly linked tunnel junction model of interest the exact time-dependent cumulant generating functional is derived being valid at arbitrary electron–electron repulsion in the Luttinger liquid leads of the junction, arbitrary temperature and arbitrary bias voltage. Respective general formula in its long-time asymptote turns into a non-perturbative Luttinger liquid generalization of the Levitov–Lesovik type of detailed balance formula for cumulant generating function. As the consequence of obtained results, a universal character of self-equilibration of tunnel current in one-dimensional weakly linked tunnel junctions is revealed and studied on the level of non-equilibrium Fano factor. As well, a new measure of disequilibrium in such systems – the ”steady flow” rate – is also introduced and discussed.

Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

Berry phase for a Bose gas on a one-dimensional ring

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(\phi)=g \delta(\phi-\phi_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\Delta q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\Delta q/\hbar \oint \mathbf{A}\cdot d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly-interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems.

Decoherence of charge density waves in beam splitters for interacting quantum wires

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-dependent expectation values of the charge density as well as the density-density correlation functions. In general a single incoming charge density wave packet will split into four outgoing wave packets with transmission and reflection coefficients depending on the strengths of the tunnelling processes between the wires at the junction. We find that when multiple charge density wave packets from different directions pass through the intersection at the same time, reflection and splitting of the packets depend on the relative phases of the waves. Active use of this phase-dependent splitting of wave packets may make Luttinger interferometry possible. We also find that coherent incident packets generally suffer partial decoherence from the intersection, with some of their initially coherent signal being transferred into correlated quantum noise. In an extreme case four incident coherent wave packets can be transformed entirely into density-density correlations, with the charge density itself having zero expectation value everywhere in the final state.

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.

Exact solutions of a model for synthetic anyons in a noninteracting system

Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting electrons in two-dimensions (2D), in a uniform magnetic field, where the probes are external solenoids with a magnetic flux that is a fraction of the flux quantum. The Hamiltonian could also be implemented in an ultracold (fermionic) atomic gas in 2D, in a uniform synthetic magnetic field, where the probes are lasers giving rise to synthetic solenoid gauge potentials. We find analytically and numerically the ground state of this system when only the lowest Landau level states are occupied. It is shown that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules of synthetic anyons are discussed for different microscopic realizations of the fusion process.

Magnetotransport in fractal network with loop sub-structures: Anisotropic effect and delocalization

We make an in-depth analysis of electronic transport and localization properties of non-interacting electrons in a Sierpinski gasket (SPG) fractal lattice in presence of magnetic field within a tight-binding framework. Unlike conventional symmetric systems, asymmetric SPG triangle leads to more conducting behavior, and thus delocalization of energy states, which we examine by calculating magnetic flux driven circular current and inverse participation ratio. The spectral peculiarity, that is the gapped nature of energy spectrum in fractal lattices, is clearly reflected from the variation of current with electron filling, yielding possibilities of getting filling dependent switching action. The effect of temperature is also discussed. Our analysis can be utilized to study magnetotransport properties in any other fractal lattices having loop sub-structures.

An investigation of pre-crystalline order, ruling out Pauli crystals and introducing Pauli anti-crystals

Fluid states of matter can locally exhibit characteristics of the onset of crystalline order. Traditionally this has been theoretically investigated using multipoint correlation functions. However new measurement techniques now allow multiparticle configurations of cold atomic systems to be observed directly. This has led to a search for new techniques to characterize the configurations that are likely to be observed. One of these techniques is the configuration density (CD), which has been used to argue for the formation of “Pauli crystals” by non-interacting electrons in e.g. a harmonic trap. We show here that such Pauli crystals do not exist, but that other other interesting spatial structures can occur in the form of an “anti-Crystal”, where the fermions preferentially avoid a lattice of positions surrounding any given fermion. Further, we show that configuration densities must be treated with great care as naive application can lead to the identification of crystalline structures which are artifacts of the method and of no physical significance. We analyze the failure of the CD and suggest methods that might be more suitable for characterizing multiparticle correlations which may signal the onset of crystalline order. In particular, we introduce neighbour counting statistics (NCS), which is the full counting statistics of the particle number in a neighborhood of a given particle. We test this on two dimensional systems with emerging triangular and square crystal structures.

Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation.

We resolve a fundamental issue associated with the conventional Kohn-Sham formulation of real-time time-dependent density functional theory. We show that unphysical multielectron excitations, generated during time propagation of the Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals and their occupations, result in incorrect electron density and, therefore, wrong predictions of physical properties. A new formulation is proposed in that the number of Kohn-Sham orbitals and their occupations are updated on the fly, the unphysical multielectron excitations are removed, and the correct electron density is determined. The correctness of the new formulation is demonstrated by simulations of Rabi oscillation, as analytical results are available for comparison in the case of noninteracting electrons.

Timescale separation solution of the Kadanoff-Baym equations for quantum transport in time-dependent fields

The interaction with time-dependent external fields, especially the interplay between time-dependent driving and quantum correlations, changes the familiar picture of electron transport through nanoscale systems. Although the exact solution of the problem of AC quantum transport of noninteracting electrons has been known for more than two decades, the treatment of correlated particles presents a significant theoretical challenge. In this paper, using the perturbative separation of fast electron tunnelling and slow driving time-scales, we developed a practical approach for time-dependent quantum transport with nonequilibrium Green's functions. The fast electronic dynamics is associated with relative time whilst the slow driving is related to the central time in the Green's functions. The ratio of characteristic electron tunneling time over the period of harmonic driving is used as a small parameter in the theory to obtain a convergent time-derivative expansions of the Green's functions. This enables the algebraic solution of the Kadanoff-Baym equations in Wigner space. Consequently, we produced analytical expressions for dynamical corrections to advanced, retarded, and lesser Green's functions, as well as an improved expression for AC electric current. The method developed is applicable to the general case of multi-channel electron transport through a correlated central region. The theory is applied to different transport scenarios: time-dependent transport through a driven single-resonant level is compared to exact results; and electron transport through a molecular junction described by the Holstein model with a time-oscillating voltage bias is also investigated.

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.