Single-channel Quantum Wire Research Articles

Localized states induced by uniaxial strain in graphene quantum dots

The construction of localized states has been one of the hot research topics in recent years. In this paper, an effective method of constructing the localized states (corner state, edge state and domain wall state) in graphene quantum dots is proposed theoretically by using the uniaxial strain effect. The research shows that the distribution characteristics and forms of these localized states are closely related to the uniaxial strain direction. Specifically, the formation of these localized states is mainly attributed to the inconsistent hopping amplitude caused by the uniaxial strain, which makes graphene quantum dots become an extended 2D Su-Schrieffer-Heeger (SSH) model. It must be emphasized that the formation of these local states only requires the effect of strain, and all of them are in the band gap of the system, so they are very easy to be directly observed and used as single-channel quantum wires. Then, we propose a method to analyze the localized states by building a two-dimensional extended SSH model through a one-dimensional SSH chain. The theoretical speculation of our proposed method is highly consistent with the simulated local states phenomenon induced by uniaxial strain applied to the monolayer graphene. This method of constructing the localized states by using uniaxial strain to realize the extended two-dimensional SSH model is not only suitable for electronic crystals like graphene, but also for artificial crystals like photonic crystals and acoustic crystals. Our findings provide a new ideas for circuit design for quantum computing.

Majorana end states in an interacting quantum wire

We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.

Resonant reflection of interacting electrons from an impurity in a quantum wire: Interplay of Zeeman and spin-orbit effects

A single-channel quantum wire with two well-separated Zeeman subbands and in the presence of weak spin-orbit coupling is considered. An impurity level which is split off the upper subband is degenerate with the continuum of the lower subband. We show that, when the Fermi level lies in the vicinity of the impurity level, the transport is completely blocked. This is the manifestation of the effect of resonant reflection and can be viewed as resonant tunneling between left-moving and right-moving electrons via the impurity level. We incorporate electron-electron interactions and study their effect on the shape of the resonant-reflection profile. This profile becomes a two-peak structure, where one peak is caused by resonant reflection itself, while the origin of the other peak is reflection from the Friedel oscillations of the electron density surrounding the impurity.

Interaction induced topological protection in one‐dimensional conductors

We discuss two one‐dimensional model systems – the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder.

Brownian scattering of a spinon in a Luttinger liquid

We consider strongly interacting one-dimensional electron liquids where elementary excitations carry either spin or charge. At small temperatures a spinon created at the bottom of its band scatters off low-energy spin and charge excitations and follows the diffusive motion of a Brownian particle in momentum space. We calculate the mobility characterizing these processes and show that the resulting diffusion coefficient of the spinon is parametrically enhanced at low temperatures compared to that of a mobile impurity in a spinless Luttinger liquid. We briefly discuss that this hints at the relevance of spin in the process of equilibration of strongly interacting one-dimensional electrons, and comment on implications for transport in clean single-channel quantum wires.

Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

Thermalization of Nonequilibrium Electrons in Quantum Wires

We study the problem of energy relaxation in a one-dimensional electron system. The leading thermalization mechanism is due to three-particle collisions. We show that for the case of spinless electrons in a single channel quantum wire the corresponding collision integral can be transformed into an exactly solvable problem. The latter is known as the Schrödinger equation for a quantum particle moving in a Pöschl-Teller potential. The spectrum for the resulting eigenvalue problem allows for bound-state solutions, which can be identified with the zero modes of the collision integral, and a continuum of propagating modes, which are separated by a gap from the bound states. The inverse gap gives the time scale at which counterpropagating electrons thermalize.

Interaction-induced corrections to conductance and thermopower in quantum wires

We study transport properties of weakly interacting spinless electrons in one-dimensional single-channel quantum wires. The effects of interaction manifest as three-particle collisions due to the severe constraints imposed by the conservation laws on the two-body processes. We focus on short wires where the effects of equilibration on the distribution function can be neglected and the collision integral can be treated in perturbation theory. We find that interaction-induced corrections to conductance and thermopower rely on the scattering processes that change the number of right- and left-moving electrons. The latter requires transition at the bottom of the band which is exponentially suppressed at low temperatures. Our theory is based on the scattering approach that is beyond the Luttinger-liquid limit. We emphasize the crucial role of the exchange terms in the three-particle scattering amplitude that was not discussed in previous studies.

Full Counting Statistics of a Luttinger Liquid Conductor

Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the non-interacting leads.

Helical Liquids and Majorana Bound States in Quantum Wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.

Domain Walls in Gapped Graphene

The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support midgap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the midgap band is partially filled, the domain wall can behave like a one-dimensional metal embedded in a semiconductor and could potentially be used as a single-channel quantum wire.

Relaxation processes in a disordered Luttinger liquid

The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in a disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of a strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of a nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be on the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.

Nondispersive backscattering in quantum wires

At a Fano resonance in a quantum wire, there is strong quantum-mechanical backscattering. When identical wave packets are incident along all possible modes of incidence, each wave packet is strongly scattered. The scattered wave packets compensate each other in such a way that the outgoing wave packets are similar to the incoming wave packets. This is as if the wave packets are not scattered and not dispersed. This typically happens for the kink-antikink collision of the sine-Gordon model. As a result of such nondispersive behavior, the derivation of semiclassical formulas, such as the Friedel sum rule and the Wigner delay time, are exact at Fano resonance. For a single-channel quantum wire, this is true for any potential that exhibits a Fano resonance. For a multichannel quantum wire, we give an easy prescription to check for a given potential if this is true. We also show that the validity of the Friedel sum rule may or may not be related to the conservation of charge. If there are evanescent modes, then even when charge is conserved, the Friedel sum rule may break down away from the Fano resonances.

Negativity of the excess noise in a quantum wire capacitively coupled to a gate

The electrical current noise of a quantum wire is expected to increase with increasing applied voltage. We show that this intuition can be wrong. Specifically, we consider a single-channel quantum wire with impurities and with a capacitive coupling to nearby metallic gates and find that its excess noise, defined as the change in the noise caused by the finite voltage, can be negative at zero temperature. This feature is present both for large $(c⪢{c}_{q})$ and small $(c⪡{c}_{q})$ capacitive coupling, where $c$ is the geometrical and ${c}_{q}$ the quantum capacitance of the wire. In particular, for $c⪢{c}_{q}$, negativity of the excess noise can occur at finite frequency when the transmission coefficients are energy dependent---i.e., in the presence of Fabry-P\'erot resonances or band curvature. In the opposite regime $c\ensuremath{\lesssim}{c}_{q}$, a nontrivial voltage dependence of the noise arises even for energy-independent transmission coefficients: at zero frequency the noise decreases with voltage as a power law when $c<{c}_{q}∕3$, while, at finite frequency, regions of negative excess noise are present due to Andreev-type resonances.

Rashba effect in quantum networks

We present a formalism to study quantum networks made up by single-channel quantum wires in the presence of Rashba spin-orbit coupling and magnetic field. In particular, linear transport through one-dimensional and two-dimensional finite-size networks is studied by means of the scattering formalism. In some particular quantum networks, the action of the magnetic field or of the Rashba spin-orbit coupling induces localization of the electron wave function. This phenomenon, which relies on both the quantum-mechanical interference and the geometry of the network, is manifested through the suppression of the conductance for specific values of the spin-orbit-coupling strength or of the magnetic field. Furthermore, the interplay of the Aharonov--Bohm phases and of the non-Abelian phases, introduced by spin-orbit coupling, is discussed in a number of cases.

Transport properties of single-channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.

Friedel sum rule for a single-channel quantum wire

Elastic scattering in a quantum wire has several novel features not seen in one dimension (1D), 2D, or 3D. In this work we consider a single channel quantum wire as its application is inevitable in making devices based on quantum interference effects. We consider a point defect or a single delta function impurity in such a wire and show how some of these novel features affect Friedel-sum-rule (FSR) in a way, that is quite unlike in 1D, 2D, and 3D.

Nonlinear ac transport and local fields in quantum wires

Nonlinear frequency-dependent transport in a single-channel quantum wire with a potential barrier in the presence of electron interaction is investigated. The bosonization method for treating the electron-electron interaction is used. The polarization and tunneling currents are evaluated in the weak tunneling region. Harmonic generation is studied. The corresponding longitudinal and transverse electromagnetic fields are evaluated. The importance of screening and local fields is discussed. It is concluded that apart from the influence of induced external screening currents, local longitudinal field corrections are automatically included if the interaction between electrons is taken into account exactly.

Charge and spin addition energies of a one-dimensional quantum dot

We derive the effective action for a one-dimensional electron island formed between a double barrier in a single-channel quantum wire including the electron spin. Current and energy addition terms corresponding to charge and spin are identified. The influence of the range and the strength of the electron interaction and other system parameters on the charge and spin addition energies and on the excitation spectra of the modes confined within the island is studied. We find by comparison with experiment that spin excitations in addition to nonzero range of the interaction and inhomogeneity effects are important for understanding the electron transport through one-dimensional quantum islands in cleaved-edge-overgrowth systems.

Current bistability and hysteresis in strongly correlated quantum wires

Nonequilibrium transport properties are determined exactly for an adiabatically contacted single-channel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter g, for very strong interactions g less, similar0.2, and sufficiently low temperatures, we find an S-shaped current-voltage relation. The unstable branch with negative differential conductance gives rise to current oscillations and hysteretic effects. These nonperturbative and nonlinear features appear only out of equilibrium.