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arXiv:cond-mat/0002290 · Physical Review Letters

Current Bistability and Hysteresis in Strongly Correlated Quantum Wires

Reinhold Egger, Hermann Grabert, A. Koutouza, Hubert Saleur, F. Siano

Published Apr 17, 2000• 23 citations
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Abstract

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.

DOI
10.1103/physrevlett.84.3682

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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.
The inhomogeneous Tomonaga-Luttinger liquid model describing an interacting quantum wire adiabatically coupled to noninteracting 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 nonmonotonic parameter dependencies of the average current. We discuss oscillations of the nonlinear 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 $\ensuremath{\omega}$ relative to vF∕gL{v}_{F}∕gLvF​∕gL, where vF{v}_{F}vF​ is the Fermi velocity, ggg the Tomonaga-Luttinger interaction parameter, and LLL 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 nonvanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.
We have recently calculated exact nonequilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V/T. The differential-conductance curve as a function of the interaction strength broadens significantly as V/T is increased, and develops a pronounced maximum at a (universal) critical value (eV/kB{\mathit{k}}_{\mathit{B}}kB​T)=7.188 68. . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.
We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage VVV. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with VVV. However, the final current-noise relation is similar to that in the case of a static point impurity.
We (re)consider in this paper the problem of tunnelling through an impurity in a quantum wire with arbitrary Luttinger interaction parameter. By combining the integrable approach developed in the case of quantum Hall edge states with the introduction of radiative boundary conditions to describe the adiabatic coupling to the reservoirs, we are able to obtain the exact equilibrium and non-equilibrium current. One of the most striking features observed is the appearance of negative differential conductances out of equilibrium in the strongly interacting regime g ⩽0.2. In spite of the various charging effects, a remarkable form of duality is still observed. New results on the computation of transport properties in integrable impurity problems are gathered in the appendices. In particular, we prove that the TBA results satisfy a remarkable relation, originally derived using the Keldysh formalism, between the order T 2 correction to the current out of equilibrium and the second derivative of this current at T = 0 with respect to the voltage: this is the first direct link between the TBA approach out of equilibrium and the traditional Keldysh one
Over recent decades, a growing number of systems, many of them quantum critical, have been shown to exhibit non-Fermi-liquid behavior, but a full analytic understanding of such systems out of equilibrium is still lacking. In this paper, we provide a distinct example with broad applications in correlated mesoscopic systems to address this issue---a two-channel Kondo-Luttinger model where a Kondo impurity couples to two voltage-biased interacting electron leads, experimentally realizable in a dissipative quantum dot. Therein, an exotic quantum phase transition has been known to exist since the 1990s from the one-channel to two-channel Kondo ground states by enhancing electron interactions in the leads, but a controlled analytic approach to this quantum critical point has not yet been established due to the breakdown of weak-coupling perturbation theory near this strong-coupling critical point. We present a controlled method to this long-standing problem by mapping the system in the strong-coupling regime to an effective spin-boson-fermion Hamiltonian. Another type of non-Fermi-liquid quantum critical point is discovered with a distinct logarithmic-in-temperature and -voltage dependence in transport. We further obtain an analytical form for the universal differential conductance out of equilibrium near the transition. Our approach can be further generalized to study nonequilibrium physics of other strong-coupling low-dimensional non-Fermi-liquid fixed points. The relevance of our results for recent experiments is discussed.
We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory, we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with the help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special nontrivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear current-voltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies, we also find an enhancement of the linear conductance of the wire to values above the unitary limit G0=2e2∕h{G}_{0}=2{e}^{2}∕hG0​=2e2∕h.