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.
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 find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.
Quantum phase transitions out of equilibrium are outstanding emergent subjects in condensed matter physics with great fundamental importance and challenges. We theoretically investigate here the nonequilibrium quantum phase transition in a generic nano-setup: the pseudogap Kondo model where a Kondo quantum dot couples to two---left (L) and right (R)---voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels ${\ensuremath{\mu}}_{L/R}$, ${\ensuremath{\rho}}_{c,L(R)}(\ensuremath{\omega})\ensuremath{\propto}{|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\mu}}_{L(R)}|}^{r}$ with 0<r<1. In equilibrium (${\ensuremath{\mu}}_{L}\ensuremath{-}{\ensuremath{\mu}}_{R}=0$) and for 0<r<1/2, with increasing Kondo correlations this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo screened phase. At finite bias voltages and near criticality, we discover new nonequilibrium universal scaling behaviors in conductance, conduction electron T matrix, and local spin susceptibility via a controlled frequency-dependent renormalization group (RG) approach. The current-induced decoherence is key to understanding these distinct universal nonequilibrium quantum critical regimes. The relevance of our results to experiment is discussed.
Nonequilibrium properties of correlated quantum matter are being intensively investigated because of the rich interplay between the external drive and the many-body correlations. Of particular interest is the nonequilibrium behavior near a quantum critical point (QCP), where the system is delicately balanced between different ground states. Although such effects are typically out of reach, we meet this challenge, providing here both both an analytical calculation of the nonequilibrium I-V curve when the system is tuned to be critical and experimental results to which the theory is compared. The system is a quantum dot coupled to resistive leads: a spinless resonant level interacting with an ohmic dissipative environment. A two-channel Kondo QCP occurs when the level is on resonance and symmetrically coupled to the leads. Using a bosonized representation, we calculate the nonlinear I-V curve at the critical value of the gate voltage corresponding to this QCP. We then show that it has a physically intuitive interpretation in terms of weak backscattering of non-interacting fermions coupled to a modified environment, thus arriving at the same result through dynamical Coulomb blockade theory. The quantitative agreement between the experimental data and our theory, with no fitting parameter, is remarkable. As our system is fully accessible to both theory and experiment, it provides an ideal setting for addressing nonequilibrium phenomena in correlated quantum matter.
The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization-group approach is applied to compute the nonequilibrium current in the presence of a finite bias voltage V. In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V<T, while it obeys a distinct nonequilibrium profile for V>T. We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].
We study correlated two-level quantum dots, coupled in effective one-channel fashion to metallic leads, with electron interactions including on-level and interlevel Coulomb repulsions, as well as the interorbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics, and electronic transport properties are considered, and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterized by a normal Fermi liquid fixed point (FP) and the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of nonintegral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first-order level-crossing transitions at high symmetry points. A ``Friedel-Luttinger sum rule'' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase, the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.
We theoretically investigate the nonequilibrium current through a quantum dot coupled to one-dimensional electron leads, utilizing a controlled frequency-dependent renormalization group approach. We compute the nonequilibrium conductance for large bias voltages and address the interplay between decoherence, Kondo entanglement, and Luttinger physics. The combined effect of large bias voltage and strong interactions in the leads, known to stabilize two-channel Kondo physics, results in nontrivial modifications in the conductance. Interestingly, these unusual changes in the conductance persist in the presence of a finite channel asymmetry.