Nonequilibrium finite-frequency noise of a resonance-level quantum dot close to a dissipative quantum phase transition: Functional Renormalization Group approaches
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.
The dynamical decoherence rate and charge susceptibility of a nonequilibrium quantum dot close to a dissipative quantum phase transition are calculated. The setup concerns a resonance-level quantum dot coupled to two spinless fermionic baths with a finite bias voltage and an ohmic bosonic bath representing a dissipative environment. The system is equivalent to an anisotropic Kondo model. As dissipation strength increases, the system at zero temperature and zero bias exhibits a quantum phase transition of the Kosterlitz-Thouless (KT) type between a conducting delocalized phase and an insulating localized phase. Within the nonequilibrium frequency-dependent renormalization group (RG) approach, the finite bias crossover in dynamical decoherence rate and charge susceptibility close to the transition are addressed. The dynamical decoherence rate is found to increase with increasing frequency. In the delocalized phase, it shows a singularity at frequencies equal to positive or negative bias voltage. As the system cross overs to the localized phase, the decoherence rate at low frequencies gets progressively smaller and the singular feature is gradually smeared out, leading to a single linear frequency dependence. The dynamical charge susceptibility at low frequencies shows a dip-to-peak crossover across the transition. Relevance of these results to the experiments is discussed.
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)].
Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number nd and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization M and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization M as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in M at the transition in equilibrium. In the limit of large bias voltages, we find M and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.
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.
We investigate the nonequilibrium transport near a quantum phase transition in a generic and relatively simple model, the dissipative resonant level model, that has many applications for nanosystems. We formulate a rigorous mapping and apply a controlled frequency-dependent renormalization group approach to compute the nonequilibrium current in the presence of a finite bias voltage V and a finite temperature T. For V-->0, we find that the conductance has its well-known equilibrium form, while it displays a distinct nonequilibrium profile at finite voltage.
We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develops a nontrivial nonlocal structure in time that is governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature dependence of the noise spectrum. For voltages that are large compared to the Kondo temperature (i.e., $\mathit{eV}\ensuremath{\gg}{k}_{B}{T}_{K}$), two sharp antiresonances are found in the noise spectrum at frequencies $\ensuremath{\hbar}\ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}eV$ and, correspondingly, two Kondo-assisted peaks appear in the ac conductance through the dot.