Kondo time scales for quantum dots: Response to pulsed bias potentials

Abstract

The response of a quantum dot in the Kondo regime to rectangular pulsed bias potentials of various strengths and durations is studied theoretically. It is found that the rise time is faster than the fall time, and also faster than time scales normally associated with the Kondo problem. For larger values of the pulsed bias, one can induce dramatic oscillations in the induced current with a frequency approximating the splitting between the Kondo peaks that would be present in steady state. The effect persists in the total charge transported per pulse, which should facilitate the experimental observation of the phenomenon.The theoretical predictions 1 of consequences of the Kondo effect for the steady state conduction through quantum dots began a decade ago. At low temperatures, a narrow resonance in the dot density of states can form at the Fermi level, leading to a large enhancement of the dot's conductance, which is strongly dependent on temperature, bias, and magnetic field. Many of these effects have been recently observed by a set of experiments by several groups. 2 These successes, supplemented by the anticipation that time dependent experiments 3 are not far behind, have spurred a number of theoretical groups 4 to consider the effects expected when sinusoidal biases or gate potentials are applied. Surprisingly, the application of steps or pulses, which can provide a less ambiguous measure of time scales, have not been considered until very recently; 5 the latter work considered the time dependent change in linear response conductance when a stepped potential was applied to a gate, thereby shifting the dot into the Kondo regime. In the present work we consider the response of a dot already in the Kondo regime to a sudden change of the bias potential across the dot. We show that the physics is qualitatively different from the latter case, 5 leading to a different range of characteristic times and physical phenomena.While Ref. 5 studied the time scale for the system to go from one equilibrium configuration to another, we study here the time scale to go from an equilibrium configuration to a nonequilibrium one; and then back to equilibrium again. We find that these latter two times scales are very different from each other, the first being much shorter-and also much shorter than the time scale of Ref. 5. Furthermore, if one applies a rectangular bias pulse large enough to split the Kondo resonance, then there appear current oscillations 6 at a frequency characterizing the splitting between the Kondo peaks. We show that these current oscillations cause oscillations in the charge transported through the dot as a function of pulse length, thus providing a clear experimental signature. The damping of the oscillations provides an additional time scale which also can be measured directly.We model the quantum dot by a single spin degenerate level of energy ⑀ dot coupled to leads through tunnel barriers, as illustrated schematically in the inset to Fig. 1. The Coulomb charging energy U prevents the level from being doub...

The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group

“…Theoretically, the Kondo effect out of equilibrium has been studied by a number of methods ranging from perturbation theory, 9,10,12,27,28,[39][40][41][42][43][44][45][46] equations of motions and self-consistent diagrammatic methods 30,[47][48][49][50][51][52][53][54][55] (using the so-called non-crossing approximation), slave-boson mean-field theories, 57-59 exact solutions for some variants of the Kondo model with appropriately chosen coupling constants, 56 the construction of approximate scattering states starting from Bethe ansatz solutions, 60 to perturbative renormalization group 28,43,61 (reviewed below). It is, however, important to note, that many of the methods which have been so successful in equilibrium cannot or have not yet been generalized even to the simplest steady-state non-equilibrium situation.…”

Kondo resonance decoherence caused by an external potential

“…The non-crossing approximation (NCA) [3], [6], being essentially numerical, can give analytical results only in the limit Ln(V /T K ) >> 1 (V being the applied bias and T K the Kondo energy), the same limit in which renormalized perturbation theory (RPT) [7], [8] is valid. It is important, however, to have analytical results for the decoherence rate, not only to make theoretical predictions, but also to be able to interpret correctly the results of calculations done for more complicated situations, i.e., when time-dependent potentials are applied to the QD [9]- [12]. A version of the nonequilibrium Kondo problem has been solved exactly to all orders in the applied bias V in [13].…”

Transient thermoelectricity in a vibrating quantum dot in Kondo regime

“…Transient current ensuing after sudden shifting of the gate or bias voltage 5,6,8 displays different time scales 9,10 . For an asymmetrically coupled system, interference between the Kondo resonance and the sharp features in the contacts' density of states gives rise to oscillations in the long time scale 11 .…”