Interplay of Ehrenfest and Dephasing Times in Ballistic Conductors

Abstract

Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.PACS numbers: 05.45.Mt, 73.20.Fz Introduction. In recent years, the Ehrenfest time τ E has been recognized as a time scale of profound relevance to the physics of systems interfacial between the mesoscopic and the nanoscopic regime [1]. Loosely speaking, τ E is the time it takes before a minimal wave packet propagating in a chaotic background looses its integrity and spreads over scales of classical proportions [2, 3]. Therefore (i) the Ehrenfest time defines a time threshold before the wave nature of electrons begins to modify the classical behavior of observable system properties. Accordingly, (ii) there is a general expectation that quantum effects are multiplied by exponential weighting factors exp(−ατ E /t 0 ), where t 0 is the (smallest) characteristic time scale of the quantum effect. This expectation has been confirmed for the Ehrenfest-time related suppression of weak localization [1,4,5,6] and shot noise [7,8] in chaotic quantum dots, with t 0 taken to be the dot's mean dwell time τ D , or Ehrenfest-oscillations of the weak localization corrections to the ac conductivity of a random collection of antidots [1] and time-dependent diffusion in periodically kicked atomic gases [9], with t 0 = iω −1 taken to be the inverse angular frequency .In this letter, we consider the competition between the Ehrenfest time and the dephasing time τ φ . Whereas τ E is the minimal time needed for quantum interference, τ φ sets the long-time cut-off for interference processes. The competition between τ E and τ φ is particularly relevant for quantum corrections in bulk conductors, for which the dwell time τ D has no significance. In particular, we'll address the question whether one may expect a suppression of quantum corrections proportional to exp(−ατ E /τ φ ), according to the general expectation (ii) mentioned above. In a subtle manner, the answer depends on whether the dephasing originates from electronelectron interactions or from an external source (such as applied microwave radiation). Conceptually, the observation of an Ehrenfest-time dependence of quantum interference corrections to the conductance has exponential sensitivity to the microscopic mechanism of dephasing.To date, there are only a few experimental signatures of the Ehrenfest time. Oberholzer et al. found a τ Erelated suppression of the shot noise of a chaotic cavity upon decreasing τ D [10]. Shot noise, however, is insensitive to the presence of dephasing. Yevtushenko et al.

Quantum corrections to transport in graphene: a trajectory-based semiclassical analysis

“…The remaining time-integration is easily evaluated with the help of equations (37) and (82) and we obtain: Note that the time τ φ enc is twice the dephasing time τ φ ball that one finds from dephasing in the loop region in the ballistic regime [105], consistent with the theory of [33]. (To compare with [105], take the energy-dependent dephasing time τ ε φ ( ) from equations (18)…”

“…( ; ) R 2 of the diffusive limit. This difference will result in a different T-dependence of the dephasing rate in comparison to the loop contribution [33].…”

“…is the diffusion propagator (see equation (30)), and P r ( ) L and P r ( ) R are defined in equation (33). For further evaluation of equation (41), we write:…”

“…where the correction  δ α t ( ) depends on the time t at which the electron exits the sample. The shift reads [33,47]:…”

“…Within the encounter region, the trajectories α and β are separated by a small distance, which does not exceed the classical correlation scale L c . Dephasing then only plays a role for interaction that transfers a momentum larger than inverse mean free path and therefore can resolve such a small distance [33,106,107]. On the other hand, for low temperatures τ ≪ T 1 tr one has ωτ ≪ 1 tr , in this limit, the imaginary part of the screened interaction reads [46]:…”