Dynamical 1/N approach to time-dependent currents through quantum dots

TL;DR

This paper introduces the dynamical 1/N approach, a systematic method for studying time-dependent electron currents in quantum dots, successfully capturing transient and steady-state behaviors in different regimes.

Contribution

The paper presents a new dynamical 1/N truncation method for analyzing time-dependent currents in quantum dots, applicable to both spinless and spinning electrons, including the Kondo regime.

Findings

Recovered expected transient current ringing for spinless fermions.

Observed persistent current oscillations in the Kondo regime.

Validated the method against previous NCA calculations and extended to finite Coulomb repulsion.

Abstract

A systematic truncation of the many-body Hilbert space is implemented to study how electrons in a quantum dot attached to conducting leads respond to time-dependent biases. The method, which we call the dynamical 1/N approach, is first tested in the most unfavorable case, the case of spinless fermions (N=1). We recover the expected behavior, including transient ringing of the current in response to an abrupt change of bias. We then apply the approach to the physical case of spinning electrons, N=2, in the Kondo regime for the case of infinite intradot Coulomb repulsion. In agreement with previous calculations based on the non-crossing approximation (NCA), we find current oscillations associated with transitions between Kondo resonances situated at the Fermi levels of each lead. We show that this behavior persists for a more realistic model of semiconducting quantum dots in which the Coulomb repulsion is finite.