Current through a multilead nanojunction in response to an arbitrary time-dependent bias

Abstract

We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide-band-limit approximation, it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et al. [Phys. Rev. B 50, 5528 (1994)] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et al. [Phys. Rev. B 89, 085131 (2014)] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally varying bias. At certain frequencies of the driving bias, we observe ``ringing'' oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude, and temperature is also investigated.