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arXiv · 1412.4118

Current through a multi-lead junction caused by applied bias with arbitrary time-dependence

Michael Ridley·Angus MacKinnon·Lev Kantorovich
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Abstract

We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-terminal 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 (WBLA), 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. [doi:10.1103/PhysRevB.50.5528] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et. al. [doi:10.1088/1742-6596/427/1/012014] 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.

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Michael Ridley, Angus MacKinnon, Lev Kantorovich. 2014-12-12. Current through a multi-lead junction caused by applied bias with arbitrary time-dependence. https://arxiv.org/abs/1412.4118

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