Quantum transport theory for AC response and its combination with electromagnetic method

Abstract

The time-dependent quantum transport theory has attracted a great deal of interest in the past decade. However, some concepts in the frequency-dependent transport theory remain confused. Based on the Keldysh non-equilibrium green’s function formalism for time-dependent quantum transport, new expressions for dynamic current and admittance are derived in this thesis, which satisfy gauge invariance and current continuity. The key concepts in this field are clarified. The derivation is under wideband limit (WBL) and first order approximations. This new formalism is validated by first-principle time-dependent calculations of three carbon-based nano-devices. Later a study on asymmetric systems is carried out by this new theory, and discussion on current conversation problem is presented.

This new ac quantum transport theory can cooperate with electromagnetic method to solve a mesoscopic problem. The active core part which is usually under atomistic scale is simulated by frequency-domain quantum transport theory, while the broad environment is tackled with electromagnetic solver. By a careful treatment at the interface between two solvers, this quantum mechanic / electromagnetic (QM/EM) method is implemented self-consistently. This QM/EM method is also validated by calculations of the transient current through a carbon-nanotube based device surrounded by silicon environment under a small ac bias voltage. The small signal and WBL approximations are also adopted in the development of this method. As a supplementary to the family of QM/EM methods (static and time-dependent QM/EM method are already established), this method shows very good efficient and high accuracy.

Beyond linear response in frequency domain, we have also studied some nonlinear effects. As one application of nonlinear effect, memristor has attracted great attention in the past few years. Through Fourier analysis method, we have now understood the physical and mathematical mechanisms of ideal memristor, memcapacitor and meminductor. We have proposed methods to verify ideal memristor, memcapacitor and memdicutor, and to find out their intrinsic parameters which can be employed to predict their behavior under various input signals. This study may also provide an instruction on experimental research.