Abstract
In the field of mesoscopic electronic transport, it is important to study the electric and thermal response in nanoscale conductors. In recent years, there has been substantial research focusing on the electric response properties under dc and ac voltages both theoretically and experimentally. With the recent experimental developments, there are increasing interests to investigate thermal response phenomena. So far, however, there are few works to study them theoretically. In this work I am tend to fill this gap and the main method used is the non-equilibrium Green's function (NEGF) method. The NEGF method is a powerful method to study transport systems which are even far from equilibrium and it is a better candidate to first principle calculation combined with the density functional theory (DFT) if we wish to study transport properties in nanoscale devices. Researchers have noticed that difficulties will occur when dealing with time-dependent thermal response not only because of the current conservation problem but also because of severe conceptual problems. According to the knowledge of quantum statistical mechanics, a well-defined temperature usually is a constant entering the electronic transport only via the Fermi-Dirac distribution. If time-dependent temperature were considered in each lead, thus the conventional quantum statistical mechanics is not valid and then a question naturally arises: how to calculate the time-dependent and space dependent thermal response using quantum transport theory? Luttinger firstly proposed that for a macroscopic system, in the linear response region, the effects of the temperature field could be equivalently described by introducing a new mechanical field ψ which is the so-called Luttinger field. Until recently, this idea has been applied to investigate nanoscale systems under dc thermal bias. However the more general ac thermal effects are still to be studied. I will show how to combine the NEGF method with the concept of Luttinger field to calculate the linear thermal response under ac bias and a current conservation theory in the linear region is obtained.