电阻率的线性响应理论和平衡方程理论

Kubo Response Theory and Balance-Equation Theory for Steady-State Resistivity

众所周知,广泛应用于计算弱电场中电子输运性质的Kubo线性响应理论是将系统对外界微扰的响应作展开,只保留电场的线性项。考虑由N个没有相互作用的电子组成的系统,从时间t=0开始受到均匀弱电场E的作用以及无规分布的弱杂质散射。把电场的作用HE及杂质的作用HI都当作微扰,可以把系统电流密度响应按电场及杂质势的幂次展开:

We demostrate that a new necessary condition, the relaxation time <τ> <<αE-1/2, must be added to the conductivity formula, a = Ne2<τ>/m, in Kubo linear response theory for its application, because of the divergencs of the perturbative expansion of the current densiity at any nonzero field for t→∞. For the balance-equation theory, in the case of weak impurity and phoaon scattering, the thermolization time τth of the system without any momentum relaxation is mainly determined by the carrier-carrier interaction, and the perturbative expansions are convergent within the τth. Therefore, employing the lowest order term is a good approximative way for the calculation of the steady state resistivity.