强无序下的费米和玻色子交流电导率
Fermionic and bosonic ac conductivities at strong disorder
摘要：
我们研究的交流传导系统中的费米子或玻色子强烈定位在一个无序阵列的网站与短程相互作用的频率大于网站间的隧道效应，但小于现场能量的特征波动。虽然对电导率的主要贡献$σ_0(ω)$来自于紧密成对的位点上的局部偶极型激发，但是三个或更多位点上的相干过程导致干扰校正$σ_1(ω)$，其取决于载流子的统计并且可以被磁场抑制。对于玻色子，修正总是正的，而对于费米子，它可以是正的或负的，这取决于传导是由有效的单粒子过程还是单空穴过程主导。我们明确地计算了电导率，假设单格位激发态密度恒定。独立于统计数据，$σ_0(ω)=const$。对于玻色子$σ_1(ω)\propto \log(C/ω)$。对于费米子$σ_1(ω)\propto\log[\max(A,ω)/ω]-\log[\max(B,ω)/ω]$，其中第一项和第二项分别是粒子和空穴贡献，$A$和$B$是粒子和空穴能量截止。交流磁阻与$σ_1(ω)$具有相同的符号。
英文摘要：
We study the ac conduction in a system of fermions or bosons strongly localised in a disordered array of sites with short-range interactions at frequencies larger than the intersite tunnelling but smaller than the characteristic fluctuation of the on-site energy. While the main contribution $σ_0(ω)$ to the conductivity comes from local dipole-type excitations on close pairs of sites, coherent processes on three or more sites lead to an interference correction $σ_1(ω)$, which depends on the statistics of the charge carriers and can be suppressed by magnetic field. For bosons the correction is always positive, while for fermions it can be positive or negative depending on whether the conduction is dominated by effective single-particle or single-hole processes. We calculate the conductivity explicitly assuming a constant density of states of single-site excitations. Independently of the statistics, $σ_0(ω)=const$. For bosons $σ_1(ω)\propto \log(C/ω)$. For fermions $σ_1(ω)\propto\log[\max(A,ω)/ω]-\log[\max(B,ω)/ω]$, where the first and the second term are respectively the particle and hole contributions, $A$ and $B$ being the particle and hole energy cutoffs. The ac magnetoresistance has the same sign as $σ_1(ω)$.
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