Semiclassical theory of transport in a random magnetic field-猫眼课题宝

随机磁场中的半经典输运理论

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发表时间：

1999

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作者：

F. Evers;A. Mirlin;D. Polyakov;P. Woelfle

研究了二维费米子在光滑变化磁场$B（{f r}）$。输运的性质主要取决于$B（{f r}）$及其平均值$ar{B}$。为$ar{B}=0$，控制参数为$alpha=d/R_0$，其中$d$为无序的关联长度，$R_0$为场$B_0$中的拉莫尔半径。而对于$dall1 $的德鲁德理论适用，在$dallagg 1$大多数粒子漂移的粘性沿着封闭的轮廓和本地化的绝热近似。电导率则由一类特殊的轨迹确定，即“蛇态”，其通过在$B（{在那里它们运动的绝热性被破坏。外场还通过产生漂移回旋加速器轨道的逾渗网络来抑制扩散。这种渗流仅仅是由于回旋加速器旋转的绝热性的弱破坏，产生了大的电导率的指数下降。ar{B}$。在该区域中，随着时间的增加，蛇态渗流与漂移轨道渗流之间的交叉ar{B}$具有相变（蛇态的局部化）的特征，该相变被非绝热效应指数地弱地涂抹。交流电导率也反映了颗粒在分形逾渗网络上运动的动力学性质。特别地，它在零频率处具有尖锐的扭结，并且在较高频率处呈指数下降福尔斯。我们还讨论了量子磁振荡的性质。详细的数值研究证实了分析结果。在α 1处的磁电阻率的形状与在α 1附近的磁电阻率区域的实验数据符合得很好。 u=1/2$。

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({f r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({f r})$ and its mean value $ar{B}$. For $ar{B}=0$, the governing parameter is $alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $alphall 1$ the Drude theory applies, at $alphagg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({f r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $ar{B}$. In the regime $alphagg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $ar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $alphasim 1$ is in good agreement with experimental data in the FQHE regime near $ u=1/2$.