Current distribution and nonequilibrium phase transition in the breakdown of the quantum Hall effect

我们从理论上研究了电子温度和电流密度在线性和非线性区域的空间变化。我们推导了非线性区域中量子霍尔系统的流体动力学方程，并研究了电子温度的空间变化。结果表明，在样品边缘附近，电子温度和电流密度呈垂直于电流的不对称空间变化。我们已经证明，在高电子温度状态下，每个朗道能级内局域态之间隧穿的对角线电导率远小于观测值。我们已经证明了电子温度分布在线性响应区表现出量子振荡。我们发展了量子霍尔系统的热流体力学理论，这是对先前理论的修正和推广。我们研究了线性响应条件下慢变约束电位下的艾汀斯豪森效应，并表明电子温度的偏差沿电位梯度在空间上振荡。我们研究了线性响应体系中沿电流具有电位不连续的系统中的珀尔帖效应，并表明电子温度在不连续的周围发生空间变化。

We have investigated theoretically spatial variations of the electron temperature and the current density in linear and nonlinear regions.[1]We have derived hydrodynamic equations in quantum Hall systems in a nonlinear region and studied spatial variations of the electron temperature. It has been shown that the electron temperature and the current density exhibit asymmetric spatial variations perpendicular to the current in the vicinity of sample edges.[2]We have shown that the diagonal conductivity due to tunneling between localized states within each Landau level in high-electron-temperature regime is much smaller than the observed value.[3]We have shown that the electron temperature distribution exhibits quantum oscillations in the linear-response regime.[4]We have developed a theory of thermohydrodynamics in quantum Hall systems, which is a revision as well as a generalization of the previous theory in [1].[5]We have studied the Ettingshausen effect in a slowly-varying confining potential in the linear-response regime and shown that the deviation of the electron temperature oscillates spatially along the gradient of the potential.[6]We have studied the Peltier effect in a system with a potential discontinuity along the current in the linear-response regime and shown that the electron temperature develops spatial variations around the discontinuity.