Thermohydrodynamics in Quantum Hall Systems

1.建立了量子化磁场中二维电子系统的热力学理论，该理论包含了非线性输运机制。用守恒方程描述了局域平衡中电子温度和化学势的时空变化。该理论被应用于计算这些变量在不同系统中的空间变化，如下所述。通过自洽求解电子数守恒方程和能量守恒方程以及泊松方程，得到了低晶格温度下具有可压缩和不可压缩条的量子霍尔系统中垂直于外加电流的电子温度的空间分布。在线性响应区，随着晶格温度的降低，电子温度的变化集中在不可压缩的条带中。电子温度呈反对称分布：在电化学势较高的样品一侧，电子温度低于晶格温度，而在相反的一侧，电子温度高于晶格温度。随着外加电流的增加，量子霍尔效应的击穿，电流密度变得高度不对称，反映了线性响应区的反对称分布。基于热力学理论，计算了量子霍尔系统中金属电流接触附近电子温度的空间变化。结果表明，在较大电流下，电子温度较高的热点出现在样品的对角。然而，在较小的电流下，一角的电子温度低于晶格温度，而另一角的电子温度高于晶格温度。

1. A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. The theory is applied to calculate spatial variations of these variables in various systems as described in the following.2. Spatial distributions of the electron temperature perpendicular to the applied current are obtained in quantum Hall systems with compressible and incompressible strips at low lattice temperatures by solving equations of electron number conservation and energy conservation as well as Poisson's equation self-consistently. In the linear-response regime, variations of the electron temperature concentrate in the incompressible strips as the lattice temperature decreases. The electron temperature indicates an anti-symmetric distribution: it becomes lower than the lattice temperature in the side of a sample with a higher electrochemical potential, and higher in the opposite side. Reflecting the anti-symmetric distribution in the linear-response regime, the current density becomes highly asymmetric as the applied current increases to the breakdown of the quantum Hall effects.3. Spatial variations of the electron temperature in the vicinity of metallic current contacts in a quantum Hall system are calculated based on thermohydrodynamics. It is shown that, at larger currents, hot spots with high electron temperatures appear at diagonally opposite corners of the sample. At smaller currents, however, the electron temperature at one of the corners is lower than the lattice temperature, while that at the other is higher than the lattice temperature.