Thermohydrodynamics in Quantum Hall Systems

1.本文发展了量子化磁场中二维电子系统的热流体力学理论，其中包括非线性输运区。局域平衡态下电子温度和化学势的时空变化由电子数和热能通量密度的守恒方程描述。该理论被应用于计算这些变量在各种系统中的空间变化，如下所述。通过自洽求解电子数守恒方程、能量守恒方程和泊松方程，得到了低晶格温度下具有可压缩带和不可压缩带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.在线性响应区域，随着晶格温度的降低，电子温度的变化集中在不可压缩条带中。电子温度表示反对称分布：在具有较高电化学电势的样品一侧，电子温度变得低于晶格温度，而在相反一侧，电子温度变得高于晶格温度。在线性响应区域，电流密度反映出反对称分布，随着施加电流的增加，电流密度变得高度不对称，直至量子霍尔效应击穿.基于热流体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。它示出，在较大的电流，具有高电子温度的热点出现在样品的对角。然而，在较小的电流下，其中一个角落的电子温度低于晶格温度，而另一个角落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.