Rycerz Adam, Rycerz Katarzyna, Witkowski Piotr
Institute for Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Krakow, Poland.
Institute of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland.
Materials (Basel). 2023 Jun 8;16(12):4250. doi: 10.3390/ma16124250.
Thermopower and the Lorentz number for an edge-free (Corbino) graphene disk in the quantum Hall regime is calculated within the Landauer-Büttiker formalism. By varying the electrochemical potential, we find that amplitude of the Seebeck coefficient follows a modified Goldsmid-Sharp relation, with the energy gap defined by the interval between the zero and the first Landau levels in bulk graphene. An analogous relation for the Lorentz number is also determined. Thus, these thermoelectric properties are solely defined by the magnetic field, the temperature, the Fermi velocity in graphene, and fundamental constants including the electron charge, the Planck and Boltzmann constants, being independent of the geometric dimensions of the system. This suggests that the Corbino disk in graphene may operate as a thermoelectric thermometer, allowing to measure small temperature differences between two reservoirs, if the mean temperature magnetic field are known.
在量子霍尔 regime 中，利用兰道尔 - 布蒂克尔形式理论计算了无边缘（科尔比诺）石墨烯盘的热电势和洛伦兹数。通过改变电化学势，我们发现塞贝克系数的振幅遵循修正的戈德斯米德 - 夏普关系，其能隙由体石墨烯中零级和第一朗道能级之间的间隔定义。还确定了洛伦兹数的类似关系。因此，这些热电性质仅由磁场、温度、石墨烯中的费米速度以及包括电子电荷、普朗克常数和玻尔兹曼常数在内的基本常数决定，与系统的几何尺寸无关。这表明，如果已知平均温度和磁场，石墨烯中的科尔比诺盘可作为热电温度计，用于测量两个储热器之间的小温差。
