Quantum Hall Resistance Effect Based on Maximum Entropy Transfer Rate Spectrum

With the continuous development of topological quantum materials, traditional mobility spectrum analysis methods can no longer meet the practical measurement needs. Based on this, starting from solving the Boltzmann formula and combining the principle of maximum entropy, a method of maximum entropy transfer rate spectrum is proposed by using numerical integration instead of analytical integration. The results show that there are five different electronic energy levels in the conduction process of PtBi2, a large magnetoresistance material with hexagonal structure, which is consistent with theoretical simulations. Among these materials, there is a hole energy spectrum with 0.964m2/Vs, which contributes 15% to the conductivity, largely due to Dirac electrons. At the same time, the study observes the existence of Dirac electrons and discovers the large magnetoresistance effect, which is not related to the compensation mechanism between their charge holes. In addition, the mobility of each band decreases with increasing temperature, while the morphology of the charge density and mobility spectra remains unchanged. The research approach proposed in the study can avoid conventional research methods and can compare and analyze the ratio of high mobility and low mobility, majority and minority carriers, to obtain the concentration and mobility of various types of carriers, providing a new approach for studying the electronic transport characteristics of multi-carrier systems.