超导拓扑表面态的自洽平均场理论

Self-Consistent Mean-Field Theory of Superconducting Topological Surface States

我们采用自洽平均场的方法,来求解FeSeTe薄膜界面处的拓扑超导表面态的能隙。用平均场近似得到近似的哈密顿量,对该哈密顿量进行粒子–准粒子变换(Bogoliubov-Valatin)简化为无相互作用的准粒子体系,得到能隙的费米算子表达式。分别在零温及有限温度下展开该表达式,利用费米算子的对易关系及准粒子体系满足的分布特性,得到两种温度状态下的能隙自洽式。通过超导转变的特殊性算出超导转变温度后,在此基础上自洽地数值解出零温到超导转变温度范围内能隙随温度的变化关系。对拓扑表面态超导能隙的研究,可以从中得到超导态的热力学性质的变化。同时对寻找适用于拓扑量子计算的马约拉纳零能摸具有参考意义。

We use the self-consistent mean-field method to solve the energy gap of the topological super-conducting surface state at the interface of the FeSeTe film. The approximate Hamiltonian is obtained by the mean field approximation. The Bogoliubov quasi-particle transformation of the Hamiltonian is simplified to a non-interacting quasi-particle system, and the Fermi operator expression of the energy gap is obtained. The expression is expanded at zero temperature and finite temperature respectively. By using the commutation relationship of Fermi operator and the distribution characteristics of quasi-particle system, the energy gap self-consistent formulas under two temperature states are obtained. After the superconducting transition temperature is calculated by the particularity of the superconducting transition, the relationship between the energy gap and temperature in the range of zero temperature to superconducting transition temperature is solved numerically. The study of the superconducting energy gap of the topological surface state can obtain the change of the thermodynamic properties of the superconducting state. At the same time, it has reference significance for finding Majorana zero modes suitable for topological quantum computing.