Ummarino Giovanni Alberto, Zaccone Alessio
Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Department of Physics 'A. Pontremoli', University of Milan, via Celoria 16, 20133 Milan, Italy.
J Phys Condens Matter. 2024 Nov 22;37(6). doi: 10.1088/1361-648X/ad92ed.
A quantitative theory of the superconductivity of materials confined at the nanoscale in parameter-free agreement with experimental data has been missing so far. We present a generalization, in the Eliashberg framework, of a BCS theory of superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. In this formulation of the Eliashberg equations the approximation of taking the normal density of states as its value at the Fermi level has been removed. By numerically solving these new Eliashberg-type equations, we find the dependence of the superconducting critical temperatureTcon the confinement size, in quantitative agreement with experimental data of Pb and Al thin films with no adjustable parameters. This quantitative agreement provides an indirect confirmation that, upon increasing the confinement, a crossover from a spherical-like Fermi surface, which contains two growing hole pockets caused by the confinement, to a strongly deformed Fermi surface, occurs. This topology of the Fermi sea is implemented in the new Eliashberg-type equations to reproduce the experimentally observed maximum in the critical superconducting temperature vs film thickness of ultra-thin Pb films.
到目前为止，尚未有一个与实验数据无参数相符的、关于纳米尺度受限材料超导性的定量理论。我们在Eliashberg框架下，对沿三个空间方向之一受限的良金属（如薄膜）的BCS超导理论进行了推广。在这种Eliashberg方程的表述中，去除了将正常态密度取为其在费米能级处值的近似。通过数值求解这些新的Eliashberg型方程，我们发现超导临界温度(T_c)对受限尺寸的依赖性，与Pb和Al薄膜的实验数据定量相符，且无可调参数。这种定量相符间接证实了，随着受限程度增加，会发生从包含由受限导致的两个不断增大的空穴口袋的类球形费米面到强烈变形费米面的转变。费米海的这种拓扑结构在新的Eliashberg型方程中得以实现，以重现实验观测到的超薄Pb膜临界超导温度与膜厚度关系中的最大值。
