标题： 超洁净、二维I型超导体的临界温度磁场振荡 显示英文标题

标题： Magnetic-field oscillations of the critical temperature in ultraclean, two-dimensional Type-I superconductor

摘要： 我们研究了由外加磁场${\bf B}$引起的朗道能级（LLs）和Zeeman能量对二维（2D）超洁净金属临界温度$T_c$的影响，采用了基于Bardeen-Cooper-Schrieffer（BCS）理论的完全量子力学方法。与标准BCS理论不同，该方法允许自旋相反且沿${\bf B}$方向动量相同的电子之间形成库珀对，这些电子既可以位于相同的朗道能级，也可以位于相邻的朗道能级。我们的量子力学处理显示，当电子配对在同一朗道能级时，$T_c({\bf B})$在较低磁场下围绕BCS临界温度出现振荡现象，这一现象类似于de Haas-van Alphen效应。Zeeman能量导致$T_c({\bf B})$随${\bf B}$增大而降低，无论电子是配对在同一朗道能级还是相邻的朗道能级上。 值得注意的是，随着$g$因子的增加，${\bf B}$振荡的振幅逐渐减小，直至在更高磁场中消失。 相反，对于较小的$g$因子，电子在同一朗道能级（LLs）或相邻朗道能级上的配对可以在非常高的磁场中导致超导相的重新进入。 显示英文摘要

摘要： We investigate the influence of Landau Levels (LLs) and Zeeman energy, induced by an applied magnetic field ${\bf B}$, on the critical temperature $T_c$ for two-dimensional (2D) ultraclean metals using a fully quantum mechanical approach within the Bardeen-Cooper-Schrieffer (BCS) theory. In contrast to standard BCS theory, it allows for Cooper pair formation between electrons with opposite spins and momenta along the ${\bf B}$ direction, both on the same or on neighboring LLs. Our quantum mechanical treatment of LLs reveals that $T_c({\bf B})$ for electrons paired on the same LLs exhibits oscillations around the BCS critical temperature at lower magnetic fields, a phenomenon analogous to the de Haas-van Alphen effect. The Zeeman energy leads to a decrease in $T_c({\bf B})$ with increasing ${\bf B}$ for electrons paired both on the same and on neighboring LLs. Notably, as the $g$-factor increases, the amplitude of the ${\bf B}$ oscillations gradually diminishes until they vanish at higher magnetic fields. Conversely, for small $g$-factors, electron pairing on the same or on neighboring LLs can result in a re-entrant superconducting phase at very high magnetic fields.