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.

Cet article explore les excursions dans le temps et leurs implications.

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