BCS theory of two-dimensional Landau-level superconductivity

J. F. Weisz

doi:10.1103/PhysRevB.48.6330

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BCS theory of two-dimensional Landau-level superconductivity

J. F. Weisz

DOI 10.1103/PhysRevB.48.6330 · Physical Review B

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Abstract

A strictly two-dimensional uniform plane with a perpendicular magnetic field is used in order to study the BCS phase diagram for Hc2, both for weak and intermediate coupling, with a uniformly vanishing order parameter. The phase diagram has a conventional form for weak coupling, but there are oscillations in Hc2(T) for stronger coupling. The slope of Hc2 near T=Tc is singular for ordered planes with g=0 but is finite if g is different from zero, or if disorder is added. Increasing the width of finite-thickness slabs rapidly gives way to fewer Landau levels and therefore to the extreme quantum limit as one moves closer to the three-dimensional crystal, confirming previous results. We show that in two dimensions, in contrast to three dimensions, finite values of Hc2 in the weak-field limit at T=0 are achievable for weak coupling.