Abstract

In this talk, I will address the problem of superconductivity in Landau levels that preserve time reversal symmetry (TRS). Those Landau levels have been experimentally observed in a class of strained honeycomb lattices (both atomic and optical), where sharply separated Landau levels are formed in the complete absence of a magnetic flux at every lattice site. I will show that superconductivity is quantum critical at integer filling of the Landau levels, when the system becomes incompressible. At partial filling, the quenching of the kinetic energy due to the Landau levels leads to a crossover to an exotic regime, where the critical temperature scales linearly with the coupling in the weak coupling limit, rather than exponentially. Due to this anomalous scaling, the critical temperature can be orders of magnitude larger than in conventional weak coupling superconductors, and may be triggered by phonons when screening is restored at length scales larger than the magnetic length. Since the system is gapped in bulk, the supercurrent flows along the edges of the system. I will show that normal-superconducting junctions have unique transport and spectroscopy signatures of those states.