Interacting Dirac fermions under a spatially alternating pseudomagnetic field: Realization of spontaneous quantum Hall effect

Abstract

Both topological crystalline insulator surfaces and graphene host multivalley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal-invariant gauge field, leading to the formation of pseudo-Landau-levels (PLLs). Here we study periodic pseudomagnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, due to the strain superlattice and PLL electronic structure, a valley-ordered state spontaneously breaking time reversal and realizing a quantum Hall phase is favored, while others are suppressed. Our analysis applies to both topological crystalline insulators and graphene.