Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect

Abstract

Both topological crystalline insulators surfaces and graphene host multi-valley 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 (PLL). Here we study periodic pseudo-magnetic 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.

13 pages + 2 appendices, 9 figures

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• Analytic solution to pseudo-Landau levels in strongly bent graphene nanoribbons
• Interaction-induced quantum spin Hall insulator in the organic Dirac electron system $\alpha$-(BEDT-TSeF)${}_2$I${}_3$
• Magnetic Phases in Periodically Rippled Graphene
• Tuning topology in thin films of topological insulators by strain gradients
• Pseudo Landau levels, negative strain resistivity, and enhanced thermopower in twisted graphene nanoribbons
• Synthesizing Weyl semimetals in weak topological insulator and topological crystalline insulator multilayers
• Designing (higher) Hall crystals
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• Gate-Tunable Resonances and 1D Channel in a Graphene Nanoslide
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