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Topological crystalline insulators in IV-VI compounds host novel topologicalsurface states consisting of multi-valley massless Dirac fermions at lowenergy. Here we show that strain generically acts as an effective gauge fieldon these Dirac fermions and creates pseudo-Landau orbitals without breakingtime-reversal symmetry. We predict the realization of this phenomenon in IV-VIsemiconductor heterostructures, due to a naturally occurring misfit dislocationarray at the interface that produces a periodically varying strain field.Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity ofthe Dirac point, and coexist with a network of snake states at higher energy.We propose that the high density of states of this flat band gives rise tointerface superconductivity observed in IV-VI semiconductor multilayers atunusually high temperatures, with non-BCS behavior. Our work demonstrates a newroute to altering macroscopic electronic properties to achieve a partially flatband, and paves the way for realizing novel correlated states of matter.

Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators