Pseudo-Landau levels of Bogoliubov quasiparticles in strained nodal superconductors

Abstract

Motivated by theory and experiments on strain-induced pseudo-Landau levels (LLs) of Dirac fermions in graphene and topological materials, we consider its extension for Bogoliubov quasiparticles (QPs) in a nodal superconductor (SC). We show, using an effective low-energy description and numerical lattice calculations for a $d$-wave SC, that a spatial variation of the electronic hopping amplitude or a spatially varying $s$-wave pairing component can act as a pseudomagnetic field for the Bogoliubov QPs, leading to the formation of pseudo-LLs. We propose realizations of this phenomenon in the cuprate SCs, via strain engineering in films or nanowires, or $s$-wave proximity coupling in the vicinity of a nematic instability, and discuss its signatures in tunneling experiments.