Pseudo-Landau Levels of Bogoliubov Quasiparticles in Strained Nodal Superconductors

Motivated by theory and experiments on strain-induced pseudo-Landau levels of Dirac fermions in graphene and topological materials, we consider its extension for Bogoliubov quasiparticles 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 pseudo-magnetic field for the Bogoliubov quasiparticles, leading to the formation of pseudo-Landau levels. 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.