Landau levels from neutral Bogoliubov particles in two-dimensional nodal superconductors under strain and doping gradients

Motivated by recent work on strain-induced pseudo-magnetic fields in Dirac and Weyl semimetals, we analyze
the possibility of analogous fields in two-dimensional nodal superconductors. We consider the prototypical case
of a d-wave superconductor, a representative of the cuprate family, and find that the presence of weak strain
leads to pseudo-magnetic fields and Landau quantization of Bogoliubov quasiparticles in the low-energy sector.
A similar effect is induced by the presence of generic, weak doping gradients. In contrast to genuine magnetic
fields in superconductors, the strain- and doping gradient-induced pseudo-magnetic fields couple in a way that
preserves time-reversal symmetry and is not subject to the screening associated with the Meissner effect. These
effects can be probed by tuning weak applied supercurrents which lead to shifts in the energies of the Landau
levels and hence to quantum oscillations in thermodynamic and transport quantities.