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

TL;DR

This paper demonstrates that weak strain and doping gradients in two-dimensional nodal superconductors can induce pseudo-magnetic fields, leading to Landau quantization of Bogoliubov quasiparticles without breaking time-reversal symmetry.

Contribution

It introduces the concept of strain- and doping gradient-induced pseudo-magnetic fields in 2D nodal superconductors, enabling Landau quantization without magnetic field screening.

Findings

Weak strain induces pseudo-magnetic fields and Landau levels.

Doping gradients also generate similar pseudo-magnetic effects.

These effects can be detected via quantum oscillations in thermodynamic and transport measurements.

Abstract

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.