Pseudo-magnetic fields in square lattices

TL;DR

This paper explores how strain and on-site potentials affect pseudo-magnetic fields in various two-dimensional square lattice configurations, revealing conditions under which these fields can be induced or suppressed.

Contribution

It demonstrates that strain alone does not induce pseudo-magnetic fields in certain square lattices, but spatially non-uniform potentials and specific lattice modifications can generate them.

Findings

Strain modulates Fermi velocities but does not induce pseudo-magnetic fields in columnar and staggered π-flux square lattices.

Spatially non-uniform on-site potentials can create pseudo-magnetic fields in these lattices.

Strain induces pseudo-magnetic fields in staggered zero-flux square lattices, which are topologically equivalent to honeycomb lattices.

Abstract

We have investigated the effects of strain on two-dimensional square lattices and examined the methods for inducing pseudo-magnetic fields. In both the columnar and staggered $\pi$-flux square lattices, we have found that strain only modulates Fermi velocities rather than inducing pseudo-magnetic fields. However, spatially non-uniform on-site potentials (anisotropic hoppings) can create pseudo-magnetic fields in columnar (staggered) $\pi$-flux square lattices. On the other hand, we demonstrate that strain does induce pseudo-magnetic fields in staggered zero-flux square lattices. By breaking a quarter of the bonds, we clarify that a staggered zero-flux square lattice is topologically equivalent to a honeycomb lattice and displays pseudo-vector potentials and pseudo-Landau levels at the Dirac points.