Pseudomagnetic fields in square lattices

We have investigated the effects of strain on two-dimensional square lattices and examined the methods for inducing pseudomagnetic fields. In both the columnar and staggered π-flux square lattices, we have found that strain only modulates Fermi velocities rather than inducing pseudomagnetic fields. However, spatially nonuniform on-site potentials (anisotropic hoppings) can create pseudomagnetic fields in columnar (staggered) π-flux square lattices. On the other hand, we demonstrate that strain does induce pseudomagnetic 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 pseudovector potentials and pseudo-Landau-levels at the Dirac points.