Phase transitions induced by a lateral superlattice potential in a two-dimensional electron gas

We study the phase transitions induced by a lateral superlattice potential (a metallic grid) placed on top of a two-dimensional electron gas (2DEG) formed in a semiconductor quantum well. In a quantizing magnetic field and at filling factor nu = 1, the ground state of the 2DEG depends on the strength V-g of the superlattice potential as well as on the number of flux quanta piercing the unit cell of the external potential. It was recently shown that in the case of a square lateral superlattice, the potential modulates both the electronic and spin density and in some range of V-g, the ground state is a two-sublattice spin meron crystal where adjacent merons have the global phase of their spin texture shifted by pi, i.e., they are "antiferromagnetically" ordered. In this paper, we evaluate the importance of Landau-level mixing on the phase diagram obtained previously for the square lattice and derive the phase diagram of the 2DEG modulated by a triangular superlattice. When Landau-level mixing is considered, we find in this case that, in some range of V-g, the ground state is a three-sublattice spin meron crystal where adjacent merons of the same vorticity have the global phase of their spin texture rotated by 120 degrees with respect to one another. This meron crystal is preceded in the phase diagram by another meron lattice phase with a very different spin texture that does not appear, at first glance, to resolve the spin frustration inherent to an antiferromagnetic ordering on a triangular lattice.