Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

Abstract

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

“…(16) is expressed in the basis of the two intermediate bands, but it is also related to the spin degrees of freedom σ and it links the expectation value of the spin to the momentumk around the double-Weyl points. Similarly to what happens in 1D [74] and 2D [55] setups with the simultaneous presence of magnetic fluxes and non-Abelian…”

“…In previous works, theoretical investigations have shown that synthetic non-Abelian gauge potentials are an efficient way of implementing exotic quantum Hall systems [44][45][46][47][48][49][50] or topological phases [51][52][53][54][55] in two-dimensional lattices, and that laser assisted tunneling may provide useful tools for the simulation of particles like massless Dirac fermions [45], Wilson fermions [56] or Weyl fermions [57].…”

Simulation of non-Abelian lattice gauge fields with a single-component gas

“…In the Letter we focus on the effects induced by the non-zero masses of the components, whereas the detailed analysis of massless non-Abelian model can be found in Ref. [31]. In the following we assume t x = t y = 1.…”

“…] is a periodic function of m [31]. After the substitution the Schroödinger equation reduces to a generalized Harper equation and therefore we should expect a spectrum of the Hofstadter butterfly type [3,4,15].…”

Speed of the Goldstone Sound Mode of an Atomic Fermi Gas Loaded on a Square Optical Lattice with a Non-Abelian Gauge Field in the Presence of a Zeeman Field

“…It is widely accepted among the cold-atom community that the system of a two-component Fermi gas with swave attraction in square optical lattice with an external non-Abelian gauge field (or a synthetic Rashba SOC) and out-of-plane Zeeman field can be described by a negative-U Hubbard model [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. We restrict the discussion to the case of atoms confined to the lowest-energy band † 푖,휎 = (1/ ) ∑ k exp(− k.r 푖 ) † k,휎 ( 푖,휎 = (1/ )∑ k exp( k.r 푖 ) k,휎 ) creates (destroys) a fermion on the lattice site r 푖 with pseudospin projection .…”