Quantum incommensurate skyrmion crystals and commensurate to in-commensurate transitions in cold atoms and materials with spin–orbit couplings in a Zeeman field

Abstract

In this work, we study strongly interacting spinor atoms in a lattice subject to a two dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the four commensurate phases. New excitation spectra above all the five phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its four neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms N per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, Fe 0.5 Co 0.5 Si, especially the complex incommensurate magnetic ordering in Li 2 IrO 3 are given.

Fermionic Hubbard model with Rashba or Dresselhaus spin–orbit coupling

“…There are previous theoretical works to study strongly correlated spinless bosons in Abelian gauge fields [40][41][42][43][44] and spinor bosons in non-Abelian gauge fields [25,[45][46][47][48][49]. The topological quantum phase transitions of noninteracting fermions driven by a Rashba type of SOC are investigated in a honeycomb lattice [31].…”

“…It may be necessary to point out the RAFHM equation (2) is explicit for spin S 1 2 = . However, the RFHM in [25,26,48,49] is for any spin S N 2 = . As argued in [48], the critical temperature T J S 2 c~, so increasing the spin is a very effective way to raise the critical temperature.…”

“…However, the RFHM in [25,26,48,49] is for any spin S N 2 = . As argued in [48], the critical temperature T J S 2 c~, so increasing the spin is a very effective way to raise the critical temperature. It is known that if putting S 3 2 = fermions on a lattice without SOC, the resulting spin model in the strong coupling limit at half filling [52] has a higher symmetry such as SO(5) instead of SU(2), and it has even larger quantum fluctuations due to the enlarged symmetry.…”

Highly Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases

“…The 1D SO coupling has now been realized routinely in the experiments for both ultracold bosons [12,13] and fermions [14,15] as continuum atom gases or trapped in optical lattices [16,17]. Great interests have been drawn in emulating SO effects [18][19][20][21][22][23][24] and topological phases with ultracold atoms [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In particular, the simulation of broad classes of topological quantum states or phase transitions with quantum gases necessitates to synthesize 2D or higher dimensional SO couplings.…”

Class of topological phase transitions of Rashba spin-orbit coupled fermions on a square lattice

“…However, along the diagonal line α = β, there must be some quantum phase transitions from the X − (π, π) or Y − (π, π) spin-bond correlated magnetic state at weak coupling to some other spin-bond correlated magnetic states in the strong coupling 54 . The effects of a Zeeman field in the strong repulsively interacting limit was studied in 51,52 . Due to the lack of the spin SU (2) symmetry, different orientations of the Zeeman field lead to different phenomena 51,52 .…”