Fermionic atoms in a spin-dependent optical lattice potential: topological insulators with broken time-reversal symmetry

Abstract

We propose a novel approach to study the topological properties of matter. In this approach, fermionic atoms are placed in an external magnetic field and in a two-dimensional spin-dependent optical lattice (SDOL) created by intersecting laser beams with a superposition of polarizations. To demonstrate the utility of the SDOL-based technique we compute the topological invariants (Chern numbers) for the SDOL bands as a function of an external magnetic field, and show the existence of a rich topology of the energy bands for this system which does not have parity-time-reversal symmetry. We explicitly consider ${}^6$Li $F=1/2$ atoms. Using a projection matrix method we observe topological phase transitions between an ordinary insulator, an abelian topological insulator, and a non-abelian topological insulator as the external magnetic field strength is varied. Upon introducing edges for the SDOL we find topological edge states (that are correlated with the band Chern numbers) that simultaneously exhibit non-trivial density and spin currents with both a rotational flow contribution and flow along the edge of the SDOL.

13 pages, 15 eps figures

References in corpus (28)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological quantum matter with symmetries
• Experimental realisation of the topological Haldane model
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Light-induced gauge fields for ultracold atoms
• Topological Bands for Ultracold Atoms
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Non-Abelian band topology in noninteracting metals
• Artificial gauge fields in materials and engineered systems
• Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Spin-orbit coupling and Berry phase with ultracold atoms in 2D optical lattices
• Four-band non-Abelian topological insulator and its experimental realization
• Atoms trapped by a spin-dependent optical lattice potential: realization of a ground state quantum rotor
• Atoms in a spin dependent optical potential: ground state topology and magnetization
• Measuring the degree of unitarity for any quantum process