Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism

Abstract

We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large offsite interactions on top of a small onsite interaction. Here we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in $A$ and $B$ sublattices makes the onsite interaction Pauli-forbidden, while a sizeable inter-site interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt the density functional theory for cold-atoms, here extended to accommodate non-collinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.

5+8 pages, 3+3 figures

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Experimental realisation of the topological Haldane model
• Theory of ultracold Fermi gases
• Topological Mott Insulators
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Correlation effects in two-dimensional topological insulators
• Direct imaging of topological edge states in cold-atom systems
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Tomography of band insulators from quench dynamics
• Spin-orbit coupling and Berry phase with ultracold atoms in 2D optical lattices
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Nematic, topological and Berry phases when a flat and a parabolic band touch
• Direct Probe of Topological Order for Cold Atoms
• Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers

Cited by in corpus (7)

• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Stabilization of Topological Insulator Emerging from Electron Correlations on Honeycomb Lattice and Its Possible Relevance in Twisted Bilayer Graphene
• Chern Kondo Insulator in an Optical Lattice