Electron Correlation Effects on Topological Phases

Abstract

Topological insulators are found in materials that have elements with strong spin orbit interaction. However, electron Coulomb repulsion also potentially generates the topological insulators as well as Chern insulators by the mechanism of spontaneous symmetry breaking, which is called topological Mott insulators. The quantum criticality of the transition to the topological Mott insulators from zero-gap semiconductors follows unconventional universality distinct from the Landau-Ginzburg-Wilson scenario. On the pyrochlore lattice, the interplay of the electron correlation and the spin orbit interaction provides us in a rich phase diagram not only with simple topological insulators but also with Weyl semimetal and topologically distinct antiferromagnetic phases. Magnetic domain wall of the all-in-all-out type antiferromagnetic order offers a promising candidate of magnetically controlled transport, because, even when the Weyl points disappears, the domain wall maintains robust gapless excitations with Fermi surfaces around it embedded in the bulk insulator and bears uniform magnetization simultaneously. The ingap state is protected by a mechanism similar to the solitons in polyacetylene. Puzzling experimental results of pyrochlore iridates are favorably compared with the prediction of the domain wall theory.

8 pages, 14 figures

References in corpus (21)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Hidden Order in the Cuprates
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological Mott Insulators
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Topological insulators and metal-insulator transition in the pyrochlore iridates
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Surface States of Topological Insulators
• Three-dimensional Topological Insulators on the Pyrochlore Lattice
• Topological insulators in three dimensions from spontaneous symmetry breaking
• Continuous Transition between Antiferromagnetic Insulator and Paramagnetic Metal in the Pyrochlore Iridate Eu2Ir2O7
• Topological Insulators from Spontaneous Symmetry Breaking Induced by Electron Correlation on Pyrochlore Lattices
• Giant Magnetoresistance Effect in the Metal-Insulator Transition of Pyrochlore Oxide Nd2Ir2O7
• Magnetization and Hall effect studies on the pyrochlore iridate Nd2Ir2O7
• Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario

Cited by in corpus (7)

• Recent progress on correlated electron systems with strong spin-orbit coupling
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings
• Topological Insulators from Electronic Superstructures
• Coupled Spin-Charge-Phonon Fluctuation in the All-In/All-Out Antiferromagnet Cd${}_2$Os${}_2$O${}_7$
• Multitude of phases in correlated lattice fermion systems with spin-dependent disorder
• Phase transitions of the Kane-Mele-Hubbard model with a long-range hopping