Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors

Abstract

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these peculiar phases and study their properties, a critical step is to construct experimentally relevant Hamiltonians which support these topological phases. We propose a general and systematic method based on the quaternion algebra to construct the tight binding Hamiltonians for all the three-dimensional topological phases in the periodic table characterized by arbitrary integer topological invariants, which include the spin-singlet and the spin-triplet topological superconductors, the Hopf and the chiral topological insulators as particular examples. For each class, we calculate the corresponding topological invariants through both geometric analysis and numerical simulation.

7 pages (including supplemental material), 1 figure, 1 table

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• On the $Z_2$ classification of Quantum Spin Hall Models
• Topological surface states in three-dimensional magnetic insulators
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry

Cited by in corpus (19)

• Classification of topological quantum matter with symmetries
• Nodal-link semimetals
• Topological semimetals with double-helix nodal link
• Nodal-knot semimetals
• Topological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon's-Knot, Trefoil-Knot and Other Semimetals
• Hopf-link multi-Weyl-loop topological semimetals
• Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice
• Floquet Hopf Insulators
• Realizing Hopf Insulators in Dipolar Spin Systems
• Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors
• Observation of topological links associated with Hopf insulators in a solid-state quantum simulator
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Topological quantum quench dynamics carrying arbitrary Hopf and second-Chern numbers
• Topological insulation in a ladder model with particle-hole and reflection symmetries
• Quench dynamics of Hopf insulators
• Effect of incommensurate potential on nodal-link semimetals
• Quantized electromagnetic response of three-dimensional chiral topological insulators
• Induced topological order at the boundary of 3D topological superconductors
• Simple Models for All Topological Phases