Topological invariant for two-dimensional open systems

Abstract

We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge bands arising from the poles and zeros of the Green's function. Meanwhile, we define another topological invariant via the single-particle density matrix, which works for general gapped systems and is equivalent to the former for the case of weak coupling to an environment. We also discuss two applications. For time-reversal-invariant insulators, the $Z_2$ index can be expressed by the invariant of each spin subsystem. As a second application, we consider the proximity effect when an ordinary insulator is coupled to a topological insulator.

9 pages, 3 figures (This version is the published one.)

References in corpus (16)

• Topological Field Theory of Time-Reversal Invariant Insulators
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Robustness of the Spin-Chern number
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
• Gradient expansion approach to multiple-band Fermi liquids
• Interaction induced topological phase transition in Bernevig-Hughes-Zhang model
• Topological order of mixed states in quantum many-body systems
• Classification of Mixed State Topology in One Dimension
• Artificial electric field in Fermi Liquids
• Entanglement Chern number for an extensive partition of a topological ground state
• Topological transport in a spin-orbit coupled bosonic Mott insulator

Cited by in corpus (16)

• Topological charge pumping in the interacting bosonic Rice-Mele model
• Interacting Hofstadter Interface
• Topological proximity effects in a Haldane-graphene bilayer system
• Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics
• Interaction-enhanced integer quantum Hall effect in disordered systems
• Higher order topological matter and fractional chiral states
• Measuring the topological phase transition via the single-particle density matrix
• Topological Green function of interacting systems
• Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Bulk topological proximity effect in multilayer systems
• Local vs non-local correlation effects in interacting quantum spin Hall insulators
• Defect bulk-boundary correspondence of topological skyrmion phases of matter
• Quantum Hall and Light Responses in a 2D Topological Semimetal