Erlangen 2018 – scientific programme

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A: Fachverband Atomphysik

A 12: Cold atoms IV - topological systems (joint session A/Q)

A 12.3: Talk

Monday, March 5, 2018, 16:45–17:00, K 0.011

Topological invariant for 2D open systems — •Jun-Hui Zheng and Walter Hofstetter — Goethe-Universität, 60438 Frankfurt am Main, Germany

We study the topology of 2D open systems in terms of the Green’s function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems and the equivalent descriptions through topological Hamiltonian and Berry curvature are developed separately. The invariant is well-defined iff all of the eigenvalues of the Green’s function for imaginary frequency are finite nonzero numbers. 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, we explain the relation between the invariant for each spin-subsystem and the Z₂ index of the full system. As a second application, we consider the interference effect when an ordinary insulator is coupled to a topological insulator. The bulk-boundary correspondence of the open system shows new features.