Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation

• URL: http://arxiv.org/abs/2002.07490v2
• Date: Tue, 19 May 2020 02:33:00 GMT
• Title: Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Authors: Wei Xin Teo, Linhu Li, Xizheng Zhang, Jiangbin Gong
• Abstract summary: Majorana's stellar representation (MSR) is applied to 1D multiband models consisting of asymmetric nearest-neighbor hopping and imaginary on-site potentials. The number of edge states isolated from the continuous bulk bands in the complex energy plane is successfully linked with a topological invariant constructed from MSR. Cases with the so-called non-Hermitian skin effect are also studied, showing that the bulk-boundary correspondence between our defined winding numbers and isolated edge states can be restored.
• Score: 1.5484595752241122
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For topological characterization of non-Hermitian multiband systems, Majorana's stellar representation (MSR) is applied to 1D multiband models consisting of asymmetric nearest-neighbor hopping and imaginary on-site potentials. The number of edge states isolated from the continuous bulk bands in the complex energy plane is successfully linked with a topological invariant constructed from MSR. Specifically, the number of isolated edge states can be obtained from a winding number defined for the Majorana stars, which also allows for a geometric visualization of the topology related to the isolated edge modes. A remarkable success of our approach is that our winding number characterization remains valid even in the presence of exceptional points of the continuous bulk bands, where the Hamiltonian becomes non-diagonalizable and hence conventional topological invariants such as the Zak phase and the Chern number cannot be properly defined. Furthermore, cases with the so-called non-Hermitian skin effect are also studied, showing that the bulk-boundary correspondence between our defined winding numbers and isolated edge states can be restored. Of particular interest is a four-band example with an odd number of isolated edge states, where the Zak phase approach necessarily fails upon removing the skin effect, but our MSR-based characterization works equally well. For these reasons, our study is expected to be widely useful in topological studies of non-Hermitian multiband systems, regardless of the skin effect or the presence of the exceptional points in non-Hermitian systems.

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