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Phase diagram for the non-Hermitian SSH model, obtained from the non-Hermitian winding numbers (W+(0), W−(0)). The invariants come in pairs, where the first one is calculated around the gap closing point k = 0 and the second one around the point k = π/a.
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Non-Hermitian systems have provided a rich platform to study unconventional topological phases.These phases are usually robust against external perturbations that respect certain symmetries of thesystem. In this work, we provide a new method to analytically study the effect of disorder, usingtools from quantum field theory applied to discrete model...
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... SSH model. One of the paradigmatic models to study non-Hermitian topological matter in one dimension is the non-Hermitian SSH model for fermions. The SSH model describes a bipartite one-dimensional chain with A and B sites obeying a sub-lattice symmetry (see Fig. S1 of the SM). Here, we consider the nonHermitian SSH model with intracell hopping that is nonreciprocal in its magnitude. This gives rise to a model in which it is easier to move in one direction than in the other. The corresponding real-space tight-binding Hamiltonian is given ...
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... the functions f 1,2 are introduced in Eq. (1). Note that W(E) is evaluated at E = 0. This is the natural choice of energy to calculate the vorticity because the non-Hermitian SSH model possesses sublattice symmetry. Fig. 1 shows the phase diagram of the non-Hermitian SSH model. It is noteworthy that this invariant renders all phases that are adiabatically connected to the Hermitian model (g = 0) indistinguishable from each other. This is a result of the purely non-Hermitian nature of the energy vorticity W ± (E). Upon including disorder in the ...
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... Fig. 2 shows the averaged energy vorticity of the nonHermitian SSH model for parameter choices corresponding to different regions in Fig. 1. From the figure, it is clear that the introduction of disorder drives the system from a topological to a trivial phase when the disorder strength is around four times the energy scale w. We observe that W + (0) (W − (0)) is driven from minus (plus) one to zero [ Fig. 2(a)]. For phases where either W ± (0) is already zero in the ...
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... the remainder of this section, we will set E = 0, which we argued to be the correct choice in the main text. The phase diagram corresponding to Eq. (S11) is shown in Fig. 1. It is noteworthy that this invariant renders all phases that are adiabatically connected to the Hermitian model (g = 0) indistinguishable from each other. This is a result of the purely non-Hermitian nature of the energy vorticity W ± (E). In order to find the self-energy for delta-peaked disorder, we first evaluate ...
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