Abstract
In this work, the authors show that it is possible to realize an anomalous configuration of Weyl cones in a three-dimensional, non-Hermitian Weyl semimetal. It is thus possible to probe the boundary physics of four-dimensional quantum Hall models in three-dimensional setups with gain and loss.
Highlights
Topological phases of matter have been at the forefront of research in condensed-matter physics over the last decades [1,2,3,4,5,6,7,8]
We find that introducing modulated gain and loss in the Weyl semimetal (WSM), which renders the Hamiltonian of the model non-Hermitian (NH), results in the appearance of an anomalous configuration of Weyl cones in the bulk spectrum in the long-time limit: The spectrum of NH Hamiltonians is generally complex, where the imaginary part is associated with the inverse lifetime, such that only states with Im(E ) > 0 survive when t → ∞ [34]
The three-dimensional NH WSM studied in this paper is ensured to be equivalent to the four-dimensional quantum Hall (QH) system by making use of arguments that are grounded in topology
Summary
Topological phases of matter have been at the forefront of research in condensed-matter physics over the last decades [1,2,3,4,5,6,7,8]. The three-dimensional NH WSM studied in this paper is ensured to be equivalent to the four-dimensional QH system by making use of arguments that are grounded in topology This means that there exists a connection between the topological invariants of the two models: Whereas the chiralities of the Weyl cones that appear in the bulk spectrum of the NH WSM are found to be directly related to the values of the second Chern number of the QH model, we find that the total chirality of the Weyl cones in the positive imaginary energy plane is given by a three-dimensional spectral winding number [35], which captures the point-gap topology of the NH WSM, where point gaps are a purely NH phenomenon with the complex energy bands not crossing a reference point [35] [cf Fig. 2(a)].
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