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Register a new userThe topological counterparts of non-Hermitian SSH models
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The breakdown of the conventional bulk-boundary correspondence due to non-Hermitian skin effect leads to the non-Bloch bulk-boundary correspondence in the generalized Brillouin zone. Inspired by the case of the equivalence between the non-reciprocal hopping and imaginary gauge field, we propose a method to construct the topological equivalent models of the non-Hermitian dimerized lattices with the similarity transformations. The idea of the constructions is from that the imaginary magnetic flux vanishes under the open boundary condition and the period boundary spectra can be well approximated by open boundary spectra. As an illustration, we apply this approach to several representative non-Hermitian SSH models, efficiently obtaining topological invariants in analytic form defined in the conventional Bloch bands. The method gives an alternative way to study the topological properties of non-Hermitian system.
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We study coupled non-Hermitian Rice-Mele chains, which consist of Su-Schrieffer-Heeger (SSH) chain system with staggered on-site imaginary potentials. In two dimensional (2D) thermodynamic limit, the exceptional points (EPs) are shown to exhibit topological feature: EPs correspond to topological defects of a real auxiliary 2D vector field in k space, which is obtained from the Bloch states of the non-Hermitian Hamiltonian. As a topological invariant, the topological charges of EPs can be $pm$1/2, obtained by the winding number calculation. Remarkably, we find that such a topological characterization remains for a finite number of coupled chains, even a single chain, in which the momentum in one direction is discrete. It shows that the EPs in the quasi-1D system still exhibit topological characteristics and can be an abridged version for a 2D system with symmetry protected EPs that are robust in perturbations, which proves that topological invariants for a quasi-1D system can be extracted from the projection of the corresponding 2D limit system on it.
Nonlinearities in lattices with topologically nontrivial band structures can give rise to topological solitons, whose properties differ from both conventional lattice solitons and linear topological boundary states. We show that a Su-Schrieffer-Heeger-type lattice with both nonlinearity and nonreciprocal non-Hermiticity hosts a novel oscillatory soliton, which we call a topological end breather. The end breather is strongly localized to a self-induced topological domain near the end of the lattice, in sharp contrast to the extended topological solitons previously found in one-dimensional lattices. Its stable oscillatory dynamics can be interpreted as a Rabi oscillation between two self-induced topological boundary states, emerging from a combination of chiral lattice symmetry and the non-Hermitian skin effect. This demonstrates that non-Hermitian effects can give rise to a wider variety of topological solitons than was previously known to exist.
We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the non-Hermitian skin effect in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of $mathcal{PT}$-symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to identify different Floquet topological phases of time periodic non-Hermitian systems via the generation of Floquet band gaps in frequency space. In non-Floquet theory, the eigenstates of non-Hermitian Floquet Hamiltonian are temporally deformed to be of Wannier-Stark localization. Remarkably, we show that different choices of starting points of driving period can result to different localization behavior, which effect can reversely be utilized to design detectors of quantum phases in dissipative oscillating fields. Our protocols establish a fundamental rule for describing topological features in non-Hermitian dynamical systems and can find its applications to construct new types of Floquet topological materials.
Non-Hermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulk-boundary correspondence. Here, we implement the non-Hermitian Su-Schrieffer-Heeger (SSH) Hamiltonian, which is a prototypical model for studying non-Hermitian topological phases, with a solid-state quantum simulator consisting of an electron spin and a $^{13}$C nuclear spin in a nitrogen-vacancy (NV) center in a diamond. By employing a dilation method, we realize the desired non-unitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. Our result paves the way for further exploiting and understanding the intriguing properties of non-Hermitian topological phases with solid-state spins or other quantum simulation platforms.
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