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Register a new userDisorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
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Non-Hermitian skin effect exhibits the collapse of the extended bulk modes into the extensive number of localized boundary states in open boundary conditions. Here we demonstrate the disorder-driven phase transition of the trivial non-Hermitian system to the higher-order non-Hermitian skin effect phase. In contrast to the clean systems, the disorder-induced boundary modes form an arc in the complex energy plane, which is the manifestation of the disorder-driven dynamical phase transition. At the phase transition, the localized corner modes and bulk modes characterized by trivial Hamiltonian coexist within the single-band but are separated in the complex energy plane. This behavior is analogous to the mobility edge phenomena in the disordered Hermitian systems. Using effective medium theory and numerical diagonalizations, we provide a systematic characterization of the disorder-driven phase transitions.
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We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle which is an integer multiple of $2pi$, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the effective surface Dirac fermion(s) in the presence of a pseudomagnetic flux induced by disclinations. Furthermore, we find that our results have a field theoretic description, and the corresponding geometric response actions (e.g., the Euclidean Wen-Zee action) enrich the topological field theory of non-Hermitian systems.
Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-Andr{e} model, and a textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a textit{bulk-bulk} correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.
In conventional Hermitian systems with the open boundary condition, Blochs theorem is perturbatively broken down, which means although the crystal momentum is not a good quantum number, the eigenstates are the superposition of several extended Bloch waves. In this paper, we show that Blochs theorem can be non-perturbatively broken down in some Hermitian Bosonic systems. The quasiparticles of the system are the superposition of localized non-Bloch waves, which are characterized by the complex momentum whose imaginary part determines the localization properties. Our work is a Hermitian generalization of the non-Hermitian skin effect, although they share the same mechanism.
Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness - topological protection, as well as the non-Hermitian skin effect. In this work, we report the first experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various novel states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for new applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.
Based on a general transport theory for non-reciprocal non-Hermitian systems and a topological model that encompasses a wide range of previously studied models, we (i) provide conditions for effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption, (ii) identify which effects are compatible and linked with each other, and (iii) determine by which levers they can be tuned independently. For instance, the directed amplification inherent in the non-Hermitian skin effect does not enter the spectral conditions for reflectionless transport, lasing, or coherent perfect absorption, but allows to adjust the transparency of the system. In addition, in the topological model the conditions for reflectionless transport depend on the topological phase, but those for coherent perfect absorption do not. This then allows us to establish a number of distinct transport signatures of non-Hermitian, nonreciprocal, and topological behaviour, in particular (I) reflectionless transport in a direction that depends on the topological phase, (II) invisibility coinciding with the skin-effect phase transition of topological edge states, and (III) coherent perfect absorption in a system that is transparent when probed from one side.
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