Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the necessary condition of critical skin effect.
In this paper, we investigate theoretically the spin-orbit torque as well as the Gilbert damping for a two band model of a 2D helical surface state with a Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the spin-orbit torque (SOT). Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D Topological Insulator (TI) and predicted its dependence on the direction of the magnetization precession axis.
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the…
We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum system, which does not rely on boundary conditions. We define the value of information constraint ($I_C$) as the ratio of different decay rates and derive the analytical representation of $I_C$ for general quadratic Lindbladian systems. Based on information constraint, we can provide a simple and elegant explanation of chiral and helical damping, and get the local maxi…
We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase tr…
Nontrivial topology of interfaces separating anti-chiral phases in helical magnets result in new effects as they interact with spin polarized current. These interfces or vortex walls consist of a one dimensional array of vortex lines. Topological Hall effect comes as a natural expectation. Also Lenz's law will result in a new damping mechanism in these systems. We study the dynamics of these wall interacting with electric current and use fundamental electromagntic laws to calculate this effect. On the other hand discrete nature of these walls affects their pinning and result in low depinning c…
Non-Hermitian skin effect was observed in one-dimensional systems with short-range chiral interaction. Long-range chiral interaction mediated by traveling waves also favors the accumulation of energy, but has not yet showed non-Hermitian topology. Here we find that the strong interference brought by the wave propagation is detrimental for accumulation. By suppression of interference via the damping of traveling waves, we predict the non-Hermitian skin effect of magnetic excitation in a periodic array of magnetic nanowires that are coupled chirally via spin waves of thin magnetic films. The loc…
We study theoretically helical edge states of 2D and 3D topological insulators (TI) tunnel-coupled to metal leads and show that their transport properties are strongly affected by contacts as the latter play a role of a heat bath and induce damping and relaxation of electrons in the helical states of TI. A simple structure that produces a pure spin current in the external circuit is proposed. The current and spin current delivered to the external circuit depend on relation between characteristic lengths: damping length due to tunneling, contact length and, in case of 3D TI, mean free path and …
We present magnetotransport measurements in HgTe quantum well with inverted band structure, which expected to be a two-dimensional topological insulator having the bulk gap with helical gapless states at the edge. The negative magnetoresistance is observed in the local and nonlocal resistance configuration followed by the periodic oscillations damping with magnetic field. We attribute such behaviour to Aharonov-Bohm effect due to magnetic flux through the charge carrier puddles coupled to the helical edge states. The characteristic size of these puddles is about 100 nm.
We analyze a correlated system in equilibrium with special emphasis on non-Hermitian topology inducing a skin effect. The pseudo-spectrum, computed by the real-space dynamical mean-field theory, elucidates that additional pseudo-eigenstates emerge for the open boundary condition in contrast to the dependence of the density of states on the boundary condition. We further discuss how the line-gap topology, another type of non-Hermitian topology, affects the pseudo-spectrum. Our numerical simulation clarifies that while the damping of the quasi-particles induces the non-trivial point-gap topology…
The interplay between dissipation, topology and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open boundary condition (OBC) and periodic boundary condition (PBC). We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution o…
We present the microscopic treatment of edge magnetoplasmons (EMPs) for the regime of not-too-low temperatures defined by the condition $\hbar ω_{c}\gg k_{B}T\gg \hbar v_{g}/2\ell_{0}$, where $v_{g}$ is the group velocity of the edge states, $\ell_{0}=\sqrt{\hbar /m^{\ast}ω_{c}}$ is the magnetic length and $ω_{c}$ is the cyclotron frequency. We find a weakly damped symmetric mode, named helical edge magnetoplasmon, which is localized at the edge states region for filling factors $ν=1, 2$ and \textit{very strong dissipation} $η_{T}=ξ/k_{x}\ell_{T}\agt\ln (1/k_{x}\ell_{T})\gg 1$, where the chara…
Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical ed…
We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity a…
