Non-Hermitian Skin Effect and Electronic Nonlocal Transport

Abstract

Open quantum systems governed by non-Hermitian effective Hamiltonians exhibit unique phenomena, such as the non-Hermitian skin effect, where eigenstates localize at system boundaries. We investigate this effect in a Rashba nanowire coupled to a ferromagnetic lead and demonstrate that it can be detected via non-local transport spectroscopy: while local conductance remains symmetric, the non-local conductance becomes non-reciprocal. We account for this behavior using both conventional transport arguments and the framework of non-Hermitian physics. Furthermore, we explain that exceptional points shift in parameter space when transitioning from periodic to open boundary conditions, a phenomenon observed in other non-Hermitian systems but so far not explained. Our results establish transport spectroscopy as a tool to probe non-Hermitian effects in open electronic systems.

Figures (4)

• Figure 1: Rashba nanowire coupled to a ferromagnetic reservoir transport setup. Sketch of a semiconductor nanowire of length $L$ (yellow) strongly coupled to a grounded ferromagnet (gray), whose degrees of freedom are included through a spin-dependent self-energy $\Sigma$. The device is contacted by normal metallic leads $\alpha = \left\{\rm L, R\right\}$ (blue) at both sides that allow local and nonlocal transport measurements by varying the applied voltages $V_\alpha$ and measuring the resulting currents $I_\alpha$. Gate voltages $V_T$ and $V_G$ control the coupling strength to the leads and the chemical potential, respectively. An axial magnetic field $\vec{B}$ is applied parallel to the nanowire axis. In the helical regime, left-movers' spin is mostly parallel to the ferromagnet polarization axis ($\uparrow_y$), while right-movers' spin ($\downarrow_y$) is mostly antiparallel. Consequently, dissipation of left movers is favored over right movers. This is depicted schematically over the sketch.
• Figure 2: Local and nonlocal conductance. (a, d) Local conductance on both sides of the wire, $G_{\rm{LL}}$ and $G_{\rm{RR}}$, versus source voltage $V$ and Zeeman energy $B$. $G_{\rm{LL}}$ and $G_{\rm{RR}}$ are symmetric (equal). Conductance peaks at low $B$ bifurcate close to $B = \gamma_y$. $\gamma_y$ quantifies the spin-oriented dissipation. (b, c) Same as (a, d) but for nonlocal conductance. $G_{\rm{LR}}$ and $G_{\rm{RL}}$ are different (nonreciprocal) for large $B$. Parameters: $m^* = 0.023 m_e$, $\alpha = 10$meVnm, $\mu = 0$ meV, $L = 500$ nm, $\gamma_0 = \gamma_y = 0.05$ meV, and $a_0=5$ nm.
• Figure 3: Relation of the non-Hermitian skin effect with dissipation. (a) Real part of the bulk spectrum versus momentum along the wire, colored with the magnitude of its imaginary part. In the helical regime, the spin of the left (right) movers (represented by arrows) is locked to a direction mostly parallel (antiparallel) to the ferromagnet polarization axis $\hat{y}$. Thus, left movers are dissipated more than right movers. (b) Squared norm of the lowest-energy right eigenstates (orange) and LDOS (blue) along the wire axis of the finite-length device. Dashed (solid) lines distinguish parallel (antiparallel) spin components along the ferromagnet polarization axis. The right eigenstates are pushed to one end of the wire, a manifestation of the NHSE, which indicates the direction favored for transport. The LDOS remains symmetric, thus the local conductance results. Parameters as in Fig. \ref{['fig:cond']}, except for $L \rightarrow \infty$ in panel (a) and $L=5$$\rm \mu$m in panel (b).
• Figure 4: Non-Hermitian topological phase transition. (a, b) Spectrum of the bulk system before (a) and after (b) the topological phase transition at $B = \gamma_y$. In (a), there is a gap in the imaginary part around the spin-independent dissipation $\gamma_0$, while in (b), there is a gap in the real part around the chemical potential $\mu$. (c) Local conductance at one end of the device versus Zeeman energy $B$. The four lowest-energy levels are overplotted with different colors. Vertical black dashed line indicates the bulk topological phase transition. For the lower (upper) pair, Eq. \ref{['eq:kappa']} predicts an exceptional point at the white (blue) dashed line, matching the conductance peak bifurcations. Parameters as in Fig. \ref{['fig:cond']} except for $L \rightarrow \infty$ for panels (a, b)