Observation of gauge field induced non-Hermitian helical skin effects

Abstract

Synthetic gauge fields and non-Hermitian skin effects are pivotal to topological phases and non-Hermitian physics, each recently attracting great interest across diverse research fields. Realizing skin effects typically require nonreciprocal couplings or on-site gain and loss. Here, we theoretically and experimentally report that, under gauge fields, reciprocal dissipative couplings can nontrivially give rise to an unprecedented nonreciprocal skin effect, hosting pseudospin degree of freedom and featuring helical transport, dubbed as the ``helical pseudospin skin effect". Before introducing the gauge fields, this model exhibits localized pseudospin edge modes and extended bulk modes, without skin effects. As the gauge field strength is applied from $0$ to $π$, we observe the emergence of two distinct pseudospin skin effects and their topological transitions: the hybrid-order and second-order helical pseudospin skin effects. Our findings not only highlight gauge field enriched non-Hermitian topology, but also brings pseudospin-momentum locking into skin effects.

Figures (4)

• Figure 1: Schematic of HSEs induced and enriched by gauge fields. In a non-Hermitian system with reciprocal couplings and without on-site gain and loss, nonreciprocal SEs are generally not expected. This work shows that the introduction of gauge fields into such system can induce nonreciprocal HSEs. For the zero gauge field ($\theta = 0$), the system hosts localized pseudospin edge modes and extended bulk modes, while no SEs are observed. When the gauge field is turned on ($\theta > 0$), the pseudospin-up and pseudospin-down eigenmodes are respectively accumulated towards opposite corners or edges of the $x$-direction, regardless of whether they are edge or bulk modes, resulting in hybrid-order HSEs. When $\theta=\pi$, the pseudospin-up and pseudospin-down edge modes continue to collapse towards opposite corners, while the bulk modes begin to delocalize, leading to second-order HSEs. Reversing the sign of the gauge field phase can flip the directions of the HSEs.
• Figure 2: Model and helical SEs. (a) Non-Hermitian lattice model with reciprocal dissipative couplings $-it_3$ and synthetic gauge fields $e^{i\theta}$. (b) Energy spectra under different boundary conditions, varying with five distinct gauge field phases. (c) Density distributions for all the pseudospin-up and pseudospin-down modes as a function of $\theta$ for four different y. The black and green dashed lines indicate the points where the SE vanishes for the edge and bulk modes, respectively. As shown, with increasing $\theta$, the pseudospin-up and pseudospin-down skin modes feature helical evolutions along the x-direction. The parameters are $t_1 = 0.22t_2$, $t_3 = 0.5t_2$, $N_x = 20$ and $N_y = 10$.
• Figure 3: Implementation of synthetic gauge fields and measurement of topological winding numbers. (a) Schematic of the couplings between two unit cells. The coordinates for each unit cell are labelled as $(m,n)$. (b) The corresponding printed circuit board. (c) Specific circuit connections for implementing $t_1$, $t_2$, $\pm t_3$, $\pm t_3e^{i\theta}$ and $-it_3$ to implement the gauge field phase $\theta=\pi/2$. (d) The left panel shows measured (circles) and simulated (lines) energy spectra under x-PBC and y-OBC at $\theta = \pi/2$, while the right panel presents the corresponding three-dimensional illustration of the spectral winding topology
• Figure 4: Observation of non-Hermitian HSEs. Measured and simulated density distributions for pseudospin-up $(a)$ and pseudospin-down $(b)$ edge modes varying with the gauge field phases $\theta = -\pi, -\pi/2, 0, \pi/2, \pi$. (c,d) Same as (a,b) but for the bulk modes. As shown, for the gauge field phase $\theta = 0$, the system exhibits no SE. While for $\theta=\pm\pi/2$, the system exhibits a hybrid-order HSE, where pseudospin-up and pseudospin-down edge and bulk modes are maximally localized at opposite boundaries. At $\theta =\pm\pi$, the system transitions to a second-order HSE, with only edge modes remaining localized.