Universal non-Hermitian valley filtering via uniform dissipation

Abstract

Valley, as a ubiquitous degree of freedom in lattices, has found wide applications in both electronic and classical-wave devices in recent years. However, achieving valley-polarized states, a prerequisite for valley-based operations, still remains challenging. Here, we propose and experimentally demonstrate a universal non-Hermitian mechanism for valley filtering using only uniform background dissipation, which creates a propagation length contrast between valleys through their intrinsic group velocity differences. We implement this concept in an acoustic crystal, observing switchable and robust valley polarization of sound through large-scale field mapping. Remarkably, our approach is solely based on uniform loss, without the need for any special lattice structures, tailored excitations, or external fields. We further provide designs of our non-Hermitian valley filter on photonic and electronic platforms. Our results offer a simple and effective solution to valley-polarized state generation and may advance the development of novel valley-based devices in both classical and quantum regimes.

Figures (4)

• Figure 1: General construction of the non-Hermitian valley filter. (a) Schematic of a non-Hermitian valley filter on a graphene lattice with a uniform background dissipation. The inset illustrates the unequal decay rates of the modes at the two valleys due to the difference in their group velocity. (b) Band diagram for the model in (a) under a slab geometry with 20 unit cells along the $y$ direction. The color represents the group velocity. (c)-(d) Propagation lengths of the right-moving modes near the valleys inside the energy windows indicated by the grey boxes in (b). (e) Calculated valley polarizations against propagation distance for left-moving (blue curve) and right-moving modes (red curve) at $E=0.4$. In all calculations, we set the lattice constant to be unity, $t=1$, $m=0.2$, and $\gamma=0.1$.
• Figure 2: Non-Hermitian valley filter in an acoustic crystal. (a) Schematic of the experimental setup, consisting of the fabricated sample, a speaker, a microphone, and a signal generation and data acquisition system. The inset shows the structural detail of the unit cell. (b) Band diagram for the acoustic crystal under a slab geometry with 13 unit cells along the $y$ direction. The color represents the imaginary part of the eigenfrequency. (c) Propagation lengths of the right-moving modes near the valleys inside the frequency windows indicated by the grey boxes in (b). (d) Measured (solid curves) and simulated (dashed curves) valley polarizations under an excitation at the left side of the sample [indicated by the red star in (a)]. The valley polarization is calculated using the fields inside a region whose center is 1846.25 mm away from the source. The insets show the intensity and phase distributions inside a small area in the measured region. (e) Measured Fourier spectra at the frequencies indicated by the black arrows in (d). The hexagon and the circle denote the first Brillouin zone and the area to evaluate the weights of the two valleys, respectively. (f)-(g) The same as (d) and (e) but for a right-side excitation.
• Figure 3: Analysis of the acoustic non-Hermitian valley filter. (a) Plots of the measured (red dots) and simulated (black curve) acoustic intensities against propagation distances at 8420 Hz. The dashed lines represent the decays of the three eigenmodes at the same frequency. The insets show the enlarged plots of the measured data at the early and later stages of the propagation, with the dashed lines showing the linear fits. (b) Plots of the measured (red dots) and simulated (black curve) valley polarizations against propagation distances at 8420 Hz. The insets display the measured Fourier spectra at three selected propagation distances.
• Figure 4: Valley filtering performance under arbitrary excitation positions. The plot shows the measured (solid curves) and simulated (dashed curves) valley polarizations under an excitation at the grey triangle, purple square, and green hexagon in Fig. \ref{['fig2']}(a).