Observation of dislocation bound states and skin effects in non-Hermitian Chern insulators

TL;DR

The study tackles how non-Hermitian topology interfaces with crystalline defects by realizing a line-gap NH Chern insulator in a 2D acoustic lattice featuring an edge dislocation-antidislocation pair. The authors implement programmable active couplings to realize imaginary hoppings and perform Green's-function spectroscopy to directly measure complex spectra and biorthogonal eigenstates. They observe dislocation-bound states within the line gap (NHDS) and a dislocation-induced NH skin effect (D-NHSE), and show that exceptional points drive a localization-delocalization transition that melts NHDS into bulk/skin states. The work establishes defective sites as versatile probes of NH topology and points to defect-engineered devices for acoustic applications and sensing.

Abstract

The confluence of non-Hermitian (NH) topology and crystal defects has culminated significant interest, yet its experimental exploration has been limited due to the challenges involved in design and measurements. Here, we showcase experimental observation of NH dislocation bound states (NHDS) and the dislocation-induced NH skin effect in two-dimensional acoustic NH Chern lattices. By embedding an edge dislocations-antidislocation pair in such acoustic lattices and implementing precision-controlled hopping and onsite gain/loss via active meta-atoms, we reveal robust defect-bound states localized at dislocation cores within the line gap of the complex energy spectrum. We experimentally identify the emergence of bulk exceptional points (EPs) via spectral coalescence and phase rigidity analysis. We demonstrate that the NHDS survive against moderate NH perturbations but gradually delocalize and merge with the bulk (skin) states driven by these EPs under periodic (open) boundary conditions. Furthermore, our experiments demonstrate that the dislocation core can feature weak NH skin effects when its direction is perpendicular to the Burgers vector in periodic systems. Our findings, therefore, pave an experimental pathway for probing NH topology via lattice defects and open new avenues for defect-engineered topological devices.

Figures (7)

• Figure 1: (A) Schematic implementation of a NH Chern insulator [Eq. \ref{['eq:Hamiltonian']}] in the presence of an edge dislocation-antidislocation pair with Burgers vectors $\vb{b} = \pm a \vb{e}_x$, where $\vb{e}_x$ is the unit vector in the $x$ direction and $a$ is the lattice spacing, set to be unity. Each unit cell consists of two sites labeled by a (red ball) and b (blue ball). Solid bars of the same color represent the reciprocal hopping amplitudes of equal strength, and those with arrows indicate nonreciprocal hopping amplitudes. Bottom left inset shows the top view, where circles represent unit cells. (B, C) Phase diagram of NH Chern insulators with NH perturbations for (B) $h_x$ (or $h_y$) and (C) $h_z$. The eigenenergies are line-gapped only in the red and blue shaded regions, where the NH Chern number is $C=-1$ and $C=1$, respectively. White regions support EPs. Experimental measurements are performed along the dashed gray lines.
• Figure 2: (A) A photograph of the experimental setup. The acoustic non-Hermitian lattice consists of an array of acoustic cavities, where 56 are used in the final configuration. Onsite potential and hoppings are implemented using microphone-loudspeaker pair. The hoppings are tuned using phase shifters integrated in a controller. (B) Sketch of tuning onsite potential of acoustic cavities. (C) Measured and fitted magnitude responses for two typical configurations that emulate the sublattices: (C1) sublattice 'a' and (C2) sublattice 'b' within a unit cell as annotated in Fig. 1A. (D) Schematic illustration of the unidirectional hopping implmeneted using a detector and a source. The bottom microphone (tuning detector) in cavity 1 captures the acoustic pressure signal, which is processed by the controller to adjust its phase and amplitude before being emitted by the bottom loudspeaker (tuning source) in cavity 2. Experimentally measured and numerically fitted amplitude (E1 and F1) and phase (E2 and F2) responses of the cross-power spectral density between the acoustic signals measured in cavities 1 and 2.
• Figure 3: Experimental observation of bulk EPs in a pristine $4\times 4$ acoustic Chern lattice without dislocations under PBCs with NH perturbations for $t_0=-m_0 = 3\,\mathrm{Hz}$. (A, B, C) Experimental observations and (D, E, F) corresponding theoretical predictions of the complex energy spectra. The spectra are shown for varying NH perturbation strengths $h_x$ (A, D), $h_y$ (B, E), and $h_z$ (C, F) at values of $0.9t_0$ (left), $1.0t_0$ (middle), and $1.1t_0$ (right). The phase rigidity, $r_n$, of the $n$th state is indicated by the color bar. (G1--G3) Measured (red) and predicted (blue) averaged phase rigidity of all near-zero-energy states as a function NH perturbation strength $h_j$ for $j=x,y,z$. (H1--H3) The energy gap, $\Delta E$, defined in (A1) as a function of NH perturbation strength $h_j$ for $j=x,y,z$. Here, $\Delta E_0 = 6\,\mathrm{Hz}$ denotes the line gap in the Hermitian limit ($h_x=h_y=h_z=0$).
• Figure 4: Hermitian ($\vb{h}=0$) acoustic Chern insulators in the presence of an edge dislocation-antidislocation pair under PBCs, showing (A1)-(E1) experimental observations and (A2)-(E2) theoretical computations. Energy spectrum [(A1) and (A2)], amplitude distributions of right eigenstates of the dislocation modes, shown by red dots in (A1) and (A2) within unit cells [(B1) and (B2)] and all the states [(C1) and (C2)] in the ${\rm M}$ phase with $t_0=-m_0 = 3\,\mathrm{Hz}$. Energy spectra [(D1) and (D2)] and amplitude distributions of all the right eigenstates [(E1) and (E2)] in the $\Gamma$ phase with $t_0=m_0 = 3\,\mathrm{Hz}$.
• Figure 5: (A, C, E) Experimental observations and (B, D, F) corresponding theoretical predictions on an acoustic Chern lattice with an edge dislocation-antidislocation pair under PBCs and moderate NH perturbations for $t_0=-m_0 = 3\,\mathrm{Hz}$. (A1, B1) Complex energy spectrum for $\vb{h}=(1.8\,\mathrm{Hz},0,0)$. (A2, B2) Total amplitude of two right eigenvectors of NHDS marked by red dots in (A1, B1). (A3, B3) Total amplitude of all the right eigenstates from (A1, B1). Panels (C)-(D) [(E)-(F)] are analogous to (A)-(B), respectively, but with $\vb{h}=(0, 1.8\,\mathrm{Hz},0)$ [$\vb{h}=(0, 0, 1.8\,\mathrm{Hz})$].