Non-Hermitian higher-order topological insulators enabled by altermagnet engineering

TL;DR

Problem: engineering non-Hermitian higher-order topology in 2D systems. Approach: proximitize a non-Hermitian TI with an altermagnet to gap edge states ($H(oldsymbol{k})=H_ ext{TI}(oldsymbol{k})+H_ ext{NH}(oldsymbol{k})+H_ ext{AM}(oldsymbol{k})$) and enable nonreciprocal hopping to produce the NHSE; the resulting edge spectrum exhibits a winding number $\mathcal{W}(E)$ under cylindrical geometry. Key results: $\mathcal{W}(E)=+2$ for a given set of parameters and reverses to $\mathcal{W}(E)=-2$ when the nonreciprocal direction is flipped, aligning edge and corner localization, with a weak- to strong-coupling transition at $J_c \approx 0.57$ and a bipolar regime near finite $m_0$. Significance: demonstrates tunable altermagnetic control of skin–topological states with potential implementations in cold-atom, photonic, acoustic, circuit and electronic platforms.

Abstract

We show that proximitizing an altermagnet to a non-Hermitian topological insulator provides a powerful mechanism for engineering non-Hermitian higher-order topological phases. The altermagnetic order opens a gap at the topological edge states and drives a topological phase transition from a first-order to a second-order topological phase. When combined with nonreciprocal hopping, the system exhibits both the non-Hermitian skin effect and a hybrid skin-topological effect, whereby first-order edge states and second-order corner states accumulate at selected corners of the lattice. We demonstrate that the spectral winding number of the edge states under cylindrical geometry dictates this corner localization and can be reversed by tuning the altermagnetic order. Consequently, both edge and corner modes become directionally controllable. Our results establish altermagnets as a versatile platform for realizing and tuning skin-topological phenomena in non-Hermitian higher-order topological systems.

Figures (4)

• Figure 1: Energy spectrum and spatial distributions in the presence of strong altermagnetism. (a) Energy spectrum for a $30 \times 30$ square lattice under PBC (gray) and OBC (others), respectively. (b) Average probability distributions of bulk states under OBC. (c) Probability distributions of second-order corner states. The inset shows the average probability distributions of first-order edge states. (d) and (e) Real and imaginary parts of the energies as a function of $k_y$ for the system under OBC$_x$-PBC$_y$. Edge states with positive (negative) real energies are marked in blue (green). (f) Complex energy spectrum of the system under OBC$_x$-PBC$_y$. The insects show the spectrum winding of edge states. Parameters: $t_x=t_y=A_x=A_y=1$, $\delta_x=\delta_y=0.2$, $J=0.7$, and $m_0=0$.
• Figure 2: Weak altermagnetism case ($J=0.3$). (a) and (b) Real and imaginary parts of the energies as functions of $k_y$ for the system under cylindrical geometry. Topological edge states with positive (negative) real energies are marked in blue (green). (c) Complex energy spectrum of the edge states as a function of $k_y$. (d) Average probability distributions of bulk states under OBC. Inset: average probability distribution of zero states.
• Figure 3: The critical points with $J=0.57$. (a) Complex energy spectrum. (b) Average probability distribution of the bulk states. (c) Average probability distribution of the corner states and first-order edge states (inset) of the system under OBC. (d) The complex spectrum of the system under OBC$_x$-PBC$_y$. The inset shows the real parts of energies as a function of $k_y$.
• Figure 4: The bipolar skin-topological effect. (a) The gray points depict the energies of the edge states under OBC$_x$-PBC$_y$, while colorful points represent the energies under full OBC with $m_0=0.2$. The inset shows the complex spectrum under cylindrical geometry as a function of $k_y$. (b) Average probability distribution of the edge states under full OBC, with colors corresponding to the energies highlighted in (a).