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.
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.
Non-Hermitian skin effect, which is a unique feature of non-Hermitian systems, exhibits the formation of an extensive number of boundary modes under open boundary conditions. However, its manifestation in higher dimensions remains elusive. In our work, we demonstrate a hybrid skin-topological effect arising from the interplay between first-order band topology and non-reciprocal hopping in an engineered two-dimensional brick-wall geometry. The non-Hermitian brick-wall lattice under open boundary conditions in both directions exhibits several unconventional spectral features. Notably, the eigenvalues associated with the corner skin modes do not exhibit non-trivial windings in the complex energy plane; instead, they exhibit dynamically stable exceptional point-like features that do not originate from eigenvector coalescence. In contrast, the remaining modes accumulate at the opposite pair. Of all the corner skin modes, only the two that originate from the topological corner states of the Hermitian brick-wall lattice remain localized at individual corners, while the rest accumulate at the pair of opposite corners. This spatial distribution contrasts sharply with the second-order skin effect, where corner skin modes are more uniformly distributed. Finally, for the non-Hermitian Brick-wall lattice, we design and implement the corresponding topolectrical circuit (circuit for a square lattice is included for comparison) to directly visualize the hybrid skin-topological modes.
We investigate the non-Hermitian skin effect (NHSE) and topological phases in a ladder model with staggered nonreciprocal inter-leg hopping, consisting of an Su-Schrieffer-Heeger (SSH) chain coupled to a normal tight-binding chain. By tuning the system parameters, we show that the direction of the NHSE under open boundary conditions can be reversed and can even become energy dependent. The NHSE is further characterized by the spectral winding number under periodic boundary conditions. We further demonstrate that the inter-leg coupling significantly enlarges the topologically nontrivial parameter regime. Remarkably, the zero-energy topological edge modes reside on different legs of the ladder and are characterized by real-space winding numbers W=±1. Furthermore, increasing the nonreciprocity of the inter-leg hopping modifies the topological phase boundaries and eventually drives the system into a topologically trivial phase. Our results establish staggered nonreciprocal inter-leg hopping as an effective mechanism for engineering both the non-Hermitian skin effect and topological phases in ladder systems.
Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme of constructing non-Abelian HOTPs and analyze a non-Abelian second-order topological insulator as its minimal model. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time-reversal plus sublattice symmetries and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origins arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits both non-Abelian and Abelian topological phase transitions, providing a unified platform that bridges these two distinct topological classes. Our work extends the understanding of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum systems, such as photonic or acoustic metamaterials.
The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of mid-gap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.
The non-Hermitian skin effect (NHSE) -- the anomalous boundary accumulation of an extensive number of bulk modes -- has emerged as a hallmark of non-Hermitian physics, with broad implications for transport, sensing, and topological classification. A central open question is how magnetic or synthetic gauge fields influence this boundary phenomenon. Here, we develop a theoretical framework for magnetic control of the NHSE along line boundaries in two-dimensional single-band lattices. Using a non-Hermitian extension of the anisotropic Harper--Hofstadter model as a representative example, we show that magnetic fields suppress the geometric skin effect in reciprocal models, whereas skin localization can persist in nonreciprocal systems. The analysis disentangles the interplay of flux, nonreciprocity, and boundary geometry, revealing that magnetic fields mitigate or suppress the NHSE through distinct physical mechanisms -- such as bulk localization via Landau or Anderson physics, or the restoration of effective reciprocity. In particular, the geometry-dependent skin effect in reciprocal systems is found to be fragile against even weak magnetic fields.
Conventional Chern insulators rely on breaking time-reversal symmetry via magnetic fields or synthetic gauge fields. Here we introduce a fundamentally different paradigm: a static lattice without any gauge field becomes a Chern insulator solely through the cooperation of two non-Hermitian ingredients: on-site loss and non-reciprocal coupling. Neither effect alone suffices; only their synergy opens a topological gap and gives rise to robust chiral edge states with a nonzero Chern number. The underlying mechanism originates from a non-Hermitian chiral molecule formed by the lossy sites, whose dynamically dominant mode carries an orbital angular momentum that effectively generates a synthetic flux after the fast-decaying degrees of freedom are eliminated. Our results establish non-Hermitian cooperation as a versatile resource for inducing Chern topology without external fields or temporal modulations, opening a new route to topological phases in open classical and quantum systems.