Non-Hermitian skin effect without point-gap topology in 2D quasicrystals

The non-Hermitian skin effect refers to the accumulation of an extensive number of eigenstates at the boundaries of particular dissipative systems. This phenomenon has sparked widespread interest across various fields of physics. It has been dramatically improving our understanding of non-Hermitian systems and paving the way for new opportunities in fundamental and applied research of topological phenomena. It is generally believed to be associated with a nontrivial point-gap spectral topology. Nevertheless, we report observing the non-Hermitian skin effect without point-gap topology in the two-dimensional nonreciprocal Hofstadter model subjected to an incommensurate magnetic field- a quasicrystal. Under periodic boundary conditions, the spectrum is real without point-gap topology but has significant degeneracy. However, when open boundary conditions are applied, eigenstates are exponentially localized at edges, showing the non-Hermitian skin effect, and the degeneracy is broken. This degeneracy-breaking-induced non-Hermitian skin effect results in anomalous wave packet dynamics. It is commonly believed that non-trivial complex spectral winding is necessary for the non-Hermitian skin effect. However, in this work, the authors show how this requirement can be circumvented through the interplay of non-reciprocal couplings and flat bands in a quasi-periodic setting.