Reversing non-Hermitian skin accumulation with a non-local transverse switch

Abstract: Asymmetrically directed couplings in non-Hermitian systems cause directional amplification that leads to boundary skin state accumulation. However, counter-intuitively, the direction of accumulation may not follow that of the directed couplings. In this work, we demonstrate new mechanisms where this accumulation can be systematically reversed without modifying the couplings at all, just by adjusting the system size or boundary conditions in a different, transverse direction. Moreover, the reversed skin dynamics can be made very robust by suppressing the amplification in the original non-reversed direction. We motivate our approach through a series of warm-up models, culminating in a designed non-Hermitian Kagome lattice whereby wavepacket simulations demonstrate how robust reversed skin dynamics can be switched on/off in a non-local transverse manner. Our findings highlight how the non-trivial entanglement between the spectral loops of different PBC directions can be harnessed as a directional amplification switch, paving the way for new avenues of non-Hermitian sensing and lasing.