Topological Corner States in Non-Unitary Coinless Discrete-Time Quantum Walks

Abstract

The discrete-time quantum walk provides a versatile platform for exploring abundant topological phenomena due to its intrinsic spin-orbit coupling. In this work, we study the non-Hermitian second-order topology in a two-dimensional non-unitary coinless discrete-time quantum walk, which is realizable in the three-dimensional photonic waveguides. By adding the non-unitary gain-loss substep operators into the one-step operator of the coinless discrete-time quantum walk, we find the appearance of the four-degenerate zero-dimensional corner states at ReE = 0 when the gain-loss parameter of the system is larger than a critical value. This intriguing phenomenon originates from the nontrivial second-order topology of the system, which can be characterized by a second-order topological invariant of polarizations. Finally, we show that the exotic corner states can be observed experimentally through the probability distributions during the multistep non-unitary coinless discrete-time quantum walks. Our work potentially pave the way for exploring exotic non-Hermitian higher-order topological states of matter in coinless discrete-time quantum walks.