Topological phases have recently witnessed a rapid progress in non-Hermitian systems. Here we study a one-dimensional non-Hermitian Aubry-André-Harper model with imaginary periodic or quasiperiodic modulations. We demonstrate that the non-Hermitian off-diagonal AAH models can host zero-energy modes at the edges. In contrast to the Hermitian case, the zero-energy mode can be localized only at one edge. Such a topological phase corresponds to the existence of a quarter winding number defined by eigenenergy in momentum space. We further find the coexistence of a zero-energy mode located only at one edge and topological nonzero energy edge modes characterized by a generalized Bott index. In the incommensurate case, a topological non-Hermitian quasicrystal is predicted where all bulk states and two topological edge states are localized at one edge. Such topological edge modes are protected by the generalized Bott index. Finally, we propose an experimental scheme to realize these non-Hermitian models in electric circuits. Our findings add a new direction for exploring topological properties in Aubry-André-Harper models. arXiv:1901.08060v2 [cond-mat.mes-hall]

We investigate a generalized Aubry-André-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of 1/α. In the incommensurate case [α = ( √ 5 − 1)/2], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case (α = 1/2), we find that this model shows three different phases when we tune the system parameters: SuSchrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases.

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays 4π periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD-Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.

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