Localization Properties of a Quasiperiodic Ladder under Physical Gain and Loss: Tuning of Critical Points, Mixed-Phase Zone and Mobility Edge

Abstract

We explore the localization properties of a double-stranded ladder within a tight-binding framework where the site energies of different lattice sites are distributed in the cosine form following the Aubry–André–Harper (AAH) model. An imaginary site energy, which can be positive or negative, referred to as physical gain or loss, is included in each of these lattice sites which makes the system a non-Hermitian (NH) one. Depending on the distribution of imaginary site energies, we obtain balanced and imbalanced NH ladders of different types, and for all these cases, we critically investigate localization phenomena. Each ladder can be decoupled into two effective one-dimensional (1D) chains which exhibit two distinct critical points of transition from metallic to insulating (MI) phase. Because of the existence of two distinct critical points, a mixed-phase (MP) zone emerges which yields the possibility of getting a mobility edge (ME). The conducting behaviors of different energy eigenstates are investigated in terms of inverse participation ratio (IPR). The critical points and thus the MP window can be selectively controlled by tuning the strength of the imaginary site energies which brings a new insight into the localization aspect. A brief discussion on phase transition considering a multi-stranded ladder was also given as a general case, to make the present communication a self-contained one. Our theoretical analysis can be utilized to investigate the localization phenomena in different kinds of simple and complex quasicrystals in the presence of physical gain and/or loss.

Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model

“…It was shown that an intermediate regime characterized by the coexistence of localized and extended states at different energies may occur 3,4 . The theoretical findings were confirmed in an experimental realization of a system with a single-particle mobility edge 5 .Recently, in non-Hermitian systems mobility edges have been explored for various 1D tight-binding models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In non-Hermitian systems, in comparison to the Hermitian ones, the mobility edges not only separate localized states from the extended states but also indicate the coexistence of complex and real energies.…”

“…Recently, in non-Hermitian systems mobility edges have been explored for various 1D tight-binding models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In non-Hermitian systems, in comparison to the Hermitian ones, the mobility edges not only separate localized states from the extended states but also indicate the coexistence of complex and real energies.…”

“…On the other hand, in the nonreciprocal lattices, MBC leads to the coexistence of extended and localized eigenstates even in the absence of any onsite potentials. Note that such a coexistence was shown to appear only in the presence of tailored quasi-periodical potentials and coupling constant [7][8][9][10][11][12][13][14][15][16][17][18][19][20] . However, we see it in our system as a result of the boundary condition sensitivity of the nonreciprocal non-Hermitian systems.…”

Spectral properties of two coupled Fibonacci chains

“…Although the behavior of aperiodic chains has been investigated extensively and in great detail, comparatively little work has been dedicated to the case where two or more chains are coupled to each other, forming an aperiodic ladder [11][12][13][14][15]. In this work, we take a step into this realm by analyzing a range of different coupling schemes between two identical one-dimensional Fibonacci chains.…”

Circular current in a one-dimensional Hubbard quasi-periodic Su–Schrieffer–Heeger ring

“…Due to such a non-zero critical point, the system provides different anomalous and divergent features which lead the scientist to proceed further and extract several exceptional properties as well as materialize different new areas in the branch of electronic and phononic transport. Along with AAH modulation [15][16][17][18][19][20][21][22][23][24][25][26], a further constraint can be introduced through hopping dimerization to extract more non-trivial features of the system. The Su-Schrieffer-Heeger (SSH) model [27][28][29][30][31][32][33][34][35][36] is a straightforward example of such kind of topological system.…”