Non-Hermitian topological Anderson insulators

Abstract

Non-Hermitian systems can exhibit exotic topological and localization properties. Here we elucidate the non-Hermitian effects on disordered topological systems by studying a nonreciprocal disordered Su-Schrieffer-Heeger model. We show that the non-Hermiticity can enhance the topological phase against disorders by increasing energy gaps. Moreover, we uncover a topological phase which emerges only under both moderate non-Hermiticity and disorders, and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes. Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators. We also find that the system has unique non-monotonous localization behaviour and the topological transition is accompanied by an Anderson transition.Topological states of matter have been widely explored in condensed-matter materials [1-5] and various engineered systems, which include ultracold atoms [6-8], photonic lattices [9, 10], mechanic systems [11], classic electronic circuits [12][13][14][15], and superconducting circuits [16][17][18][19][20]. One hallmark of topological insulators is the robustness of nontrivial boundary states against certain types of weak disorders, since the topological band gap (topological invariants) preserves under these perturbations [1][2][3]. However, the band gap closes for sufficiently strong disorders and the system becomes trivial as all states are localized according to the Anderson localization [21]. Surprisingly, there is a topological phase driven from a trivial phase by disorders, known as topological Anderson insulator (TAI) [22]. The TAI was first predicted in two-dimensional (2D) quantum wells and then shown to exhibit in a wide range of systems [22][23][24][25][26][27][28][29][30], such as Su-Schrieffer-Heeger (SSH) chains [31]. Recently, the TAI has been observed in one-dimensional (1D) cold atomic wires and 2D photonic waveguide arrays [32,33].

Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential

“…We consider a BEC in a symmetric double-well trapping potential with N weakly interacting atoms, and assume that the atoms are coherently transferred from one well to the other with laser-induced tunable nonreciprocal hopping [44]. Within the two-mode approximation [55][56][57][58][63][64][65][66], the system can be described by the following two-site Bose-Hubbard Hamiltonian with the nonreciprocal hopping [13][14][15][16][17][18][19][20][21][22][23][24][25][26]:…”

“…Apart from the gain-and-loss effect, the nonreciprocity is another kind of non-Hermiticity. It has been theoretically revealed that nonreciprocal systems exhibit exotic topological and localization physics [4,5,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In experiments, the nonreciprocity can be realized in classical electric circuits [27,28], optical systems [29][30][31][32][33][34][35][36][37], and optomechanical devices [38][39][40][41][42][43].…”

A Perfect Andreev Reflection Induced by Anderson Disorder in a Normal–Superconductor Junction

“…Since proposed, TAI has attracted lots of attentions. Recently, this concept has been extended to Anderson topological superconductors, [25] non-Hermitian TAI, [26] and higher-order TAI. [27] In this work, we numerically study the transport properties of an NS junction, where the normal lead is a non-inverted HgTe/ CdTe quantum well.…”

“…Since proposed, TAI has attracted lots of attentions. Recently, this concept has been extended to Anderson topological superconductors, [ 25 ] non‐Hermitian TAI, [ 26 ] and higher‐order TAI. [ 27 ]…”

Untying links through anti-parity-time-symmetric coupling

“…The creation, observation, and investigation on the static and dynamical properties of quantum knots in Bose-Einstein condensates are reported [2]. Besides, topological phases are extremely stable [3][4][5][6][7][8][9][10][11]. In topological systems, zero-energy Fermi surfaces can form knotted or linked nodal lines [12][13][14][15][16][17][18]; alternatively, the fictitious magnetic field of a topological system with topological defects, associated with vortex or antivortex textures, reflects nontrivial topology [19,20].…”