Fate of zero modes in a finite Su-Schrieffer-Heeger model with PT symmetry

Abstract

Due to the boundary coupling in a finite system, the zero modes of a standard Su-Schrieffer-Heeger (SSH) model may deviate from exact-zero energy. A recent experiment has shown that by increasing the system size or the altering gain or loss strength of the SSH model with parity-time (PT ) symmetry, the real parts of the energies of the edge modes can be recovered to exact-zero value [W. Song et al. Phys. Rev. Lett. 123, 165701 (2019)]. To clarify the effects of PT -symmetric potentials on the recovery of the nontrivial zero modes, we study the SSH model with different forms of PT -symmetric potentials in both infinite and finite systems. Our results indicate that the energies of the edge modes in infinite size cases decide whether or not the success of the recovery of the zero modes by tuning the strength of PT -symmetric potential in a finite system. If the energies of the edge modes amount to zero in the thermodynamic limit under open boundary condition (OBC), the recovery of the zero modes will break down by increasing the gain or loss strength for a finite system. Our results can be easily examined in different experimental platforms and inspire more insightful understanding on nontrivial edge modes in topologically non-Hermitian systems.

Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model

“…The Su-Schrieffer-Heeger (SSH) model is the simplest two-band topological system initially introduced to research the polyacetylene that exhibits rich physical phenomena [7], such as fractional charge soliton excitation [8,9]and nontrivial edge modes [10]. Its chiral symmetry leads to nontrivial topology confirmed by a nonzero winding number and the emergence of the zero-energy edge modes under open boundary conditions (OBCs) [11,12,13].…”

Non-Hermitian dynamics and $\mathcal{PT}$-symmetry breaking in interacting mesoscopic Rydberg platforms

“…in optics [11? -15], photonics [16][17][18][19], quantum many-body systems [7,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], systems with topological models [40][41][42][43][44][45][46][47][48][49][50] and in curved space [51]. The PT transition was verified experimentally for a cold atomic dissipative Floquet system, in which the PT symmetry transitions can occur by tuning either the dissipation strength or the coupling strength.…”

Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model

“…The progresses on the non-Hermitian Su-Schrieffer-Heeger (SSH) models [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104], Aubry-André-Harper models [105][106][107][108][109][110], and Rice-Mele models [111][112][113] provide fundamental understanding of the non-Hermitian topological phase of matter. In the non-Hermitian SSH model with asymmetric couplings, nonzero imaginary magnetic flux [55], persistent current [59], and non-Hermitian skin effect exist.…”

“…In the non-Hermitian SSH model with asymmetric couplings, nonzero imaginary magnetic flux [55], persistent current [59], and non-Hermitian skin effect exist. In the parity-time (PT ) sym- * jinliang@nankai.edu.cn metric non-Hermitian SSH model with gain and loss [87][88][89][90][91][92][93], the PT symmetry prevents nonzero imaginary magnetic flux and ensures the BBC. In the exact PT symmetric region with real spectrum, the Berry phase for each separable band is quantized; in the broken PT symmetric region with complex spectrum [114], the Berry phase for each separable band is not quantized [92].…”