Topological nodal points in two coupled Su-Schrieffer-Heeger chains

Abstract

We study two coupled Su-Schrieffer-Heeger (SSH) chains system, which is shown to contain rich quantum phases associated with topological invariants protected by symmetries. In the weak coupling region, the system supports two non-trivial topological insulating phases, characterized by winding number N = ±1, and two types of edge states. The boundary between the two topological phases arises from two band closing points, which exhibit topological characteristics in onedimensional k space. By mapping Bloch states on a vector field in k space, the band degenerate points correspond to a pair of kinks of the field, with opposite topological charges. Two topological nodal points move and merge as the inter-chain coupling strength varies. This topological invariant is protected by the translational and inversion symmetries, rather than the antiunitary operation. Furthermore, we find that when a pair of nodal points is created, a second order quantum phase transition (QPT) occurs, associating with a gap closing and spontaneously symmetry breaking. This simple model demonstrates several central concepts in the field of quantum materials and provides a theoretical connection between them.

Simulation of topological phases with color center arrays in phononic crystals

“…For the generalized SSH Hamiltonian, the interaction between different sites of a 1D chain is described by the alternating off-diagonal elements. Due to the intrinsic topological features of the SSH model, various quantum systems are employed to simulate the SSH model, and to explore interesting applications in quantum information processing [12][13][14][15][16][17][18][19][20][21][22][23][24]. However, the simulation of topological phenomena in the quantum domain is still challenging in practice due to stringent conditions.…”

Topological Phase Transition and Phase Diagrams in a Two‐Leg Kitaev Ladder System

“…Recently, various compound topological systems, called the ladder system composed of simple tight‐binding chains, are becoming nice examples to investigate abundant novel physical behaviors and topological properties. Specifically, the coupled Su–Schrieffer–Heeger (SSH) ladder system, including two well‐known SSH chains coupled to each other, has been explored sufficiently via the phase diagram and energy spectrum . A large amount of intriguing topological phases beyond that presenting in the traditional SSH model are shown in these models.…”

Phase-dependent topological interface state and spatial adiabatic passage in a generalized Su-Schrieffer-Heeger model

“…The tight-binding Su-Schrieffer-Heeger (SSH) model [43], which in its most basic version only includes a real intracell hopping term and a real nearest-neighbor intercell hopping term, has been widely studied as a one-dimensional prototype allowing for a nontrivial topological phase [44,45]. This model has been extended in a variety of Hermitian [46][47][48][49] and non-Hermitian forms [16,20,21,27,[39][40][41][50][51][52][53][54][55][56][57][58]. In particular, the non-Hermitian extensions, which are also called complex SSH models, are a powerful platform for studying interactions of topological properties with non-Hermiticity, and many breakthroughs have been made based on them, such as anomalous edge states [21], non-Bloch bulk-edge correspondence [27], topological lasing [39][40][41], and spontaneous topological pumping [58].…”