Engineering edge states in two-leg SSH ladder and their topoelectric circuit realization

Abstract

We study the topological phase transition in a two-leg Su-Schrieffer-Heeger (SSH) ladder by redefining the unit-cell structure. For both identical hopping dimerization pattern (uniform) and alternate hopping dimerization pattern (staggered) along the legs of the ladder, we demonstrate that different unit-cell choices generate different topological phases and phase transitions. In the uniformly dimerized ladder, variation of the inter-leg coupling induces a transition from topological phase to another topological phase through a gapless region. In contrast, the staggered dimerization configuration exhibits a richer phase structure, supporting both topological-topological and trivial-topological transitions occurring through a single gap-closing point, depending on the unit-cell definition. The phases are characterized through bulk-boundary correspondence, edge-state analysis, and bulk topological invariants. Interestingly, we obtain that while all the topological phases host two zero energy edge states each, the topological phase for the staggerred dimerization case at small inter-leg coupling hosts four edge states. We then perform topoelectric circuit simulation and experiments to observe the signatures of the topological phases. By using circuit impedance and voltage responses we establish the emergence of distinct edge modes in the circuit. Our analysis provides a route to engineer topological edge modes in a two-leg ladder SSH set-up.