Quantum charge pumps with topological phases in a Creutz ladder

Abstract

Quantum charge pumping phenomenon connects band topology through the dynamics of a onedimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zakphase-difference of π and 2π, respectively, various charge pumping schemes are studied by applying an elaborate Peierl's phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This puts cold atoms with artificial gauge fields as an unique system where this kind of phenomena can be realized. PACS numbers:Introduction -Quantum charge pumping was one of the early example of a counterintuitive one-dimensional (1D) transport phenomenon as a result of the subtle interplay between nontrivial band topology and quantum adiabatic transport [1]. It underpins the many facets of understanding topological physics ranging from the integer quantum Hall effect [2, 3] to modern studies of electric polarization [4,5], and most recently, topological Floquet physics [6][7][8][9][10][11][12][13][14][15][16]. Explicit models of a quantum pump, however, are surprisingly rare [17][18][19][20][21]. The prototype of its realization is the one based on the Su-SchriefferHeeger/Rice-Mele (SSH/RM) model [22,23] for polyacetylene. It has generated renewed interests thanks to various recent experimental realizations in ultracold atoms and condensed matter systems, where the Zak phase [24], quantum pumping phenomena [25][26][27], and chiral solitonic edge states [28] are directly measured. In this Letter, we present a generalized Creutz scheme [29] as a distinct microscopic two-band quantum pump model utilizing quantum interference effect. The model points to a new quasi-one-dimensional tight-binding quantum pump displaying rich topological physics, and realizable with artificial gauge fields in a cold atomic setting.In the SSH/RM quantum pump, the physical picture is one based on confining quantum particle in a periodic potential that 'slides' slowly in time [17,30]. Specifically, the sliding potential interpolates the two possible alternations of bond strength, such that two dimerization phases of the SSH are realized in a time periodic manner.In the quasi-1D Creutz model (Fig. 1a with φ = 0) [29,31], there actually exists three distinct phases, a feature not apparent by inspection of the tight-binding model. An intuition is provided as follows. First, notice that cross-link hoppings and external flux in the two-leg ladder lattice enhance quantum interference effect. As a result, a complete basis in the topological regime, as found by Creutz [29], takes the form of pla...

Topological characterizations of an extended Su–Schrieffer–Heeger model

“…By extending the one dimensional model to two chains, one can study the Creutz ladder model [75,76].…”

Creutz ladder in a resonantly shaken 1D optical lattice

“…[42]. For example, when the direct link parametersj t , v {˜} are controlled to adiabatically encircle one of the critical points in the parameter space, the Zak phase γ Z [47] continuously changes by 2π per cycle (figure 8), which would result in one lattice site shift of atoms in the ladder.…”

Realization of a Cross-Linked Chiral Ladder with Neutral Fermions in a 1D Optical Lattice by Orbital-Momentum Coupling

“…It was theoretically anticipated that a chiral ladder system may undergo a topological phase transition with an increasing cross link strength [16][17][18][19]. Indeed, we find that in the parameter space of our three-leg ladder system for t s 0 /t d 0 < 2, there are multiple regions where the orbital-mixed ground band becomes topologically nontrivial with a non-zero Zak phase ( Fig.…”