Transport signatures of topological commensurate off-diagonal Aubry-André-Harper chain

TL;DR

This paper addresses how topology shapes quantum transport in a one-dimensional commensurate off-diagonal AAH chain with b=1/6. It employs a tight-binding junction model incorporating leads and Büttiker probes to capture both coherent and dephasing dynamics, and analyzes the effective transmission T_eff(E) across topological transitions. The study identifies two critical transitions at $W_{c1}=rac{2}{ uth{3}}$ and $W_{c2}=2$, where zero-energy and quantum Hall edge states undergo gap closures and mergings with bulk bands, and reveals a strong even-odd lattice-size effect that yields ballistic transport at Dirac points for odd chains; dephasing can further enhance transport in certain regimes. These results offer a realistic, tunable platform for exploring topology, finite-size effects, and decoherence, with potential experimental realizations in photonic, cold-atom, and semiconductor systems.

Abstract

We study the interplay between quantum transport and topology in a one-dimensional off-diagonal commensurate Aubry-André-Harper (AAH) chain. The model, formulated within AAH framework, effectively represents a one-dimensional lattice with two competing commensurate modulations, supporting two distinct types of topological edge modes: zero-energy states in the central gapless region and quantum Hall (QH) edge states bridging the gapped bulk bands. These edge modes govern the transport behavior and give rise to sharp variations in transmission across the corresponding gap-closing transitions. A pronounced even-odd effect further emerges, where chains with an odd number of sites exhibit nearly perfect zero-energy transmission at the Dirac points, independent of system-lead coupling, system size, or modulation strength; a robust signature of ballistic transport. To capture the influence of environmental decoherence, we also incorporate Büttiker dephasing probes, which enable a phenomenological description of inelastic scattering and reveal how dephasing modifies, and in some regimes enhances, coherent transport.

Figures (7)

• Figure 1: Energy spectra of the isolated off-diagonal commensurate AAH chain with modulation strength $\delta_t$ at $b=\frac{1}{6}$ and lattice size $N=120$ for two representative modulation phases: $\phi_{\lambda}=0$ in (a) and $\pi/2$ in (b). Zero-energy edge states merge with central bulk bands in (a), while a complete band narrowing occurs at $E=0$ eV in (b) at first transition point $\delta_t=W_{c1}=\frac{2}{\sqrt{3}}$. The closing and reopening of the central bulk gap are observed at $\delta_t=W_{c2}=2$ in both configurations.
• Figure 2: Energy spectra of the same AAH chain in Fig. \ref{['fig1']}, plotted as a function of $\phi_{\lambda}/\pi$ for five representative values of modulation strength: (a) $\delta_t=1.0$, (b) $\delta_t=W_{c1}=2/\sqrt(3)$, (c) $\delta_t=1.5$, (d) $\delta_t=W_{c2}=2$, and $\delta_t=3.0$.
• Figure 3: Simultaneous variation of transmission probability as a function of incoming electronic energy (in eV, vertical axis) and AAH phase $\phi_{\lambda}/\pi$ (horizontal axis) for the identical configurations as in Fig. \ref{['fig2']}. The color scale represents the magnitude of transmission.
• Figure 4: Comparison of energy-resolved transmission between the adjacent Diract points $\phi_{\lambda}=\pi/2$ in (a) and $\phi_{\lambda}=5\pi/6$ in (b) for several strengths of $\delta_t$. Results correspond to $\delta_t = 0$ (red), $1$ (green), $W_{c1}$ (orange), $1.5$ (black) and $W_{c2}$ (blue). A narrow energy window is used to capture the detailed features around the Dirac points.
• Figure 5: Ballistic transmission at $E=0$ eV for two adjacent Diract points $\phi_{\lambda}=\pi/6$ in (a) and $\phi_{\lambda}=\pi/2$ in (b) for several values of $\delta_t$ using identical color scheme as in Fig. \ref{['fig4']}. To highlight the robustness of zero-energy transmission $\tau_S=\tau_D$ are fixed at $0.3$ eV.