DC Current Generation in the Driven Damped Haldane Model

TL;DR

The paper investigates nonequilibrium topological physics in an open quantum system by studying a Haldane model driven with a continuous-wave field and coupled to a thermal bath via a Lindblad master equation. To characterize the resulting quasi-steady state, it introduces an occupation-weighted Chern number $ u_o$, constructed from time-averaged occupations and Bloch states, which reveals residual topological signatures even though the state is not a true projector. The work further analyzes DC transport, showing that breaking inversion symmetry with a staggered sublattice potential generates a finite unit-cell-averaged DC current, with current direction sensitive to the driving strength through effective hopping renormalization. Collectively, the results illuminate the interplay between topology, driving, and dissipation in open systems and provide a practical framework for diagnosing topological features in non-equilibrium steady states.

Abstract

The interplay between topological phenomena and nonequilibrium dynamics in open quantum systems represents a rapidly developing frontier in condensed matter physics. In this work, we investigate the nonequilibrium steady states of the Haldane model driven by a continuous-wave laser and coupled to a thermal reservoir. Dissipation is modeled within the Lindblad formalism adapted for quadratic fermionic systems, enabling us to study both the relaxation dynamics and the emergence of quasi-steady states. While conventional topological invariants and the bulk-boundary correspondence do not directly apply to such nonequilibrium settings, we introduce an occupation-weighted Chern number that captures the residual topological character of this quasi-steady state. We additionally examine the charge transport of this system under simultaneous driving and damping, showing that inversion symmetry breaking via a staggered sublattice potential generates a finite DC current. The magnitude and direction of this DC current are sensitive to the driving strength, highlighting the intricate interplay between topology, symmetry, and dissipation in open quantum systems.

Figures (5)

• Figure 1: (a) The honeycomb lattice of the Haldane model, with all salient features, including the nearest- and next-nearest-neighbor hoppings and the staggered sublattice potential. The two sublattices A and B are shown using red and blue sites, respectively. (b) Phase diagram of the Chern number of the Haldane model in the $\phi$-$M/t_2$ plane. $\nu=\pm1$ corresponds to the topological phase, and $\nu=0$ corresponds to the trivial phase.
• Figure 2: The occupation-weighted Chern number $\nu_o$ plotted as functions of (a) Driving frequency $\omega$; (b) Driving strength $A$; (c) Damping strength $\gamma$.
• Figure 3: The occupations of the driven damped Haldane model relative to half-filling change when nonzero driving and damping are applied. The top row displays the absolute changes in occupations as functions of (a) Driving frequency $\omega$; (b) Driving strength $A$; (c) Damping strength $\gamma$. Half-filling, depicted in these plots with an orange dashed line, shows that the valence band is filled and the conduction band is empty, while both bands are partially filled when the driving field is turned on. The bottom row displays the relative changes in occupations relative to half-filling as functions of (d) Driving frequency $\omega$; (e) Driving strength $A$; (f) Damping strength $\gamma$.
• Figure 4: The net current per lattice site plotted for the cases of (a) $M=0$; (b) $M=0.1$. The red crosses denote the lattice sites, and the blue arrows denote the direction and relative magnitude of the current at each lattice site. When M=0, the unit-cell averaged net current is $7.12 \times10^{-9}$, and when M=0.1, the unit-cell averaged net current is $1.32\times10^{-2}$.
• Figure 5: The (a) $x$- and (b) $y$-components of the unit-cell averaged net current plotted as functions of the driving strength $A$. The direction of the current clearly reverses near $A=3$.