Nonequilibrium Dynamics of Gating-Induced Resistance Transition in Charge Density Wave Insulators

Abstract

We present a comprehensive numerical investigation of the gate-induced insulator-to-metal transition in the charge-density-wave (CDW) phase of the Holstein model. Large-scale Brownian dynamics simulations are performed, in which the forces acting on the lattice degrees of freedom are evaluated using the nonequilibrium Green's function formalism. We demonstrate that the onset of CDW instability requires a threshold bias voltage set by the energy of in-gap edge modes. At sufficiently large voltages, the system undergoes an abrupt transition to a metallic state, reminiscent of dielectric breakdown. In the intermediate-voltage regime, our simulations reveal that the transition to a low-resistance state is initiated by the nucleation of a thin conducting layer at the gated electrode. The resulting metal-insulator interface subsequently propagates across the system under the applied bias, leading to the growth of a metallic domain. We further analyze the voltage- and temperature-dependent dynamics of the associated domain walls.

Figures (5)

• Figure 1: (Color online) (a) Schematic illustration of the gate-induced transition from a charge-density-wave (CDW) insulator to a metallic state in the adiabatic Holstein model. (b) Energy-level alignment of the two electrodes and the central Holstein system. In the CDW phase, the system is a band insulator with an energy gap $E_g = 2 g Q_0$. The Fermi level $\epsilon_F$ in the bulk and the chemical potential $\mu_R$ of the right electrode are aligned at the center of the gap. The chemical potential of the left electrode is lowered relative to $\epsilon_F$ by the applied gate voltage, $\mu_L = \epsilon_F - eV$.
• Figure 2: (Color online) NEGF-BD simulations of a driven Holstein model on a $40 \times 30$ square lattice. The bias voltage is applied along the longitudinal $x$ direction. Panels (a)--(c) display snapshots of the local electronic density, $n_i = \langle \hat{c}^\dagger_i \hat{c}^{\,}_i \rangle$, at different simulation times. The parameters used are: electron-phonon coupling constant $g=1.5 t_{\rm nn}$, the effective spring constant $k_1=0.67g$, nearest-neighbor elastic coupling $\kappa=0.12 g$, damping constant $\lambda=0.2g$, $\Gamma_{\text{lead}}=1.0$, $\Gamma_{\text{bath}}=0.001$, $k_BT=0.1$, and the bias voltage $eV = 2.5 t_{\rm nn}$.
• Figure 3: (Color online) Time dependence of (a) the transmission current $I$ and (b) the charge-density-wave (CDW) order parameter $\Phi$ at zero temperature. A constant voltage $eV = 2.5 t_{\rm nn}$ is applied to the Holstein system over the time interval $0\leq t \leq t_{\text{off}}=400$.
• Figure 4: (Color online) (a) Average position $\xi$ of the CDW-metal domain wall as a function of time for different gating voltages at zero temperature. (b)Velocity $v$ of the CDW–metal domain wall as a function of the applied gate voltage $eV$, extracted from the average slope of the $\xi(t)$ curves shown in panel (a).
• Figure 5: (Color online) Average position $\xi$ of the CDW-metal interface as a function of time for several temperatures under a constant driving voltage $eV=2.5 t_{\rm nn}$. The inset shows the CDW-metal domain-wall velocity as a function of temperature.