Percolative Instabilities and Sparse-Limit Fractality in 1T-TaS$_2$

Abstract

The low-temperature metallic phase of 1T-TaS2 may originate from current- and voltage-driven destabilization of the commensurate charge density wave (CDW) in a strongly correlated Mott insulator, alongside the robust yet rarely realized influence of intrinsic electronic distortions. Electrical pulse-driven transport, combined with second harmonic response, reveals abrupt switching, negative differential resistance (NDR), and multiscale domain-wall reorganization. The free energy analysis identifies a critical order parameter threshold for the Mott-metal transition, with scaling exponents (β approx 1.3) consistent with 2D percolation. The sparse limit fractal dimension D_{f} approx 0.3 at 10 K, rising to approx 0.9 at 300 K, reflects the hierarchical evolution of the conductive pathways throughout the temperature. These findings establish a direct connection between fractal percolation, pulse-induced instabilities, and correlated electron transport, offering a framework for controlled access to non-equilibrium phase transitions in low-dimensional quantum materials.

Figures (4)

• Figure 1: Temperature-dependent resistance ($R$) and free-energy landscape $F(\phi)$.(a)$R$–$T$ for two flakes of differing thickness, showing low-$T$ Mott (red) and metallic (black) ground states. Inset: 2$\omega$ response of resistance (50–150 K) for the Mott device, where a resistance dip coincides with a Gaussian-like 2$\omega$ peak, indicating structural reorientation and coexistence of metallic and Mott fractions. (b) At $I=0$, $F(\phi)$ exhibits a double well with minima at $\phi=0$ (Mott) and $\phi=1$ (metallic), separated by a maximum at $\phi=0.5$. Inset:$I$ shifts the endpoint energy $F(\phi=1)$ set by $a/b$ ($a$: scattering coefficient, $b$: $R\times t$). Above $I_{\mathrm{th}}$, the metallic state is energetically favored.
• Figure 2: Voltage–current characteristics of MI and ML states.(a)$V$–$I$ of the Mott-insulating (MI) state at 10 K for successive current loops ($n$), showing a gradual transition from $\phi=0$ to $\phi=1$ with the emergence of pronounced negative differential resistance (NDR). (b)$V$–$I$ of the metal-like (ML) state from 10–300 K. At low $T$, strong NDR accompanies current-induced transitions to highly conductive states; with increasing $T$, NDR sharpness diminishes, indicating reduced resistance-switching dynamics. Inset: threshold power for NDR vs $T$, reflecting the temperature-dependent coupling between current-driven percolation and structural instabilities.
• Figure 3: Device-dependent responses and tuning of the $\phi=0 \rightarrow 1$ transition.(a)$V$–$I$ and $R$–$T$ for two devices (yellow, red) with differing metallic fractions. The critical current $I_c$ (where $R$ jumps) correlates with the $R$–$T$ dip (50–150 K), with larger dips yielding higher $I_c$, indicating a link between $I_c$ and order parameter $\phi$ for $I\leq0.5$. No NDR is observed in this regime. (b) Effect of voltage pulses: without pulse (blue) and after a 2 V, 100 kHz, 60 s pulse (pink). Pulse application shifts $I_c$ higher for $I\leq0.5$, consistent with increased metallic fraction. Inset:$R$–$T$ for the same device at $I=3~\mu$A and $30~\mu$A; larger currents deepen the $R$–$T$ dip, indicating current-induced growth of the metallic fraction.
• Figure 4: (a) Characteristics of order parameter ($\phi$) with channel length (d) ($\phi$vs. d), for different values of domain channel ratio. Here x/d is the domain to channel ratio, for smaller value of x, $\phi$ easily approach 1 with variation of d, as x increases sufficiently $\phi$ can never reach 1 (metallic state). (b) Calculated $V-I$ characteristics of the Metallic state for varying $p_c$. The Metallic state demonstrates a lower resistance and smoother transition, indicating the formation of continuous conductive channels. The inset illustrates the percolation model: red denotes closed (blocked) sites, yellow represents open (waiting) sites, and blue highlights the continuous channels formed by the connected open sites. This schematic emphasizes the role of percolation dynamics in the emergence of conductive pathways across the system, as described in the text.