Flux-Driven Conductance Scaling in Disordered Topological Insulator Nanowires

Abstract

We study quantum transport in disordered topological insulator nanowires (TINWs) under axial magnetic flux. At integer flux quanta, spin-momentum locking produces weak anti-localization peaks, while at half-integer flux quanta a helical mode protected by time-reversal symmetry (TRS) suppresses backscattering. By analyzing the flux dependence of the localization length, we uncover critical scaling around half-integer flux quanta, reflecting the competition between disorder scattering and flux-induced breaking of TRS protection. As the disorder strength increases, we identify a crossover in scaling behavior that drives the system into a regime governed by a universal critical exponent. Our results demonstrate a scaling collapse across flux values, establishing a universal regime of flux-driven delocalization in TINWs.

Figures (4)

• Figure 1: Variation of the conductance with the wire length and the dimensionless axial flux. With $\mu[\hbar\Omega]=2.751$, $5$-$6$ channels participate in the conductance, depending on $\Phi/\Phi_0$. $R[10^3\ell_c]=0.2$ and the disorder strength is $W=0.05$. The results are averaged over $1000$ realizations.
• Figure 2: Variation of the conductance with the chemical potential and the dimensionless axial flux, for wire lengths $L[10 \ell_c]=0 \text{ (a)},\text{ }30 \text{ (b)},\text{ }300 \text{ (c)},\text{ and }3000 \text{ (d)}$. The diamond pattern in the clean limit transitions as $L$ increases into a sharp peak at $\eta=1/2$, where the helical state persists; while the weak anti-localization peak remains visible at $\eta=1$ for moderate system lengths. The parameters are the same as in Fig. \ref{['fig:conductance-L-eta']}.
• Figure 3: Variation of the weak anti-localization peaks with the chemical potential, at zero flux, for wire length $L[10\ell_c]=5000$ ($L[10\ell_c]=50$ in the inset). The parameters are the same as in Fig. \ref{['fig:conductance-L-eta']}.
• Figure 4: Delocalization transition near half-flux quantum, $\eta=1/2$. (a) The raw $\xi_L$ for $L=10^5 \ell_c$ and $\mu[\hbar\Omega]=2.751$ (orange), and rescaled localization length $\xi$ (blue) as function of $1/2-\eta$. A linear fit to the rescaled data (red) in the scaling regime gives a critical exponent of $\nu=1.64$, near $\eta=\Phi/\Phi_0=1/2$. The inset shows the collapse to a universal function of $\xi_L/L$ as a function of $\xi/L$ for different flux values. (b) The localization length $\xi$ as function of $1/2-\eta$, for two values of $\mu$ ($\mu[\hbar\Omega]=0.751,2.751$) and several disorder strengths. In the inset, the critical exponent $\nu$ is displayed as function of the disorder strength. For $W>0.1$, the critical exponents are $\nu=2.02\pm0.03$, and $\nu=1.7\pm0.1$ respectively.