Magnetic moments in a helical edge can make weak correlations seem strong

We study the effect of localized magnetic moments on the conductance of a helical edge. Interaction with a local moment is an effective backscattering mechanism for the edge electrons. We evaluate the resulting differential conductance as a function of temperature $T$ and applied bias $V$ for any value of $V/T$. Backscattering off magnetic moments, combined with the weak repulsion between the edge electrons, results in a power-law temperature and voltage dependence of the conductance; the corresponding small positive exponent is indicative of insulating behavior. Local moments may naturally appear due to charge disorder in a narrow-gap semiconductor. Our results provide an alternative interpretation of the recent experiment by Li et al. [Phys. Rev. Lett. 115, 136804 (2015)] where a power-law suppression of the conductance was attributed to strong electron repulsion within the edge, with the value of Luttinger-liquid parameter $K$ fine tuned close to $1/4$.

Figure 1

Log-log plot of the scaled conductance, $G{T}^{-\alpha }$, in the presence of many impurities, $G\propto 1/\delta G$. Here, $\delta G=d〈\delta I〉/dV$ and $\alpha =2-2K>0$ are taken from Eq. (14), valid at intermediate energies $max(T,eV)>T^{*}$. The conductance has two crossover scales in its $V$ dependence. The higher crossover is at $eV\sim T$: Above it, conductance increases (upon increasing $V$) asymptotically as a power law with exponent $\alpha >0$ (dashed line). Below it, $G$ stays roughly constant until the lower crossover scale, $eV\sim \rho J_{\text{eff}}\left(T\right)T$, is reached. Below it, the conductance changes by a factor $1/b\left(T\right)>1$ that depends weakly on temperature [see the discussion below Eq. (16)]. The inset shows $G\left(V\right)$ at three different temperatures $T$ (increasing from the lowest to highest curve).