Revealing Superconducting Chiral Edge Modes via Resistance Distributions

TL;DR

The paper addresses identifying superconducting chiral edge modes in QAH systems and distinguishing topological SC phases by analyzing the full probability distribution of charge transmission, not merely its mean. It develops a transfer-matrix framework that maps edge transport under disorder to random Bloch-sphere rotations, deriving distinct distributions for $N=1$ and $N=2$ CBEMs in both short and long junctions. Numerical lattice simulations validate the analytical predictions, and the authors study the impact of decoherence and particle loss, finding the qualitative distributional differences robust to weak decoherence. The findings propose resistance-distribution signatures as a powerful diagnostic for topological superconducting phases with potential experimental accessibility via nonlocal resistances in linear response, offering a stronger probe than mean transmission alone.

Abstract

Inducing superconducting correlations in quantum anomalous Hall (QAH) states offers a promising route to realize topological superconductivity with chiral Majorana edge modes. However, the definitive identification of these modes is challenging. Here we propose detecting superconducting chiral edge modes via the probability distribution of the resistance, or equivalently the charge transmission of QAH-superconductor heterojunctions. Remarkably, the distribution for coherent edge exhibits distinct characteristics for different topological superconducting phases in sufficiently long junctions, and this difference remains robust against weak decoherence. These findings provide insights into transport phenomena beyond the clean limit and highlight the resistance distribution as a compelling signature for distinguishing topological superconducting phases.

Figures (4)

• Figure 1: (a) The QAH-SC-QAH junction with $N=2$ CBEM. The orange and dashed blue arrows represent the chiral electron edge mode of QAH state and the CBEM of TSC state, respectively. (b) Transfer matrix construction for the junction shown in (a). (c) Evolution of the state on the Bloch sphere. Both the axis and rotation angle exhibit weak fluctuations. The north (south) pole on the Bloch sphere represents a pure electron (hole) state. (d), (e) The QAH-SC-QAH junction with $N=1$ CBEM, and the corresponding transfer matrix construction. (f) The QAH-SC junction with $N=1$ CBEM.
• Figure 2: Mean and distribution of the charge transmission fraction $T$ for the junction in Fig. \ref{['fig1']}(a). (a), (b) $\overline{T}$ vs $L$, where solid lines and shaded region indicate the mean and standard deviation, respectively. (c-e) The distributions of $T$ for different $L$, with histograms representing numerical results and red lines showing fitted distributions. (c) The distribution is fitted with a normal distribution $f(T)=\frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(T-E)^2}{2 \sigma ^2}}$. (d) The distribution is fitted with a chi-squared distribution $f(T)=\frac{1}{\sigma\sqrt{\pi(1-T)}}e^{-\frac{1-T}{\sigma ^2}}$. (e) The mean and standard deviation of $T$ are $8.54\times10^{-3}$ and 0.582, respectively, which match those of a uniform distribution $U[-1,1]$.
• Figure 3: (a), (b) Numerical results of $T$ for junction in Fig. \ref{['fig1']}(d). (a) $\overline{T}$ vs $L$, where $\varepsilon$ denotes the incident electron energy. The solid lines and shading indicate the mean and standard deviation, respectively. (b) Distribution of $T$ for $\varepsilon=0.28$, which follows a normal distribution depicted as a red line. (c), (d) Numerical results for junction of Fig. \ref{['fig1']}(f). (c) $\overline{T}$ vs $L$. (d) Distribution of $T$, with the red line showing the fitting distribution as a generalized arcsine distribution in Eq. (\ref{['arcsine']}).
• Figure 4: (a), (b), (c) Decoherence effect in scenarios Figs. \ref{['fig1']}(a), \ref{['fig1']}(d) and \ref{['fig1']}(f), respectively. The distribution is calculated from Monte Carlo sampling sm, and we set $p=0.4$. We set the distribution of $T$ without decoherence follows $U[-1,1]$, $\mathcal{N}(0.3,0.05^2)$ and arcsin distribution with $A=0.6$ for Figs. \ref{['fig1']}(a), \ref{['fig1']}(d) and \ref{['fig1']}(f), respectively.