Shot noise in strongly correlated double quantum spin Hall edges

TL;DR

This work analyzes how interactions modify the edges of double quantum spin Hall insulators realized in moiré TMDs. Using bosonization, RG, and a folded Luttinger-liquid framework, it shows two symmetry-preserving edge phases: a weakly correlated phase with two helical edge pairs and a strongly correlated phase with a single pair in which single-electron excitations are gapped but paired excitations remain gapless. A key prediction is that shot-noise measurements at a quantum point contact yield a Fano factor of $\mathcal{F}=1$ for the weakly correlated edge and $\mathcal{F}=2$ for the strongly correlated edge, because the minimal backscattered charge changes from $e$ to $2e$. The results generalize to $N$-fold QSHIs, with the strongly correlated edge exhibiting a factor of $\mathcal{F}=N$, and have direct relevance for moiré TMD platforms where strong correlations are accessible. Overall, the paper provides a concrete, experimentally accessible diagnostic for interaction-driven edge physics in topological moiré materials.

Abstract

We consider the effects of interactions on the edges of ``double" quantum spin Hall insulators (DQSHIs), motivated by recent experiments on moiré twisted metal dichalcogenides. Without interactions, a DQSHI can be understood as two copies of a conventional quantum spin Hall insulator. If interactions are present and $s^z$-spin is conserved, we show that there are two possible phases for the DQSHI edge. First is a weakly correlated edge which has two pairs of helical modes and is adiabatically equivalent to two conventional quantum spin Hall edges. Second is a strongly correlated edge with only one pair of helical modes. The strongly correlated edge also has a gap to single electrons, but is gapless to pairs of electrons. In a quantum point contact geometry, this single-electron gap leads to a Fano factor of $2$ in shot noise measurements, compared to a Fano factor of $1$ for a weakly correlated edge.

Figures (2)

• Figure 1: (a) Effect of the interactions on the DQSHI edge. Without interactions, there are two pairs of helical edge modes (blue arrows indicate the direction of propagation, and gray arrows indicate spin of the mode). If the edge interactions (depicted in the dashed circle) are irrelevant, the number of helical modes is unchanged. If the interactions are relevant, the edge enters a strongly correlated phase with only a single pair of helical modes that carry twice the charge and twice the spin of the original helical modes. (b) Edge interaction depicted in energy-momentum space.
• Figure 2: Depiction of the quantum point contact geometry. In the weakly correlated edge, the lowest possible charge that may tunnel across the point contact is $e$, via any of the terms in Eq. \ref{['eq:electronTun']}. However, for the strongly correlated edge the minimal charge that can tunnel across the point contact is $2e$.