Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

Abstract

Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counter-propagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counter-propagating modes, which, by way of mode renormalization, may give rise to non-topological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.

Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

“…For Slater determinants, the energy ( H ) of the variational states may be evaluated trivially given the matrix elements of the Coulomb interaction and the confining potential [33]. On the other hand, for Laughlin states these may be evaluated using standard classical Monte-Carlo techniques [45,[52][53][54][55]. In our analysis, we evaluate the energy of the states in each variational class as a function of d, which controls the slope of the confining potential.…”

“…In the early 90s, it was realized that in the presence of a smooth confining potential at the boundary, electronic interactions may induce quantum phase transitions at the edge (which leave the bulk unperturbed). Such edge transitions (or edge reconstructions) may occur in both integer [24][25][26][27][28][29][30][31][32][33] and fractional [34][35][36][37][38][39][40][41][42][43][44][45][46] QH phases, as well as in time-reversal-invariant topological insulators [47,48]. The reconstructed edge structure may differ in terms of the number, order, or even the nature of the edge modes.…”

“…Here, we describe our recent attempts [33,45] to theoretically account for the experimental surprises described above, in terms of reconstruction and the subsequent renormalization of the edge for ν = 1 and 1/3 QH phases. Additionally, we present new analysis of edge reconstruction of the ν = 2/5 QH phase.…”

“…Figures 1, 2 depict some of the a priori possible configurations of the reconstructed edge at ν = 1, 1/3 and 2/5. Here, we find the lowest energy state among these structures as a function of the slope of the confining potential through a variational analysis [33,34,45], which allows us to include a large number of electrons while accounting for quantum correlations inherently present in QH states. Specifically, we treat the strip-size (N S ) and separation (L S ) as variational parameters.…”