Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems

TL;DR

This paper investigates how nematic fluctuations influence the balance of various strongly correlated phases in half-filled quantum Hall systems using a controlled theoretical approach, revealing conditions for different phases and potential experimental signatures.

Contribution

It introduces a controlled double expansion method to analyze the interplay of gauge and nematic fluctuations near a nematic quantum critical line in quantum Hall systems.

Findings

Nematic fluctuations can stabilize multiple correlated phases depending on interaction screening.

Near the nematic quantum critical line, RG flows lead to all four phases: NFL, FQH, nematic, and FQH nematic.

Nematic fluctuations may enhance FQH phase stability at low tilt angles.

Abstract

Half-filled Landau levels form a zoo of strongly correlated phases. These include non-Fermi liquids (NFL), fractional quantum Hall (FQH) states, nematic phases, and FQH nematic phases. This diversity poses the question: what keeps the balance between the seemingly unrelated phases? The answer is elusive because the Halperin-Lee-Read (HLR) description that offers a natural departure point is inherent strongly coupled. But the observed nematic phases suggest nematic fluctuations play an important role. To study this possibility, we apply a recently formulated controlled double expansion approach in large-$N$ composite fermion flavors and small $\epsilon$ non-analytic bosonic action to the case with both gauge and nematic boson fluctuations. In the vicinity of a nematic quantum critical line (NQCL), we find that depending on the amount of screening of the gauge- and nematic-mediated interactions controlled by $\epsilon$'s, the RG flow points to all four mentioned correlated phases. When pairing preempts the nematic phase, NFL behavior is possible at temperatures above the pairing transition. We conclude by discussing measurements at low tilt angles which could reveal the stabilization of the FQH phase by nematic fluctuations.