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

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.

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Enhancement of superconductivity near a nematic quantum critical point
• Are non-Fermi-liquids stable to Cooper pairing?
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Geometry of Fractional Quantum Hall Fluids
• Nematic Valley Ordering in Quantum Hall Systems
• Theory of Nematic Fractional Quantum Hall State
• Pairing in half-filled Landau level
• Superconducting Order Parameter for the Even-denominator Fractional Quantum Hall Effect
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Condensation of Lattice Defects and Melting Transitions in Quantum Hall phases

Cited by in corpus (4)

• Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling
• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• Pathways from a chiral superconductor to a composite Fermi liquid
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures