Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level

Fractional Quantum Hall States of the A Phase in the Second Landau Level

A proposal of the existence of an Anomalous phase (A phase) [Das et al., Phys. Rev. Lett. 131, 056202 (2023)PRLTAO0031-900710.1103/PhysRevLett.131.056202] at the experimental range of moderate Landau-level-mixing strength has recently been made for the 5/2 state. We here report that the gapped A phase is generic to the sequence of spin-polarized fractional quantum Hall states with filling fractions ν=n/(nm-1) and ν=1-n/(nm-1), (n≥1,m≥3), that exhausts almost all the observed states and also predicts some states in the second Landau level for GaAs systems. Our proposed trial wave functions for all these states have remarkably high overlaps with the corresponding exact ground states and can support non-Abelian quasiparticle excitations with charge e/[2(nm-1)]. By analyzing edge modes, we predict experimentally verifiable thermal Hall conductance 2.5(π^{2}k_{B}^{2}T/3h) for all the states in these sequences.

Cooling low-dimensional electron systems into the microkelvin regime

Two-dimensional electron gases (2DEGs) with high mobility, engineered in semiconductor heterostructures host a variety of ordered phases arising from strong correlations, which emerge at sufficiently low temperatures. The 2DEG can be further controlled by surface gates to create quasi-one dimensional systems, with potential spintronic applications. Here we address the long-standing challenge of cooling such electrons to below 1 mK, potentially important for identification of topological phases and spin correlated states. The 2DEG device was immersed in liquid 3He, cooled by the nuclear adiabatic demagnetization of copper. The temperature of the 2D electrons was inferred from the electronic noise in a gold wire, connected to the 2DEG by a metallic ohmic contact. With effective screening and filtering, we demonstrate a temperature of 0.9 ± 0.1 mK, with scope for significant further improvement. This platform is a key technological step, paving the way to observing new quantum phenomena, and developing new generations of nanoelectronic devices exploiting correlated electron states.

Fractionalization and Dynamics of Anyons and Their Experimental Signatures in the ν=n+1/3 Fractional Quantum Hall State

We show the low-lying excitations at filling factor ν=n+1/3 with realistic interactions can be understood as quantum fluids with "Gaffnian quasiholes" as the proper elementary degrees of freedom. Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons." Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bound and can fractionalize with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.