Transference of transport anisotropy to composite fermions

Abstract

When interacting two-dimensional electrons are placed in a large perpendicular magnetic field, to minimize their energy, they capture an even number of flux quanta and create new particles called composite fermions (CFs). These complex electron-flux-bound states offer an elegant explanation for the fractional quantum Hall effect. Furthermore, thanks to the flux attachment, the effective field vanishes at a half-filled Landau level and CFs exhibit Fermi-liquid-like properties, similar to their zero-field electron counterparts. However, being solely influenced by interactions, CFs should possess no memory whatever of the electron parameters. Here we address a fundamental question: Does an anisotropy of the electron effective mass and Fermi surface (FS) survive composite fermionization? We measure the resistance of CFs in AlAs quantum wells where electrons occupy an elliptical FS with large eccentricity and anisotropic effective mass. Similar to their electron counterparts, CFs also exhibit anisotropic transport, suggesting an anisotropy of CF effective mass and FS.

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

“…Striking recent experiments from Princeton by Gokmen et al 1 , Kamburov et al 2,3 and Mueed et al 4,5 have investigated the role of electron mass anisotropy on the composite fermion (CF) Fermi sea, which was predicted in the early 1990s by Halperin, Lee and Read…”

Valley degeneracy in biaxially strained aluminum arsenide quantum wells

“…Quantum confinement to a one-dimensional multi-valley system has been achieved in cleaved-edge overgrown quantum wires 15,16 and quantum point contacts 17 . Novel interaction effects in QWs include anisotropic composite Fermion mass 18 and valley skyrmions, whereby electrons populate linear superpositions of two valleys at once 19 . Such interaction effects that result from exchange splitting of a perfect SU(2) symmetry 20 may prove useful in future quantum device applications, where the valley degree of freedom functions as a pseudospin.…”

Possible realization of a chiralp-wave paired state in a two-component system

“…The finite width corrections should be negligible in graphene. We note that extensive investigation of the spin or valley physics of the FQHE states of the form ν = n/(2n ± 1) has been performed experimentally in GaAs and AlAs quantum wells as well as graphene [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and these results have been analyzed quantitatively by the CF theory [54][55][56]. One may wonder about the role of CF skyrmions; these are estimated to be relevant only for very small values of κ < 0.007 close to ν = 1/3 [57], but are not relevant for the physics of the ground state at 3/8 [54].…”