TY - JOUR

T1 - Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea

AU - Balram, Ajit C.

AU - Jain, J. K.

N1 - Funding Information:
We thank M. Mulligan, T. Senthil, and D. Son for useful communications, and C. Tőke for help with computer calculations and useful discussions. A.C.B. was supported in part by the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation Programme, Grant Agreement No. 678862; by the Villum Foundation; and by The Center for Quantum Devices funded by the Danish National Research Foundation. J.K.J. was supported by the U.S. National Science Foundation Grant No. DMR-1401636. Some calculations were performed with Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - The fully spin-polarized composite-fermion (CF) Fermi sea at the half-filled lowest Landau level has a Fermi wave vector kF∗=4πρe, where ρe is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from ν=1/2, the area is seen to be consistent with kF∗=4πρe for ν<1/2 but kF∗=4πρh for ν>1/2, where ρh is the density of holes in the lowest Landau level. This result is consistent with particle-hole symmetry in the lowest Landau level. We investigate in this article the Fermi wave vector of the spin-singlet CF Fermi sea (CFFS) at ν=1/2, for which particle-hole symmetry is not a consideration. Using the microscopic CF theory, we find that for the spin-singlet CFFS the Fermi wave vectors for up- and down-spin CFFSs at ν=1/2 are consistent with kF∗↑,↓=4πρe↑,↓, where ρe↑=ρe↓=ρe/2, which implies that the residual interactions between composite fermions do not cause a nonperturbative correction for spin-singlet CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by kF∗↑=4πρe↑ and kF∗↓=4πρe↓.

AB - The fully spin-polarized composite-fermion (CF) Fermi sea at the half-filled lowest Landau level has a Fermi wave vector kF∗=4πρe, where ρe is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from ν=1/2, the area is seen to be consistent with kF∗=4πρe for ν<1/2 but kF∗=4πρh for ν>1/2, where ρh is the density of holes in the lowest Landau level. This result is consistent with particle-hole symmetry in the lowest Landau level. We investigate in this article the Fermi wave vector of the spin-singlet CF Fermi sea (CFFS) at ν=1/2, for which particle-hole symmetry is not a consideration. Using the microscopic CF theory, we find that for the spin-singlet CFFS the Fermi wave vectors for up- and down-spin CFFSs at ν=1/2 are consistent with kF∗↑,↓=4πρe↑,↓, where ρe↑=ρe↓=ρe/2, which implies that the residual interactions between composite fermions do not cause a nonperturbative correction for spin-singlet CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by kF∗↑=4πρe↑ and kF∗↓=4πρe↓.

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U2 - 10.1103/PhysRevB.96.235102

DO - 10.1103/PhysRevB.96.235102

M3 - Article

AN - SCOPUS:85039412509

SN - 2469-9950

VL - 96

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 23

M1 - 235102

ER -