Composite Fermion Groundstate of

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Composite Fermion Groundstate of  Rashba
Spin-Orbit Bosons
Alex Kamenev
Fine Theoretical Physics Institute, School of
Physics Astronomy, University of Minnesota
Tigran Sedrakyan

Leonid Glazman
ArXiv1208.6266
Chernogolovka QD2012
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Motivation
Four-level ring coupling scheme in 87Rb involving
hyperfine states F,mFgt Raman-coupled by a total
of five lasers marked s1, s2, s3, p1, and p2
Spin-orbit coupling constant
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Rashba
spin-orbit-coupling
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Bose-Einstein condensates of Rashba
bosons
Interaction Hamiltonian
density operators
Chunji Wang, Chao Gao, Chao-Ming Jian, and Hui
Zhai, PRL 105, 160403 (2010)
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Chemical
Potential
density
However, let us look at Rashba fermions
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Reminder
spinless 1D model
mean-field bosons
spinless fermions
exact bosons Lieb - Liniger 1963
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Can one Fermionize Rashba
Bosons?
Yes, but

1. Particles have spin
2. The system is 2D not 1D

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Fermions with spin do
interact
Hartree
Fock
Variational Fermi surface
minimizing w.r.t.
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Self-consistent Hartree-Fock for Rashba
fermions
Berg, Rudner, and Kivelson, (2012) nematic
state
Elliptic Fermi surface at small density
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Fermionization in 2D?
Chern-Simons!
Chern-Simons phase
fermionic wave function
bosonic wave function

• (plus/minus) One flux quantum per particle
• Broken parity P
• Higher spin components are uniquely determined
• by the projection on the lower Rashba
  brunch
• Fermionic wave function is Slater determinant,
• minimizing kinetic and interaction energy

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Chern-Simons magnetic
Field
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Integer Quantum Hall
State
Particles with the cyclotron mass
in a uniform magnetic field
One flux quanta per particle, thus n1 filling
factor IQHE

• Gapped bulk and chiral edge mode
• 
  interacting topological insulator

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Phase
Diagram
chemical potential
Bose Condensate
broken R and T
Spin-Density Wave
broken R
broken R, T and P
Composite Fermions
spin anisotropic interaction
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Phase
Separation
total energy per volume
Bose condensate
composite fermions
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Rashba Bosons in a
Harmonic Trap

• high density Bose condensate in the middle and
• low density composite fermions in the
  periphery

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Conclusions

• At low density Rashba bosons exhibit
• Composite Fermion groundstate
• CF state breaks R, T and P symmetries
• CF state is gaped in the bulk, but supports
• gapless edge mode, realizing interacting
• topological insulator
• CF equation of state
• There is an interval of densities where CF
• coexists with the Bose condensate
• In a trap the low-density CF fraction is pushed
• to the edges of the trap

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Lattice
Model