Pairing in half-filled Landau level

Abstract

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current-current interactions. Our results show that there can be a continuous transition from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that = 1 angular momentum channel is quite different from higher angular momenta ≥ 3. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction ν = is quantitatively changed from the previously established results but not qualitatively.

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

“…This is consistent with some of the previous numerical studies[44,45,46] 6. Eliashberg theory has been applied to the problem of pairing of the HLR state in past[48,49,50], although with no formal justification 7. We will be primarily interested in (2 + 1)−dimensions, but our constructions work in any number of dimensions.…”

Pairing of particle-hole symmetric composite fermions in half-filled Landau level

“…where all quantities with tilde are dimensionless: frequencies ω = ω/ F , ω = ω / F and the pairing gap ∆ ( ω) = ∆ (ω)/ F . As emphasized in our previous work 30,31 , a complete solution to the paring problem needs to take into account the fermion wavefunction renormalization factor Z(ω). This factor has an anomaly on the Fermi surface: Z(ω) → 0 as ω → 0 in the Dirac CF liquid phase, similar to the HLR picture.…”

UV/IR mixing in non-Fermi liquids: higher-loop corrections in different energy ranges

“…Depending on the system, the critical boson can carry zero momentum or some finite momentum. In the former case, examples include the Ising-nematic critical point [7,11,[19][20][21][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and the Fermi surface coupled with an emergent gauge field [22,23,[39][40][41][42], when the fermions lose coherence across the entire Fermi surface. The latter scenario is realised in systems like the spin density wave (SDW) or charge density wave (CDW) critical points [12-14, 18, 43, 44], where electrons on hot spots (or hot lines) play a special role because these are the ones which remain strongly coupled with the critical boson in the low energy limit.…”

“…The latter is inherited from that of the underlying Fermi liquid before the coupling with a gapless boson is turned on right at the quantum phase transition point. The effect of such coupling of the Fermi surface with critical bosons on potential pairing instability is another topic which has been examined carefully [22,23,47,48].…”