Cooper pairing in non-Fermi liquids
States of matter with a sharp Fermi surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include (i) quantum critical points associated with the onset of order in metals; (ii) spinon Fermi-surface [U(1) spin-liquid] state of a Mott insulator; (iii) Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the order-parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between (i)U(1) and Z_2 spin-liquid states; (ii) Halperin-Lee-Read and Moore-Read states.
© 2015 American Physical Society. Received 20 July 2014; revised manuscript received 21 January 2015; published 4 March 2015. We would like to thank S. Parameswaran, Z. Papic, A. Chubukov, S.-S. Lee, P. A. Lee, D. Scalapino, S. Kivelson, C. Nayak, L. Balents, and M. P. A. Fisher for useful discussions. This research was supported in part by the National Science Foundation under Grants No. NSF PHY11-25915 and No. DMR-1360789, and by the Templeton Foundation. The work of T.S. was supported by Department of Energy DESC-8739-ER46872, and partially by a Simons Investigator grant from the Simons Foundation. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Submitted - 1403.3694v2.pdf
Published - PhysRevB.91.115111.pdf