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Are non-Fermi-liquids stable to pairing?

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Recording Details

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States of matter with a sharp Fermi-surface but no well-defined Landau
quasiparticles are expected to arise in a number of physical systems.
Examples include i) quantum critical points associated with the onset
of order in metals, ii) the spinon Fermi-surface (U(1) spin-liquid)
state of a Mott insulator and iii) the Halperin-Lee-Read composite
fermion charge liquid state of a half-filled Landau level. In this
talk, I will use renormalization group techniques to investigate
possible instabilities of such non-Fermi-liquids to pairing. I will
show that for a large class of phase transitions in metals, the
attractive interaction mediated by order parameter fluctuations always
leads to a superconducting instability, which preempts the
non-Fermi-liquid effects. On the other hand, the spinon Fermi-surface
and the Halperin-Lee-Read states are stable against pairing for a
sufficiently weak attractive short-range interaction. However, once
the strength of attraction exceeds a critical value, pairing sets in.
I will describe the ensuing quantum phase transition between i) the
U(1) and the Z_2 spin-liquid states, and ii) the Halperin-Lee-Read and
Moore-Read states.