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Volumn 91, Issue 11, 2015, Pages

Cooper pairing in non-Fermi liquids

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EID: 84924358537     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.91.115111     Document Type: Article
Times cited : (378)

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    • Strictly speaking, it is not known whether higher-loop terms in the RPA resummed expansion are suppressed by powers of (Equation presented). Thus, the validity of the perturbative expansion in (Equation presented) with (Equation presented) finite, as well as of the results at (Equation presented) both with (Equation presented) finite and with (Equation presented), has not been firmly established. On the other hand, the calculations in the double-scaling limit (Equation presented), (Equation presented), (Equation presented) are certainly controlled [32]. In this paper, we will assume that the first expansion is controlled, as well
    • Strictly speaking, it is not known whether higher-loop terms in the RPA resummed expansion are suppressed by powers of (Equation presented). Thus, the validity of the perturbative expansion in (Equation presented) with (Equation presented) finite, as well as of the results at (Equation presented) both with (Equation presented) finite and with (Equation presented), has not been firmly established. On the other hand, the calculations in the double-scaling limit (Equation presented), (Equation presented), (Equation presented) are certainly controlled [32]. In this paper, we will assume that the first expansion is controlled, as well.
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    • Strictly speaking, this assumption is unphysical for the Ising-nematic QCP, however, it is not expected to change most of our results qualitatively (see end of Sec. III for further discussion).
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    • Strictly speaking, the HLR phase is only defined at zero temperature, where it occurs at a fixed electron density ((Equation presented) for the clean, Gallilean invariant system). For (Equation presented)
    • Strictly speaking, the HLR phase is only defined at zero temperature, where it occurs at a fixed electron density ((Equation presented) for the clean, Gallilean invariant system). For (Equation presented) deviating from (Equation presented) and (Equation presented), composite fermions see a background magnetic field (Equation presented), and so form Landau levels. At low enough temperature, one, thus, expects to see a sequence of integer QH states of composite fermions, which correspond to a sequence of FQH states of physical electrons with (Equation presented) [86]. In our discussion, we assume that the temperature (Equation presented) is much larger than the cyclotron frequency (Equation presented) of composite fermions, so that Landau-level quantization can be neglected. At the same time, for our estimates to be correct, we need the temperature to be much lower than the gap, (Equation presented), of the paired CF phase. We expect the cyclotron frequency (Equation presented). The Fermi velocity in the HLR phase runs with energy [Eq. (2.16)] (Equation presented). When Landau levels of composite fermions form, we expect that the running of (Equation presented) will be cut off at (Equation presented). We, thus, obtain, (Equation presented). At the first-order transition from the paired CF phase to the HLR phase, (Equation presented), so (Equation presented). Thus, our calculations are legitimate as long as (Equation presented).
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