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Universal linear in temperature resistivity from black hole superradiance

Aristomenis Donos and Sean A. Hartnoll
Phys. Rev. D 86, 124046 – Published 26 December 2012
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  • UNCONVENTIONAL dc AND OPTICAL…
  • EXTREMAL HORIZONS AND…
  • MECHANISM OF LINEAR RESISTIVITY
  • LATTICES AND FINITE WAVE VECTOR…
  • NUMERICS: LATTICE DEFORMED…
  • DISCUSSION
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    Observations across many families of unconventional materials motivate the search for robust mechanisms producing linear in temperature dc resistivity. Berezinskii-Kosterlitz-Thouless quantum phase transitions are commonplace in holographic descriptions of finite density matter, separating critical and ordered phases. We show that at a holographic Berezinskii-Kosterlitz-Thouless critical point, if the unstable operator is coupled to the current via irrelevant operators, then a linear contribution to the resistivity is universally obtained. We also obtain broad power law tails in the optical conductivity that shift spectral weight from the Drude peak as well as interband energy scales. We give a partial realization of this scenario using an Einstein-Maxwell-pseudoscalar bulk theory. The instability is a vectorial mode at nonzero wave vector, which is communicated to the homogeneous current via irrelevant coupling to an ionic lattice.

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    • Received 24 September 2012

    DOI:https://doi.org/10.1103/PhysRevD.86.124046

    © 2012 American Physical Society

    Authors & Affiliations

    Aristomenis Donos1 and Sean A. Hartnoll2

    • 1Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom
    • 2Department of Physics, Stanford University, Stanford, California 94305-4060, USA

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    Issue

    Vol. 86, Iss. 12 — 15 December 2012

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    Images

    • Figure 1
      Figure 1
      Theorist’s schematic view of the optical conductivity in bad metals at lower temperatures (left) and higher temperatures (right). As the temperature is raised, spectral weight is shifted from the Drude peak into the broad tail and to interband energy scales. The linear in temperature dc resistivity does not notice the melting of the Drude peak.Reuse & Permissions
    • Figure 2
      Figure 2
      Schematic phase diagram. The BKT quantum phase transition occurs at the boundary of a quantum critical phase when the scaling dimension of an operator becomes complex, signaling a condensation instability. If the unstable operator is coupled to the current via irrelevant operators, then above the critical point the quantum critical contribution to the resistivity is linear in temperature. Close to the critical point, the mode becoming unstable has a strong effect on the dc and optical conductivities.Reuse & Permissions
    • Figure 3
      Figure 3
      The IR is tuned to the boundary of an instability condensing finite wave number vectorial modes. The lattice is imposed in the UV but irrelevant in the IR. Away from the locally critical IR region, the lattice mixes modes of different wave number and couples the unstable mode to the homogeneous electric current.Reuse & Permissions
    • Figure 4
      Figure 4
      Plot of the dominant exponent ν as a function of k for n=36, ms2=−4 and c1≈8.47 illustrating the existence of a mode with ν=0 at kc≈1.27, and no unstable modes.Reuse & Permissions
    • Figure 5
      Figure 5
      Plot of the logarithmic derivative of the temperature dependence of the dc conductivity for n=36 and c1≈8.47. The top (red) curve has kL=1.5 and the bottom (blue) curve has kL=1.27. These correspond to ν=0 and ν≈0.2, respectively. At low temperatures the expected scaling σ(2)∼T2ν−1 is recovered.Reuse & Permissions
    • Figure 6
      Figure 6
      The correction to the real part of the conductivity Re(σ(2)) for n=36, ms2=−4 and c1≈8.47 at kL=1.27. The red (lower) curve has T/μ≈0.01 and the blue (top) curve has T/μ≈0.006. The left plot shows the redistribution of spectral weight at interband frequencies, while the right, log-log, plot shows the expected intermediate-low frequency scaling regime.Reuse & Permissions
    • Figure 7
      Figure 7
      Spectral weight transfer. The plots have n=36, ms2=−4 and c1≈8.47. Left, the zero frequency limit of the real part of the Green’s function correction GJyJy(2) as a function of temperature. The bottom (red) curve has kL=1.5 and the top (blue) curve has kL=1.27. The negative of this curve is the spectral weight extracted from the Drude peak. Right, the integrated spectral weight defined in (5.17). The red curve has T/μ≈0.01 and the blue curve has T/μ≈0.006. Both are at the critical lattice spacing kL=1.27. We see that the sum rule is satisfied after integrating up to a few times the UV scale μ.Reuse & Permissions
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