Universal linear in temperature resistivity from black hole superradiance

Abstract

Observations across many families of unconventional materials motivative the search for robust mechanisms producing linear in temperature d.c. resistivity. BKT quantum phase transitions are commonplace in holographic descriptions of finite density matter, separating critical and ordered phases. We show that at a holographic BKT 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 wavevector, which is communicated to the homogeneous current via irrelevant coupling to an ionic lattice.

Figures (7)

• 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 d.c.$\,$resistivity does not notice the melting of the Drude peak.
• 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 d.c.$\,$and optical conductivities.
• Figure 3: The IR is tuned to the boundary of an instability condensing finite wavenumber 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 wavenumber and couples the unstable mode to the homogeneous electric current.
• Figure 4: Plot of the dominant exponent $\nu$ as a function of $k$ for $n=36$, $m_s^2 = -4$ and $c_{1}\approx 8.47$ illustrating the existence of a mode with $\nu=0$ at $k_{c}\approx 1.27$, and no unstable modes.
• Figure 5: Plot of the logarithmic derivative of the temperature dependence of the d.c.$\,$conductivity for $n=36$ and $c_{1}\approx 8.47$. The top (red) curve has $k_L = 1.5$ and the bottom (blue) curve has $k_L = 1.27$. These correspond to $\nu =0$ and $\nu \approx 0.2$, respectively. At low temperatures the expected scaling $\sigma^{(2)}\sim T^{2\nu-1}$ is recovered.