Resistivity bound for hydrodynamic bad metals

We obtain a rigorous upper bound on the resistivity $\rho$ of an electron fluid whose electronic mean free path is short compared to the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a non-thermal diffusion process -- such as an imbalance mode between different bands -- we show that the resistivity bound becomes $\rho \lesssim A \, \Gamma$. The coefficient $A$ is independent of temperature and inhomogeneity lengthscale, and $\Gamma$ is a microscopic momentum-preserving scattering rate. In this way we obtain a unified and novel mechanism -- without umklapp -- for $\rho \sim T^2$ in a Fermi liquid and the crossover to $\rho \sim T$ in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides and heavy fermion compounds and has presented a longstanding challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.Comment: 1 + 11 + 9 pages; 1 figur

Theory of universal incoherent metallic transport

In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound $D \gtrsim \hbar v_F^2/(k_B T)$ on the underlying diffusion constants in an incoherent metal. Such a bound is loosely motivated by results from holographic duality, the uncertainty principle and from measurements of diffusion in strongly interacting non-metallic systems. Metals close to saturating this bound are shown to have a linear in temperature resistivity with an underlying dissipative timescale matching that recently deduced from experimental data on a wide range of metals. This bound may be responsible for the ubiquitous appearance of high temperature regimes in metals with $T$-linear resistivity, motivating direct probes of diffusive processes and measurements of charge susceptibilities.Comment: 1+17 pages + references. 2 figures, v2 minor improvements to discussion, v3 improved presentation and discussio

Reprocessed emission from warped accretion discs with application to X-ray iron line profiles

Flourescent iron line profiles currently provide the best diagnostic for active galactic nuclei (AGN) engine geometries. Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalises previous calculations of reprocessing by accretion discs by including non-axisymmetric effects. We include a relativistic treatment of shadowing by ray-tracing photon paths along Schwarzchild geodesics. We apply this method to two classes of warped discs, and generate a selection of resulting line profiles. New profile features include the possibility of sharper red, and softer blue fall-offs, a time varying line profile if the warp precesses about the disc, and some differences between `twisted' and `twist-free' warps. We discuss some qualitative implications of the line profiles in the context of Type I and II Seyfert AGN.Comment: 15 pages, LaTeX + eps files + 6 separate gif files, Submitted to MNRA

Universal scaling properties of extremal cohesive holographic phases

We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical exponents, independently of the details of the setup. Solutions fall into two classes, depending on whether they break relativistic symmetry or not. The critical exponents determine key properties of these phases, like thermodynamic stability, the (ir)relevant deformations around them, the low-frequency scaling of the optical conductivity and the nature of the spectrum for electric perturbations. We also study the scaling behaviour of the electric flux through bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and characterize the deviation from the Ryu-Takayanagi prescription in terms of the critical exponents.Comment: v4: corrected a typo in eqn (3.29), now (3.28). Conclusions unchange

Reprocessed emission line profiles from dense clouds in geometrically thick accretion engines

The central engines of active galactic nuclei (AGN) contain cold, dense material as well as hot X-ray emitting gas. The standard paradigm for the engine geometry is a cold thin disc sandwiched between hot X-ray coronae. Strong support for this geometry in Seyferts comes from the study of fluorescent iron line profiles, although the evidence is not ubiquitously air tight. The thin disc model of line profiles in AGN and in X-ray binaries should be bench marked against other plausible possibilities. One proposed alternative is an engine consisting of dense clouds embedded in an optically thin, geometrically thick X-ray emitting engine. This model is further motivated by studies of geometrically thick engines such as advection dominated accretion flows (ADAFs). Here we compute the reprocessed iron line profiles from dense clouds embedded in geometrically thick, optically thin X-ray emitting discs near a Schwarzchild black hole. We consider a range of cloud distributions and disc solutions, including ADAFs, pure radial infall, and bipolar outflows. We find that such models can reproduce line profiles similar to those from geometrically thin, optically thick discs and might help alleviate some of the problems encountered from the latter.Comment: 9 Pages LaTex, + Figs, submitted to MNRA

Ohm's Law at strong coupling: S duality and the cyclotron resonance

We calculate the electrical and thermal conductivities and the thermoelectric coefficient of a class of strongly interacting 2+1 dimensional conformal field theories with anti-de Sitter space duals. We obtain these transport coefficients as a function of charge density, background magnetic field, temperature and frequency. We show that the thermal conductivity and thermoelectric coefficient are determined by the electrical conductivity alone. At small frequency, in the hydrodynamic limit, we are able to provide a number of analytic formulae for the electrical conductivity. A dominant feature of the conductivity is the presence of a cyclotron pole. We show how bulk electromagnetic duality acts on the transport coefficients.Comment: 23 pages, 11 figures, typos corrected and references added. Improved discussion of S dualit

Holography, Fractionalization and Magnetic Fields

Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly interacting matter in magnetic fields. v2: Updated references and adjusted some phrasing in the introductio