Notes on properties of holographic strange metals

Physical Review D, 2013

We provide a simple method for writing the Dirac-Born-Infeld (DBI) equations of a Dp-brane in an arbitrary static background whose metric depends only on the holographic radial coordinate z. Using this method we revisit the Karch-O'Bannon's procedure to calculate the DC conductivity in the presence of constant electric and magnetic fields for backgrounds where the boundary is four or three dimensional and satisfies homogeneity and isotropy. We find a frame-independent expression for the DC conductivity tensor. For particular backgrounds we recover previous results on holographic metals and strange metals.

Fortschritte der Physik, 2011

We review a recent holographic analysis [1] of charged black holes with scalar hair in view of their applications to the cuprate high temperature superconductors. We show in particular that these black holes show an interesting phase structure including critical behaviour at zero temperature or charge, describe both conductors and insulators (including holographic Mott-like insulators), generically have no residual entropy and exhibit experimentally observed scaling relations between electronic entropy, specific heat and (linear) DC resistivity. Transport properties are discussed in the companion contribution [2] in these proceedings.

Journal of High Energy Physics

We investigate a massive gravity theory involving the SL(2, R) symmetry and anisotropy. Due to the SL(2, R) invariance of the equations of motion, the complex conductivity of this model transforms covariantly under the SL(2, R) transformation and the ratio of DC conductivities in different spatial directions is preserved even after the SL(2, R) transformation. We further investigate AC and Hall conductivities by utilizing the Kubo formula. There exists a Drude-like peak in the region with a small anisotropy, while such a Drude peak disappears when anisotropy becomes large. We also show that the complex conductivity can have a cyclotron frequency pole even beyond the hydrodynamic limit.

Journal of High Energy Physics, 2015

We develop a general framework for computing the holographic 2-point functions and the corresponding conductivities in asymptotically locally AdS backgrounds with an electric charge density, a constant magentic field, and possibly non-trivial scalar profiles, for a broad class of Einstein-Maxwell-Axion-Dilaton theories, including certain Chern-Simons terms. Holographic renormalization is carried out for any theory in this class and the computation of the renormalized AC conductivities at zero spatial momentum is reduced to solving a single decoupled first order Riccati equation. Moreover, we develop a first order fake supergravity formulalism for dyonic renormalization group flows in four dimensions, allowing us to construct analytically infinite families of such backgrounds by specifying a superpotential at will. These RG flows interpolate between AdS 4 in the UV and a hyperscaling violating Lifshitz geometry in the IR with exponents 1 < z < 3 and θ = z + 1. For 1 < z < 2 the spectrum of fluctuations is gapped and discrete. Our hope and intention is that this analysis can serve as a manual for computing the holographic 1-and 2-point functions and the corresponding transport coefficients in any dyonic background, both in the context of AdS/CMT and AdS/QCD. We write µνρσ = e µ a e ν b e ρ c e σ d abcd with ntxy = 1, wheren is the Lorentz frame index corresponding to the direction orthogonal to the boundary of ∂M in M.

Cornell University - arXiv, 2022

High T c cuprate strange metals are characterized by a DC-resistivity that scales linearly with T from the onset of superconductivity to the crystal melting temperature, characterized by a current life time τ /(k B T), the "Planckian dissipation". At the same time, the optical conductivity ceases to be of the Drude form at high temperatures, suggesting a change of the underlying dynamics that surprisingly leaves the T-linear DC-resistivity unaffected. We use the AdS/CFT correspondence that describes strongly coupled, densely many body entangled metallic states of matter to study the DC thermo-electrical transport properties and the optical conductivities of the local quantum critical Gubser-Rocha (GR) holographic strange metal in 2+1 dimensions in the presence of a lattice potential, a prime candidate to compare with experiment. We find that the electrical DC-resistivity is linear in T at low temperatures for a large range of potential strengths and wavevectors, even as it transitions between different dissipative regimes. At weak lattice potential the optical conductivity evolves as a function of increasing temperature from a Drude form to a "bad metal" characterized by a mid-IR resonance without changing the DC transport, similar to that seen in cuprate strange metals. This mid-IR peak can be fully understood as a consequence of Umklapp hydrodynamics: i.e. hydrodynamic perturbations are Bloch modes in the presence of a lattice. At strong lattice potential an "incoherent metal" is realized instead where momentum conservation no longer plays a role in the transport. We confirm that in this regime the thermal diffusivity appears to be insensitive to the breaking of translations and can be explained by Planckian dissipation originating in universal microscopic chaos. The charge diffusivity does not submit to this chaos explanation, even though the continuing linearin-T DC resistivity saturates to an apparent universal slope, numerically equal to a Planckian rate. A similar behavior has been found for holographic metals with strong homogeneous momentum relaxation and we conjecture that this may originate in chaos properties that differ between charged and neutral operators.

Journal of High Energy Physics

Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.

Physical Review D, 2013

Hyperscaling violating 'strange metal' phase of heavy fermion compounds can be described holographically by probe D-branes in the background of a Lifshitz spacetime (dynamical exponent z and spatial dimensions d) with hyperscaling violation (corresponding exponent θ). Without the hyperscaling violation, strange metals are known to exhibit zero sound mode for z < 2 analogous to the Fermi liquids. In this paper, we study its fate in the presence of hyperscaling violation and find that in this case the zero sound mode exists for z < 2(1 + |θ|/d), where the positivity of the specific heat and the null energy condition of the background dictate that θ < 0 and z ≥ 1. However, for z ≥ 2(1 + |θ|/d), there is no well-defined quasiparticle for the zero sound. The systems behave like Fermi liquid for 2|θ| = dz and like Bose liquid for 2|θ| = qdz (where q is the number of spatial dimensions along which D-branes are extended in the background space), but in general they behave as a new kind of quantum liquid. We also compute the AC conductivity of the systems and briefly comment on the results.

Physical review, 2021

The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such a system besides the chiral anomaly possesses another anomaly that is related to the Z 2 topological charge of the system. The holographic model of the system contains matter action with two Uð1Þ-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields via the kinetic mixing parametrized by the coupling α. The holographic approach in the probe limit enables us to obtain Hall conductivity. The aim of this work is to describe the phase transitions in the Z 2 Dirac semimetals between the topologically trivial and nontrivial phases. Interestingly the anomalous Hall conductivity plays a role of the order parameter of this phase transition. The holographically found prefactor of the Hall conductivity in the topologically nontrivial phase depends on the coupling α and the Chern-Simons couplings.

Journal of High Energy Physics, 2014

We study AC electric (σ), thermoelectric (α), and thermal (κ) conductivities in a holographic model, which is based on 3+1 dimensional Einstein-Maxwell-scalar action. There is momentum relaxation due to massless scalar fields linear to spatial coordinate. The model has three field theory parameters: temperature (T), chemical potential (µ), and effective impurity (β). At low frequencies, if β < µ, all three AC conductivities (σ, α,κ) exhibit a Drude peak modified by pair creation contribution (coherent metal). The parameters of this modified Drude peak are obtained analytically. In particular, if β µ the relaxation time of electric conductivity approaches to 2 √ 3µ/β 2 and the modified Drude peak becomes a standard Drude peak. If β > µ the shape of peak deviates from the Drude form (incoherent metal). At intermediate frequencies (T < ω < µ), we have analysed numerical data of three conductivities (σ, α,κ) for a wide variety of parameters, searching for scaling laws, which are expected from either experimental results on cuprates superconductors or some holographic models. In the model we study, we find no clear signs of scaling behaviour.

Fortschritte der Physik, 2011

We briefly explain the consistency conditions imposed on the effective holographic theories, which are parameterized by two real exponents (γ, δ) that control the IR dynamics. The general scaling of DC resistivity with temperature at low temperature and AC conductivity at low frequency across the whole (γ, δ) plane are explained. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for (2 + 1)-dimensional systems. Regions are identified where the theory at finite density is a Mott-like insulator. This contribution is based on [C. Charmousis, et al. JHEP 1011, 151 (2010)] [1] with emphasis on the transport properties of charged dilatonic black holes with potential.