Person:

Lucas, Andrew James

We compute the direct-current resistivity of a scale-invariant, d-dimensional strange metal with dynamic critical exponent z and hyperscaling-violating exponent θ, weakly perturbed by a scalar operator coupled to random-field disorder that locally breaks a Z2 symmetry. Independent calculations via Einstein-Maxwell dilaton holography and memory matrix methods lead to the same results. We show that random-field disorder has a strong effect on resistivity and leads to a short relaxation time for the total momentum. In the course of our holographic calculation, we use a nontrivial dilaton coupling to the disordered scalar, allowing us to study a strongly coupled scale-invariant theory with θ≠0. Using holography, we are also able to determine the disorder strength at which perturbation theory breaks down. Curiously, for locally critical theories, this breakdown occurs when the resistivity is proportional to the entropy density, up to a possible logarithmic correction.

This dissertation provides an overview of what gauge-gravity duality, often called holography, has taught us about quantum condensed matter physics, with particular emphasis on the problem of thermoelectric transport. A comprehensive theory of transport in weakly disordered metals is subsequently developed using a variety of techniques, all of which precisely agree. The theory in its present form may be applied directly to realistic models of transport in strongly interacting strange metallic phases, and also serves as a point of direct contact between gauge-gravity duality and more traditional theories of condensed matter physics. Next, novel techniques are developed to demonstrate the absence of disorder-driven metal-insulator transitions in holographic metals in two spatial dimensions. Finally, experimental evidence is presented for hydrodynamic transport in charge neutral graphene, and new theories are developed to understanding the resulting data.

We study (2+1)-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction x with zero average: μ(x)=V cos(kx). The dynamics of such theories depends only on the dimensionless ratio V/k, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of V/k. We compute the frequency-dependent conductivity of strongly coupled CFTs using holography of the Einstein-Maxwell theory in four-dimensional anti–de Sitter space. We compare the results with the corresponding computation of weakly coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies). We find that the results of the two computations have significant qualitative similarities. However, differences do appear in the vicinities of an infinite discrete set of values of V/k: the universality class of the infrared CFT changes at these values in the weakly coupled theory, by the emergence of new zero modes of Dirac fermions which are remnants of local Fermi surfaces. The infrared theory changes continuously in holography, and the classical gravitational theory does not capture the physics of the discrete transition points between the infrared CFTs. We briefly note implications for a nonzero average chemical potential.

We present a semi-analytic method for constructing holographic black holes that interpolate from anti-de Sitter space to hyperscaling-violating geometries. These are holographic duals of conformal field theories in the presence of an applied chemical potential, μ, at a non-zero temperature, T , and allow us to describe the crossover from ‘strange metal’ physics at T≪μT≪μ, to conformal physics at T≫μT≫μ. Our holographic technique adds an extra gauge field and exploits structure of the Einstein–Maxwell system to manifestly find 1-parameter families of solutions of the Einstein-matter system in terms of a small family of functions, obeying a nested set of differential equations. Using these interpolating geometries, we re-consider holographically some recent questions of interest about hyperscaling-violating field theories. Our focus is a more detailed holographic computation of the conductivity of strange metals, weakly perturbed by disorder coupled to scalar operators, including both the average conductivity as well as sample-to-sample fluctuations. Our findings are consistent with previous scaling arguments, though we point out logarithmic corrections in some special (holographic) cases. We also discuss the nature of superconducting instabilities in hyperscaling-violating geometries with appropriate choices of scalar couplings.

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to the Einstein-Maxwell theory in an asymptotically four-dimensional anti–de Sitter space spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond nonperturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

We model strange metals as quantum liquids without quasiparticle excitations, but with slow momentum relaxation, and with slow diffusive dynamics of a conserved charge and energy. General expressions are obtained for electrical, thermal and thermoelectric transport in the presence of an applied magnetic field using the memory matrix formalism. In the appropriate limits, our expressions agree with previous hydrodynamic and holographic results. We discuss the relationship of such results to thermoelectric and Hall transport measurements in the strange metal phase of the hole-doped cuprates.

Interactions between particles in quantum many-body systems can lead to collective behavior described by hydrodynamics. One such system is the electron-hole plasma in graphene near the charge neutrality point which can form a strongly coupled Dirac fluid. This charge neutral plasma of quasi-relativistic fermions is expected to exhibit a substantial enhancement of the thermal conductivity, due to decoupling of charge and heat currents within hydrodynamics. Employing high sensitivity Johnson noise thermometry, we report the breakdown of the Wiedemann-Franz law in graphene, with a thermal conductivity an order of magnitude larger than the value predicted by Fermi liquid theory. This result is a signature of the Dirac fluid, and constitutes direct evidence of collective motion in a quantum electronic fluid.

We develop a general hydrodynamic framework for computing direct current thermal and electric transport in a strongly interacting finite temperature quantum system near a Lorentz-invariant quantum critical point. Our framework is non-perturbative in the strength of long wavelength fluctuations in the background charge density of the electronic fluid, and requires the rate of electron-electron scattering to be faster than the rate of electron-impurity scattering. We use this formalism to compute transport coefficients in the Dirac fluid in clean samples of graphene near the charge neutrality point, and find results insensitive to long range Coulomb interactions. Numerical results are compared to recent experimental data on thermal and electrical conductivity in the Dirac fluid in graphene and substantially improved quantitative agreement over existing hydrodynamic theories is found. We comment on the interplay between the Dirac fluid and acoustic and optical phonons, and qualitatively explain experimentally observed effects. Our work paves the way for quantitative contact between experimentally realized condensed matter systems and the wide body of high energy inspired theories on transport in interacting many-body quantum systems.

We present a theory of thermoelectric transport in weakly disordered Weyl semimetals where the electron-electron scattering time is faster than the electron-impurity scattering time. Our hydrodynamic theory consists of relativistic fluids at each Weyl node, coupled together by perturbatively small inter-valley scattering, and long-range Coulomb interactions. The conductivity matrix of our theory is Onsager reciprocal and positive-semidefinite. In addition to the usual axial anomaly, we account for the effects of a distinct, axial-gravitational anomaly expected to be present in Weyl semimetals. Negative thermal magnetoresistance is a sharp, experimentally accessible signature of this axial-gravitational anomaly, even beyond the hydrodynamic limit.