Condensed Matter

I will review and compare numerous models for metallic states without quasiparticle excitations. The solvable SYK model provides a useful starting point, and also has remarkable holographic connections to the quantum gravity of black holes in AdS2. Quantum critical states of two-dimensional metals are obtained by coupling the fermions to fluctuating bosonic order parameters or gauge fields: I will discuss their physical properties and possible connections to experiments.

I will discuss recent progress in understanding the consequences of hydrodynamic electron flow on measurable transport properties of metals, focusing on metals where the electrons behave as a charge neutral relativistic plasma. In graphene, I will connect our theoretical models with experimental data and show how we can explain features of transport in graphene that are inconsistent with quasiparticle transport. I will then discuss the extension of these results to Weyl semimetals, which are modeled by a system of multiple chiral fluids. Negative magnetoresistance can occur in both electric and thermal transport; the latter is a consequence of a distinct axial-gravitational anomaly. Future transport experiments on Weyl semimetals can discover this exotic type of anomaly in the lab.

The semimetal-superconductor quantum phase transition of 2D Dirac fermions, such as found on the surface of a topological insulator, is conjectured to exhibit an emergent N=2 supersymmetry, based on a one-loop renormalization group analysis. In this talk I will present further evidence for this conjecture based on a three-loop analysis. Assuming the conjecture is true, I will present exact results for certain critical properties including the optical conductivity, shear viscosity, and entanglement entropy at zero temperature, as well as the finite-temperature optical conductivity.

We present some recent developments in the framework of holographic (Lorentz violating) massive gravity. We rigorously define the most generic isotropic setup in 3+1 dimensions and we study in detail its phenomenology. We describe the electric and the viscoelastic responses of the system and we comment on the fate of the KSS viscosity bound in absence of translational symmetry. We conclude with some discussion hints and comments for the future.

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly based on numerical arguments, I will provide an analytical proof that this is indeed the case. In particular, I will present a technique which allows to explicitely compute the low-energy effective action for the boundary theory starting from the bulk system. This will be done for an arbitrary number of dimensions and an arbitrary potential. I will recover the known dispersion relation for conformal first sound.

I will present a hydrodynamic description of matter in a charge density wave (or "smectic") phase. As in superfluids, the spontaneous breaking of a continuous symmetry -- here translations in one direction -- adds a Goldstone phase to the usual long lived hydrodynamic variables. This phase propagates as a highly anisotropic "second sound" mode at low energies, affecting properties such as transport. Phase fluctuations, due to proliferating dislocations, give a finite life-time to certain collective modes, which can be experimentally probed e.g. by measuring ultrasound attenuation. Using the memory matrix, the hydrodynamic approach predicts sound attenuation to be proportional to the shear viscosity of the normal (non-smectic) state.

In 2014 Hartnoll proposed that the diffusion constants of incoherent metals should be bounded as $ D \geq \hbar v^2/ (k_B T)$, where v is a characteristic velocity. In this talk I will describe a large class of holographic theories that saturate such a bound, with $v$ being the velocity of the butterfly effect. Our results suggest a novel connection between transport at strong coupling and the field of quantum chaos.