Dynamical Electromagnetism in Holography

The “strange metal” phase, exhibited by certain types of graphene and high-Tc superconductors above the transition temperature, sits at the frontier of condensed matter physics. However, successfully describing the phase proves to be a difficult task, as it is characterized by strong correlations, making conventional methods fail. Hence there is a need of novel approaches, where an alternative method comes from high-energy physics in the form of the holographic principle. It states that the strongly coupled theory can be mapped to a dual, weakly coupled, gravitational theory in one dimension higher, making calculations go from impossible to feasible. Surface plasmon polaritons (SPPs) are a valuable tool in an experimentalists toolbox, as they can serve as a probe of their surroundings. They may therefore useful in the design of the experiments needed to answer the questions about the strange metal phase. In this thesis, we model SPPs propagating on a strange metal in a holographic setting. By numerically solving unwieldy differential equations in the dual gravitational theory, with boundary conditions specified by the SPP system, we are able to obtain some numerical dispersion relations for the plasmons, although more work is needed. The results suggest that magnetic effects, which normally are suppressed, might come into play when the material is strongly correlated.

Today’s novel materials can display many interesting phases. Two-dimensional materials with strong electron-electron interactions allow the electrons to enter a hydrodynamic regime at intermediate temperatures. This thesis presents a method for an exact description of the quasiparticle distribution in terms of kinetic theory, valid beyond the asymptotic low-temperature regime used in perturbative approaches. This is used to obtain of the full mode spectrum of the interacting electron gas. At low temperatures, the existence of long-lived modes of odd parity hint at the existence of a new transport regime in between the limits of ballistic and hydrodynamic flow. The method is also used to determine the shear viscosity of the electron liquid beyond the low temperature limit. If the coupling becomes strong enough, it invalidates the quasiparticle picture, which undermines many established methods within many-body physics. This happens in the strange metal phase of high-temperature superconductors, where the holographic duality – providing a description of a strongly coupled theory in terms of a weakly coupled gravitational theory – serves as one of the few ways to study the strongly coupled physics. Recent experiments on strange metals show an incoherent plasmon at small momenta, in qualitative agreement with previous holographic models of bulk plasmons. However, the relevant experiments also couple to collective surface excitations, which hitherto has not been considered. This thesis also presents a model for surface plasmon polaritons using the holographic duality, improving the theoretical description of plasmons in strongly correlated materials.