AdS/CFT gives a framework for using calculations from a weakly curved gravitational theory to describe phenomena in strongly correlated matter. In this work we study some holographic models this...Show moreAdS/CFT gives a framework for using calculations from a weakly curved gravitational theory to describe phenomena in strongly correlated matter. In this work we study some holographic models this has put forward, such as the Reissner-Nordstro ̈m metal and the holographic superconductor. Of these models we observe transport properties like the optical conductivity under both translational invariance and broken symmetry. Lastly, we merged the two systems into the two-charge holographic superconductor and managed to again see the phase transition, measure the optical conductivity and analyse the two- fluid model.Show less
Since the 80s, strange metals, metals where the electrons are so densely entangled that the conventional condensed matter paradigm of Short Ranged Entanglement fails, have eluded any form of study...Show moreSince the 80s, strange metals, metals where the electrons are so densely entangled that the conventional condensed matter paradigm of Short Ranged Entanglement fails, have eluded any form of study due to the sign problem, which renders numerical calculations impossible. However, holography, a duality between strongly coupled quantum field theory problems and classical general relativity problems of one spatial dimension higher, grants us a way to circumvent the sign problem. In this thesis, we will run a modified version of code that was once used to simulate binary black holes on a supercomputer to calculate the properties of two $2+1$-dimensional holographic models for strange metals, the Reissner-Nordstr\"om metal and the Gubser-Rocha metal, subject to an ionic lattice potential: the code needed to simulate the Gubser-Rocha metal was only finished last year. We then investigate whether the DC electrical conductivity $\sigma$, thermopower $\alpha$ and thermal conductivity $\bar{\kappa}$ obey four different Drude models: one basic relativistic model and three models with different extra incoherent terms, models A, B and C. We find that model A, the most conventional model, fails, while the conductivities obey model C ($\kappa$-dominated transport) for low lattice strength $A$ and model B ($\sigma_{Q=0}$-dominated transport) for high $A$. We suspect this surprising result is caused by a pole collision causing a crossover between two regimes, but more research needs to be done to verify this.Show less
In the past decades experiments have found condensed matter systems which could not be described by the conventional methods of condensed matter theory, these are densely entangled strange metals....Show moreIn the past decades experiments have found condensed matter systems which could not be described by the conventional methods of condensed matter theory, these are densely entangled strange metals. During the same period, the string theory community has developed the AdS/CFT correspondence, a duality between field theories and gravitational systems. This duality may be used to understand condensed matter field theory from a gravitational perspective. It is especially useful for densely entangled quantum matter, which can be described according to the duality by charged black hole systems of classical gravity. In this thesis we will consider the Gubser-Rocha black hole of the Einstein-Maxwell-Dilaton action to describe a metal. To understand charge and heat transport in these metals, one needs a mechanism to dissipate momentum. This is explicitly implemented by introducing a periodic lattice in the condensed matter system. Using heavy numerical codes to calculate the gravitational differential equations that are dual to the metal, we can find the transport properties of our metal. In this metal a linear in T resistivity is found, which is a famous property of the strange metals. Furthermore we find empirically a saturation of the conductivity, which could be the instance of Planckian dissipation and the minimal viscosity of the strange metal.Show less
The AdS/CFT correspondence provides a way to perform computations on strongly interacting, conformal systems living in the AdS boundary by studying the behaviour of the holographic dual in the form...Show moreThe AdS/CFT correspondence provides a way to perform computations on strongly interacting, conformal systems living in the AdS boundary by studying the behaviour of the holographic dual in the form of a black hole in the centre. Until now, such inquiries where limited to spatially homogeneous systems, however, metallic systems are characterized by the presence of an ionic lattice. We study the DC magneto-transport of a dual to Reissner-Nordstrom metal using a novel code which numerically computes its behaviour in two dimensions in the presence of an explicit lattice and a magnetic field. We find that conductivity is dominated by Drude transport at low temperatures. Furthermore, we find that the transport is described by a transverse relaxation rate of angular momentum in addition to a longitudinal rate and these depend differently on temperature. This hints that AdS/CMT may provide an explanation to the anomalous temperature scaling of the Hall Angle in the strange metal phase of high temperature superconductors.Show less
Adopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network...Show moreAdopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network model were developed. The mappings primarily serve to engineer a 2D phase transition into a higher dimensional tree network and show what holographic properties are obtained by merely invoking some conceptual ’ingredients’ from the holographic duality. The networks were studied by MC simulation of the Ising model and subsequent construction. This thesis then further reports on efforts to describe the network ensemble seeded off the Ising model independently, by a(n) (exponential) random graph model.Show less
Unconventional superconductivity comes in a variety of forms, of which the high-Tc cuprates are one with a complex phase diagram containing rich physics. Over certain doping range, strange metal...Show moreUnconventional superconductivity comes in a variety of forms, of which the high-Tc cuprates are one with a complex phase diagram containing rich physics. Over certain doping range, strange metal behaviour is seen, for which a theoretical explanation is still lacking. This thesis reviews the theoretical advances in strange metal research and provides an overview of the experimental tools available. The experimental suggestions are based on the predictions of the AdS-CFT correspondence as a possible explanation for the strange metal peculiarities. This theory of holographic duality is characterised by the prediction of unconventional hydrodynamics in the strange metal cuprates. Therefore, several suggestions for hydrodynamic experimentation are given, firstly on the boundary effects for the electron current flow profile and secondly on viscous electron backflow after a nano-sized constriction. These are phenomena only yet observed in graphene. Thirdly, the sign-reversing Hall effect as seen in graphene possibly points towards unconventional hydrodynamics in the cuprates as well. This is followed by the description of preparatory experiments conducted on exfoliated flakes of Bi2Sr2CuO6+x, with a determined Tc of 10.0 K ± 0.3 K. These strange metal experiments confirm literature values and provide a solid platform for conducting future experiments on possible unconventional electron hydrodynamics in this material.Show less
We use Inline Digital Holography to measure the diffusion coefficient of spherical colloids with a 1.06mm radius in the bulk of a liquid. We obtain a diffusion coefficient of 0.23 +/- 0.03mm2/s...Show moreWe use Inline Digital Holography to measure the diffusion coefficient of spherical colloids with a 1.06mm radius in the bulk of a liquid. We obtain a diffusion coefficient of 0.23 +/- 0.03mm2/s which is in good agreement with Stokes-Einstein theory. We attempt the measurements to active Janus colloid spheres and explore the possibilities and limitations of the technique. We use the Discrete Dipole Approximation to fit the holograms to the Lorenz-Mie theory and report on the viability of the computation. We discuss the minimum necessary requirements for performing a successful fitting and analysis of the motion of Janus colloid spheres, in the bulk of a medium, using inline holographyShow less
