Each PhD student graduates by defending his or her PhD Thesis. Contact us at firstname.lastname@example.org in case you would like your PhD Thesis to be highlighted below.
We study the hydrodynamic properties of ultraclean interacting two-dimensional Dirac electrons with Keldysh quantum field theory. We study it from a weak-coupling and a strong-coupling perspective. We demonstrate that long-range Coulomb interactions play two independent roles: (i) they provide the inelastic and momentum-conserving scattering mechanism that leads to fast local equilibration; (ii) they facilitate the emergence of collective excitations, for instance plasmons, that contribute to transport properties on equal footing with electrons. Our approach is based on an effective field theory of the collective field coupled to electrons. Within a conserving approximation for the coupled system we derive a set of coupled quantum-kinetic equations. This builds the foundation of the derivation of the Boltzmann equations for the interacting system of electrons and plasmons. From this, we explicitly derive all the conservation laws and identify the extra contributions of energy density and pressure from the plasmons. We demonstrate that plasmons show up in thermo-electric transport properties as well as in quantities that enter the energy-momentum tensor, such as the viscosity.
As it becomes more and more difficult to miniaturize electronic circuits, the information industry is faced with an existential crisis: soon, it will no longer be possible to significantly expand the computational power of tried-and-trusted electronic technology. It should come as no surprise that both science and industry are frantically searching for a way to avert this impending catastrophe, and are even willing to entertain the notion of abandoning conventional electronics altogether if a more future-proof alternative can be found. One field of research that has this potential is spintronics: the use of intrinsic angular momentum—better known as spin—of electrons to store information. One of the key promises of spintronics is the ability to transport digital information without the need to shuttle around electrons, thereby avoiding the adverse phenomenon of Joule heating. To this end, one may simply perturb the magnetic order of a magnetic material. Doing so generates a spin wave or magnon, in which spin is passed between neighboring electrons while their position remains unchanged. In the subfield of magnonics—the study of magnons—the use of electrically insulating magnetic materials is currently being studied extensively by both experimentalists and theoreticians. In this thesis, I study the theoretical properties of magnons in three different systems involving a magnetic insulator and a heavy metal. In Chapter 4, I investigate whether ferromagnetic magnons can contribute to a phenomenon known as unidirectional spin-Hall magnetoresistance (USMR): a change in magnetoresistence of spintronic systems that occurs when the direction of an electric current is reversed. I predict that such an effect can indeed exist, but will most likely be very small. In Chapter 5, I focus on ballistic transport of magnons in one-dimensional ferromagnetic insulator (FI) chains exhibiting strong aniotropy. The anisotropy causes the magnons to become elliptically polarized, which breaks spin conservation and gives rise to characteristics not seen in systems with circular magnons, one example of which is squeezing: a fundamental asymmetry in quantum noise. The strong anisotropy required to produce significant magnon ellipticity is uncommon in real FIs. In Chapter 6, I therefore extend the work of Chapter 5 to antiferromagnetic spin chains, which bear mathematical semblance to anisotropic ferromagnets, but have ellipticity-producing terms that are intrinsically large. I show that the behavior of these systems depends strongly on the coupling to the antiferromagnet’s different sublattices. Although fairly minimal representations of real systems are developed in this work, they nevertheless have large, mostly unexplored parameter spaces, providing ample opportunity for further research in the near future. In the case of magnonic USMR in particular, recent experimental work by Liu et al. [Phys. Rev. Lett., 127:207206, Nov 2021] provides observations that run counter to our model, suggesting an extension of our work is necessary to capture the full phenomenology. On longer terms, a thorough understanding of the behavior of magnons may lead to pure-spintronic devices featuring low dissipation and extremely high operating frequencies. This, in turn, may revitalize advancement of computer hardware after the expected breakdown of Moore’s law.
In this dissertation we have studied black holes from various perspectives in string theory. One common theme of all the black holes that we have studied, is that they are constructed from branes. In part I we considered supersymmetry breaking Scherk-Schwarz duality twists and their effect on black holes in string theory. Our setup was type IIB string theory compactified on a four-torus and then further compactified on a circle with a duality twist along the circle. In these reductions we have studied several different brane configurations, the D1-D5-P system and dual configurations, that give rise to five-dimensional black holes in the standard untwisted reduction. Scherk-Schwarz reductions can be lifted to string theory so long as the monodromy is an element of the discrete U-duality group. We have worked out the quantization conditions that this requirement imposes on the twist parameters. Moreover, when the duality twist is a T-duality, the theory at the minimum of the potential can be described as an asymmetric orbifold. We have explicitly constructed this orbifold, and we have argued what conditions the survival of certain D-brane configurations puts on the orbifold. In part II we studied M2-branes and D2-branes wrapping Riemann surfaces with non-constant curvature: spindles and topological discs. These give rise to 4d black hole solutions in N=2 STU supergravity, whose near-horizon is a warped product of AdS2 with the Riemann surface. We have shown that the disc and spindle solutions can be obtained from different global completions of the same local solution, and we have analyzed their properties in detail. We have uplifted various truncations of this family of near-horizon solutions to M-theory and to massive type IIA. We found that some of these uplifts yield smooth solutions, while others yield solutions that have singularities associated to smeared branes or monopoles. In part III we have classified the necessary and sufficient conditions for near-horizon geometries of extremal supersymmetric rotating black holes in 11d supergravity, which are associated to rotating M2-branes. These near-horizon geometries contain an AdS2 factor which is fibered by the internal geometry. We have allowed for the most general fibration and flux configuration supporting rotating M2-branes. Due to the generality of our ansatz the black holes covered by our classification can include both electric and magnetic charges as well as angular momentum in 4d. By use of dualities, we have also presented necessary and sufficient conditions for the near-horizon geometry of a class of rotating black string solutions in type IIB. Finally, we have embedded several known 4d black hole solutions from the literature into our classification.