Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa2-320689
Roy, Sthitadhi
Schreiber, Michael ; Moessner, Roderich (Gutachter)
Nonequilibrium and semiclassical dynamics in topological phases of quantum matter
Kurzfassung in englisch
The discovery of topological phases of quantum matter has brought about a new paradigm in the understanding of rich and exotic phases which fall outside the conventional classification of phases using Landau’s theory of broken symmetries. The thesis addresses various aspects of nonequilibrium and semiclassical dynamics in systems hosting such topological phases. While the study of nonequilibrium closed quantum systems is an exciting field in itself, it has gained a lot of importance in the context topological systems. Much of this has been fuelled by the immense progress in the experimental realisation of such topological systems with ultracold atoms in optical lattices. As measurements of real-time responses are natural in such experiments, they have served as ideal platforms to study the nonequilibrium responses of topological systems.The studies presented in this thesis can be brought under the umbrella of two broad questions, first, how non-equilibrium dynamics can be used to characterize topological phases or locate topological critical points, and second, what new topological phases can be realized out of equilibrium.
Generally, non-trivial topology of a system manifests itself via quantised responses at the edges of a system or via appropriate non-local string order parameters which are rather difficult to measure in experiments. Local measurements in the bulk are more conducive to experiments. We address this question by showing that within a non-equilibrium setup obtained via a quantum quench, local bulk observables can show sharp signatures of topological quantum criticality via a non-analyticity in parameter space at the critical point. Although via non-local basis transformations, topological phase transitions can often be mapped onto conventional phase transitions, a remarkable aspect of this result is that within the non-equilibrium setup, the local bulk observables can locate the critical point in the natural basis where the phase transition is topological and not described by a local order parameter.
The next question that the thesis explores is how nonequilibrium and semiclassical dynamics, more precisely wavepacket dynamics, can be used to probe topological phases with an emphasis on Chern insulators in two dimensions. Chern insulators are essentially similar to quantum Hall systems except that they show quantised Hall responses in the absence of external magnetic fields due to intrinsically broken time-reversal symmetry. The Hall conductance in these systems is related to an integer-valued topological invariant characterising the energy bands, known as the Chern number, which is the net flux of Berry curvature through the entire two-dimensional Brillouin zone. The Berry curvature modifies the semiclassical equations of motion describing the dynamics of a wavepacket. Hence, the real-time motion of a wavepacket is used to map out the Berry curvature and thence the topology of the band. Complementary to these bulk responses, spatially local quenches in Chern insulators are also shown as probes for the presence or absence of chiral edge modes.
The idea of semiclassical equations of motion can be extended to the case of a three-dimensional Weyl semimetal. Weyl semimetals are a new class of gapless topological systems in three dimensions, elementary fermionic excitations of which are described by the Weyl equation. Since in cold atom experiments, magnetic fields are realized synthetically via phases in complex hoppings, exploring the Hofstadter limit is a natural scenario. When the magnetic field penetrating a two-dimensional system becomes so large that the associated magnetic length becomes comparable to the lattice spacing, the energy spectrum of the system is described by fractal known as the Hofstadter butterfly. We introduce the Weyl butterfly, a set of fractals which describes the spectrum of a Weyl semimetal subjected to a magnetic field, and we characterize the fractal set of Weyl nodes in the spectrum using wavepacket dynamics to reveal their chirality and location. Moreover, we show that the chiral anomaly -- a hallmark of the topological Weyl semimetal -- does not remain proportional to the magnetic field at large fields, but rather inherits a fractal structure of linear regimes as a function of external field.
Finally, the thesis addresses the question of novel nonequilibrium topological phases of matter. In the context of phase structures of nonequilibrium systems, periodically driven, also known as Floquet systems, has received a lot of attention. Moreover, the role of disorder has been shown to be rather crucial as generically such Floquet systems heat up to featureless infinite temperature states. Also, in the context of topological systems like Chern insulators, disorder is expected to play an interesting role given that it is important in localising the bulk cyclotron orbits in an integer quantum Hall system. With this motivation, the phase diagram of the disordered Chern insulator with a Floquet drive is explored in the thesis. In the model considered there are indeed topological Floquet edge modes which are exclusive to Floquet systems, for instance, the edge modes in gaps of the quasienergy spectrum around ±pi. There are also disorder-induced topological transitions between different Floquet topological phases, due to a mechanism shown to be of levitation-annihilation type.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Theoretische Physik (-Theorie ungeordneter Systeme-) | |
| Fakultät: | Fakultät für Naturwissenschaften | |
| Dokumentart: | Dissertation | |
| Betreuer: | Schreiber, Michael (Prof. Dr.) | |
| URL/URN: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa2-320689 | |
| SWD-Schlagwörter: | Naturwissenschaften , Physik | |
| Freie Schlagwörter (Englisch): | nonequilibrium , topological , quantum , phases , physics | |
| DDC-Sachgruppe: | Naturwissenschaften und Mathematik, Physik | |
| Tag der mündlichen Prüfung | 28.03.2018 |
