Meng, Tobias (2012). Quantum Critical Matter: Quantum Phase Transitions with Multiple Dynamics and Weyl Superconductors. PhD thesis, Universität zu Köln.

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In this PhD thesis, the physics of quantum critical matter and exotic quantum state close to quantum phase transitions is investigated. We will focus on three different examples that highlight some of the interesting phenomena related to quantum phase transitions. Firstly, we discuss the physics of quantum phase transitions in quantum wires as a function of an external gate voltage when new subbands are activated. We find that at these transitions, strong correlations lead to the formation of an impenetrable gas of polarons, and identify criteria for possible instabilities in the spin- and charge sectors of the model. Our analysis is based on the combination of exact resummations, renormalization group techniques and Luttinger liquid approaches. Secondly, we turn to the physics of multiple divergent time scales close to a quantum critical point. Using an appropriately generalized renormalization group approach, we identify that the presence of multiple dynamics at a quantum phase transition can lead to the emergence of new critical scaling exponents and thus to the breakdown of the ususal scaling schemes. We calculate the critical behavior of various thermodynamic properties and detail how unusual physics can arise. It is hoped that these results might be helpful for the interpretation of experimental scaling puzzles close to quantum critical points. Thirdly, we turn to the physics of topological transitions, and more precisely the physics of Weyl superconductors. The latter are the superconducting variant of the topologically non-trivial Weyl semimetals, and emerge at the quantum phase transition between a topological superconductor and a normal insulator upon perturbing the transition with a time reversal symmetry breaking perturbation, such as magnetism. We characterize the topological properties of Weyl superconductors and establish a topological phase diagram for a particular realization in heterostructures. We discuss the physics of vortices in Weyl superconductors, and establish under which conditions they can trap zero energy Majorana modes. Our disucssion ends with some remarks on possible experimental signatures.

Item Type: Thesis (PhD thesis)
CreatorsEmailORCIDORCID Put Code
Meng, TobiasTobias.Meng@uni-koeln.deUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-47839
Date: 10 July 2012
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects: Physics
Uncontrolled Keywords:
quantum critical matterEnglish
multiple dynamicsEnglish
Weyl superconductorsEnglish
quantum wiresEnglish
quantum phase transitionsEnglish
quantum critical scalingEnglish
strong correlationsEnglish
unconventional superconductivityEnglish
topological superconductorsEnglish
Wigner crystalEnglish
Majorana fermionsEnglish
Date of oral exam: 19 June 2012
NameAcademic Title
Rosch, AchimProf. Dr.
Trebst, SimonProf. Dr.
Schmalian, JörgProf. Dr.
Refereed: Yes


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