QUANTUM PHASE TRANSITIONS AND QUANTUM TRANSPORT IN
LOW-DIMENSIONAL TOPOLOGICAL SYSTEMS
Physics, PhD Dissertation, 2017
Assoc. Prof. İnanç Adagideli (Thesis Advisor), Assoc. Prof. Emrah Kalemci, Assoc. Prof. İ. Burç Mısırlıoğlu, Assoc. Prof. Levent Subaşı, Assoc. Prof. Özgür E. Müstecaplıoğlu
Date & Time: June 28th, 2017 – 09:40 AM
Place: FENS L027
Keywords : Topological insulators, Electronic transport, Mesoscopic and nanoscale systems, Theory of electronic transport, Level Statistics
Topological insulators are novel phases of matter characterized by a topological number and feature insulating bulk and topologically protected edge states. In this thesis, we focus on quantum phase transitions that change the topological index, and transport of charge and spin in topological insulator nanostructures.
We first consider topological phases in disordered quasi-1D topological superconductors. The Majorana edge states on a topologically nontrivial nanowire are protected from disorder up to a certain strength, after which the wire transitions to a trivial state. We find that more disorder can push the system back into a topological state in multichanneled nanowires, creating previously unreported fragmentation of the topological phase diagram.
We next discuss arbitrarily-shaped and/or disordered topological superconductors and their ground state fermion parity. As external parameters are varied, even and odd parity ground states cross, causing a quantum phase transition. We find that the statistics of parity-crossings are universal and described by normal-state properties. We also determine the shape dependence of the parity crossings.
Finally, we consider quantum transport through the edge states in a quantum spin Hall insulator in the presence of nuclear spins. We find that a properly initialized nuclear spin bath can be used as a non-energetic resource to induce charge current in the device, that can power an external load using heat from electrical reservoirs. Resetting the spin-resource requires dissipation of heat in agreement with the Landauer’s principle. Our calculations show that the equivalent energy/power density stored in the device exceeds existing supercapacitors.