Quantum phase transitions and quantum transport in low-dimensional topological systems

In this thesis, we focus on quantum phase transitions that change the topological index of topological insulators and superconductors, which are states of matter featuring topologically protected edge states and insulating bulk, and on transport of charge and spin in topological insulator nanostructures. We consider topological phases in disordered quasi- 1D topological superconductors. The Majorana edge states on topologically nontrivial nanowires were previously found to be protected from disorder as long as the localization length is larger than the coherence length, after which the wire transitions to a trivial state. We find that changing 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 quantum phase transitions. We find that the statistics of parity-crossings are universal and described by normal-state properties and determine the shape dependence of the parity crossings. Finally, we consider edge state quantum transport in quantum spin Hall insulators 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, providing 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

Fermion parity switches of the ground state of Majorana billiards

Majorana billiards are finitely sized, arbitrarily shaped superconducting islands that host Majorana bound states. We study the fermion-parity switches of the ground state of Majorana billiards. In particular, we study the density and statistics of these fermion-parity switches as a function of applied magnetic field and chemical potential. We derive formulas that specify how the average density of fermion-parity switches depends on the geometrical shape of the billiard. Moreover, we show how oscillations around this average value are determined by the classical periodic orbits of the billiard. Finally, we find that the statistics of the spacings of these fermion-parity switches are universal and are described by a random matrix ensemble, the choice of which depends on the antiunitary symmetries of the system in its normal state. We thus demonstrate that “one can hear (information about) the shape of a Majorana billiard” by investigating its “fermion-parity switch spectrum.

Work extraction and Landauer's principle in a quantum spin Hall device

Landauer's principle states that erasure of each bit of information in a system requires at least a unit of energy kBTln2 to be dissipated. In return, the blank bit may possibly be utilized to extract usable work of the amount kBTln2, in keeping with the second law of thermodynamics. While in principle any collection of spins can be utilized as information storage, work extraction by utilizing this resource in principle requires specialized engines that are capable of using this resource. In this work, we focus on heat and charge transport in a quantum spin Hall device in the presence of a spin bath. We show how a properly initialized nuclear spin subsystem can be used as a memory resource for a Maxwell's demon to harvest available heat energy from the reservoirs to induce charge current that can power an external electrical load. We also show how to initialize the nuclear spin subsystem using applied bias currents which necessarily dissipate energy, hence demonstrating Landauer's principle. This provides an alternative method of “energy storage” in an all-electrical device. We finally propose a realistic setup to experimentally observe a Landauer erasure/work extraction cycle

Implementing Maxwell's demon in spintronics devices

Landauer's principle states that erasure of each bit of information in a system requires at least a unit of energy kBTln2 to be dissipated. In return, the blank bit may possibly be utilized to extract usable work of the amount kBTln2, in keeping with the second law of thermodynamics. In this work, we build on our earlier work on spin Hall devices and focus on heat and charge transport in generic spintronics devices in the presence of a spin bath. We show how a properly initialized nuclear spin subsystem can be used as a memory resource for a Maxwell's Demon to harvest available heat energy from the reservoirs to induce charge current that can power an external electrical load. We also show how to initialize the nuclear spin subsystem using charge currents which necessarily dissipate energy. This opens up a new avenue towards energy storage applications using spintronics devices

The impact of carbon capture and storage on coal resource depletion

In this work, we investigate the effect of disorder on the topological properties of multichannel superconductor nanowires. While the standard expectation is that the spectral gap is closed and opened at transitions changing the topological property of the ground state, we show that the closing and opening of a \textit{transport} gap can also cause topological transitions, even in the presence of (localized) states at both sides of the transition. Such transport gaps, induced by disorder, can thus change the topological index, driving a topologically trivial wire into a nontrivial state. We focus on nanowires exhibiting \textit{p}-wave superconductivity as well as Rashba semiconductor nanowires in proximity to a conventional superconductor, and obtain analytical formulas for topological transitions in these wires, valid for generic realizations of disorder, generalizing earlier results. Full tight-binding simulations show excellent agreement with our analytical results without any fitting parameters

Superconducting diode effect sign change in epitaxial Al-InAs Josephson junctions

Abstract There has recently been a surge of interest in studying the superconducting diode effect (SDE) partly due to the possibility of uncovering the intrinsic properties of a material system. A change of sign of the SDE at finite magnetic field has previously been attributed to different mechanisms. Here, we observe the SDE in epitaxial Al-InAs Josephson junctions with strong Rashba spin-orbit coupling (SOC). We show that this effect strongly depends on the orientation of the in-plane magnetic field. In the presence of a strong magnetic field, we observe a change of sign in the SDE. Simulation and measurement of supercurrent suggest that depending on the superconducting widths, W S, this sign change may not necessarily be related to 0–π or topological transitions. We find that the strongest sign change in junctions with narrow W S is consistent with SOC-induced asymmetry of the critical current under magnetic-field inversion, while in wider W S, the sign reversal could be related to 0–π transitions and topological superconductivity