Weyl Points In Superconducting Nanostructures

Topological band theory has contributed to some of the most astonishing developments in solid-state physics. The unique attributes that arise from topological effects are at the focus of modern experimental and theoretical research. Weyl point, a topological defect at the Fermi surface, enables topological transitions and transport phenomena. Its existence is considerably restricted in natural materials due to the tuning and dimension constraint. Recently, The Weyl points have been predicted to accommodate within superconducting nanostructures in the spectrum of Andreev bound states. Theoretically, one can easily manipulate the dimensionality and the tuning process through elementary approaches with specially designed structures. This opens up a new window for explorations in a higher dimension, high-order topological effects,Majorana states, and other complications even though it may be still experimentally challenging. One realization of such structures is the multi-terminal Josephson junction. The parameters are the superconducting phase differences of the terminals and theWeyl points reside at low energies within the superconducting gap. Chapter 2 of this thesis investigates the topological effect in the quantized transconductance of such a structure considering the presence of the continuous spectrum that is intrinsic to superconductors. This research is based on scattering formalism and relates the Landauer conductance to the continuous spectrumas a background field in the regular topological charge picture. Chapter 3 is based on a very generic superconducting nanostructure setup so long as it hosts Weyl points in it. The research proposes a unit that tunnel-couples such a setup with a quantum dot. The distinct feature of the spectrum, especially the distinction between its spin-singlet and spin-doublet due to spin-orbit coupling, leads to an exploration of the state manipulation. Eventually, through adiabatic and diabatic approaches, one can feasibly realize a full unitary transformation of the spectrum. Because of this, the unit could easily find its promising application in entangled qubits. Chapter 4 also relies on the generic low-energy Weyl point setup in the superconducting nanostructure, but instead, it is weakly tunnel-coupled to regularmetallic leads. We know that spintronics explores the intrinsic spin degree of freedom. It is usually realized on magnetic materials. In the setup of this research, the energy spectrum contains a natural spin-orbit that creates a minimalistic magnetic state in the vicinity of theWeyl point. The spin structure of the spectrum allows fine-controls over the spin and switch between magnetic/non-magnetic state. Hence this chapter’s research focuses on the possible spintronics features based on master equations. Chapter 5 furthers the research of chapter 4. It considers a universal energy scale sets up by the tunnel coupling strength. In the language of the Green’s function, this chapter studies the topological effect through the response function. This set up is a suitable example of low energy Weyl points situated in the presence of a low-energy continuous spectrum brought by electrons in the leads. We have seen in Chapter 1 how the continuous spectrum above the gap modifies the topology leading to a non-quantized contribution to the transconductance. The peculiarity of couplingWeyl points to a low energy continuous spectrum is that the dissipation gives rise to a redefinition of the Berry curvature, whichmanifests as a continuous density of topological charge instead of a pointlike one. This unusual characteristic can be captured by the tunnel current and thus can assist the detection ofWeyl points experimentally.