TY - BOOK

T1 - Quantum Dots Coupled to a Superconductor

T2 - Theory and Experiments on InAs Nanowires

AU - Jellinggaard, Anders Robert

PY - 2016

Y1 - 2016

N2 - In this thesis, sub-gap states in bottom-gated InAs N–dot–S, N–doubledot–S, and N–dot–S–dot–N devices are investigated, and several differenttheories are developed to model these states. Experimental resultsinclude tracking single levels of the dot in an N–dot–S device as thetunnel couplings are tuned electrostatically. This includes tuning theodd occupation of the dot through a quantum phase transition, whereit forms a singlet with excitations in the superconductor. We detail thefabrication of these bottom gated devices, which additionally featureancillary sensor dots connected with floating gates.A numerical technique is developed, which predicts the position ofYu-Shiba-Rusinov sub-gap states in the proximitized Anderson modelas well as properties of these states. This theory is valid for all occupationsof the dot and for weak to intermediate coupling. We compare itto the Numerical Renormalization Group (NRG) process.The thesis also details an implementation of the NRG process,which was written for this project and includes an original methodfor mapping the discretized hybridization hamiltonian to a chain. Wetake significant steps towards a justification of the NRG process, whichis based on the general properties of Krylov subspaces alone, and isthus not tied to a specific physical system.

AB - In this thesis, sub-gap states in bottom-gated InAs N–dot–S, N–doubledot–S, and N–dot–S–dot–N devices are investigated, and several differenttheories are developed to model these states. Experimental resultsinclude tracking single levels of the dot in an N–dot–S device as thetunnel couplings are tuned electrostatically. This includes tuning theodd occupation of the dot through a quantum phase transition, whereit forms a singlet with excitations in the superconductor. We detail thefabrication of these bottom gated devices, which additionally featureancillary sensor dots connected with floating gates.A numerical technique is developed, which predicts the position ofYu-Shiba-Rusinov sub-gap states in the proximitized Anderson modelas well as properties of these states. This theory is valid for all occupationsof the dot and for weak to intermediate coupling. We compare itto the Numerical Renormalization Group (NRG) process.The thesis also details an implementation of the NRG process,which was written for this project and includes an original methodfor mapping the discretized hybridization hamiltonian to a chain. Wetake significant steps towards a justification of the NRG process, whichis based on the general properties of Krylov subspaces alone, and isthus not tied to a specific physical system.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122654358505763

M3 - Ph.D. thesis

BT - Quantum Dots Coupled to a Superconductor

PB - The Niels Bohr Institute, Faculty of Science, University of Copenhagen

ER -