Observation of Quantum Correlations in Topological Solid-state Setups


Topological insulators are electronic materials that behave like an ordinary insulator internally (in the bulk), but have symmetry protected conducting states on the edge-sites or surface. The simplest case of non trivial topology found amongst these materials is the one-dimensional Su-Schreifer-Heeger (SSH) model. We analyse the unique features within the non-interacting SSH model and explicitly define both the edge states and the bound states and give the conditions of their presence. We show that the total number of bound states crucially depend on the scattering amplitudes and their phases. The sliding Luttinger liquid (SLL) phase can be destroyed by perturbations such as chargedensity wave (CDW) and superconducting (SC). We construct an analogue of the SSH model by coupling one-dimensional quantum wires packed in a two-dimensional array, with alternating couplings between wires. We calculate the scaling dimensions of the two most relevant (dangerous) perturbations, CDW and SC interwire couplings. We create a phase diagram and analyse whether nearest-neighbour interactions stabilise or destroy the SLL phase. Finally, we find a stability region for the SLL.

Additional Information: © Sulthana Begum, 2021 asserts their moral right to be identified as the author of this thesis. This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without appropriate permission or acknowledgement. If you have discovered material in Aston Publications Explorer which is unlawful e.g. breaches copyright, (either yours or that of a third party) or any other law, including but not limited to those relating to patent, trademark, confidentiality, data protection, obscenity, defamation, libel, then please read our Takedown Policy and contact the service immediately.
Institution: Aston University
Uncontrolled Keywords: Topological insulators,Su-Schreiffer-Heeger model,bound states,scattering amplitudes,Luttinger liquid,renormalization group,charge-density wave,superconductivity
Last Modified: 08 Dec 2023 08:58
Date Deposited: 28 Oct 2021 10:15
Completed Date: 2021
Authors: Begum, Sulthana



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