One-dimensional quantum transport phenomena in periodically modulated electron waveguides

Student thesis: Doctoral Thesis

Abstract

The study of quantum transport in one dimension is of great interest in many areas of condensed matter physics. This thesis is motivated by conductance measurements in modulated LAO/STO nanowires, where a strong conductance baseline of 2e 2/h is observed when a Kronig-Penney potential is applied, which survives up to external magnetic fields > 18 T. This is also observed when the nanowire is helically modulated, but an additional feature is the appearance of conductance oscillations above the 2e 2/h baseline which occur at lower energies than the 4e 2/h peak. In order to model this, we begin by constructing an electron waveguide model for the nanowire formed at the LAO/STO interface. We then include the effect of periodic modulations and associated spin-orbit coupling resulting from these, and analyse the resulting band structure and conductance, finding that a single electron model is not sufficient to explain the 2e 2/h baseline. This was found in previous work, and the solution is to include electron-electron interactions. To include the effects of these, we begin with a standard BCS-like mean-field model. To study first the effect coming from a periodic modulation of the potential in the waveguide (vertical modulation), we introduce only the associated spin-orbit coupling to this model. We find that this leads to enhanced pairing, and could potentially explain the strong baseline of 2e 2/h. Additionally, we look only at the effect of a periodic modulation in the centre of the nanowire (lateral modulation), which we find introduces triplet pairing in the waveguide region. Combining these two modulations together, we extend the mean-field model again to include the form of the modulation potential alongside associated spin-orbit couplings to study the helical waveguide. We observe enhanced pairing and triplet pairing simultaneously. To study the oscillations in conductance, we introduce a phenomenological pair scattering model where triplet pairs incedent on the interface between helical and unmodulated regions can backscatter. We find that this model can indeed produce oscillations above the 2e 2/h baseline.
Date of Award12 Aug 2024
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council) & University of Strathclyde
SupervisorAndrew Daley (Supervisor) & Gian-Luca Oppo (Supervisor)

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