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 Award | 12 Aug 2024 |
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Original language | English |
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Awarding Institution | - University Of Strathclyde
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Sponsors | EPSRC (Engineering and Physical Sciences Research Council) & University of Strathclyde |
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Supervisor | Andrew Daley (Supervisor) & Gian-Luca Oppo (Supervisor) |
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