The superconducting properties of low dimensional superconductors, in which one or more
dimensions are comparable with the coherence length, differ significantly from bulk
superconductors. Basic properties such as the critical temperature and the critical fields can be
tuned by varying the size of the specimen. Unfortunately, thermal fluctuations are strongly
enhanced in low dimensionality. They cause dissipation and destroy the long-range-ordered state
at finite temperature. In 1D superconducting wires, thermal fluctuations induce slips in the phase
of the order parameter, resulting in non-zero resistance at any finite temperatures below the
critical temperature T

_{c}. These thermally-activated phase slip (TAPS) processes are theoretically
described by the Langer–Ambegaokar–McCumber–Halperin (LAMH) theory. Unlike in 1D
superconductors, a quasi-long-range-ordered phase-coherent state is possible through the famous
Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs below the mean field critical
temperature T

_{c} in continuous 2D superconducting films or 2D Josephson junction arrays.
Vortices with opposite vorticity form bound pairs below the BKT transition temperature T

_{BKT}.
This establishes a dissipationless quasi-long-range-ordered superconducting state. This
spectacular feature in 2D Josephson junction arrays has been demonstrated to provide a
possibility for phase-coherent superconductivity in arrays of weakly-coupled 1D
superconductors. The resulting phase-ordering transition between neighboring superconducting
chains in the lateral plane then instantly quenches the phase slips in individual wires and long-range
phase coherence in both the transverse and longitudinal directions is achieved. A 3D bulk
superconducting state is therefore possible in such a quasi-1D superconductor where individual
1D superconducting atomic chains or nanowires is weakly coupled to their neighbors.

In this thesis, the superconducting properties of quasi-1D superconductors, including 5 nm
Pb nanowire arrays embedded in the pores of mesoporous silica SBA-15 and the quasi-1D
carbide superconductor Sc

_{3}CoC

_{4}, as well as the properties of 2D superconductivity at the
interface of Bi

_{2}Te

_{3}/FeTe have been studied in great detail.

The 5 nm Pb nanowire arrays were fabricated in the 6 nm pores of mesoporous silica SBA-15
by Prof. Xijun Hu and Prof. Frank L. Y. Lam using a chemical vapor deposition (CVD) method.
Weakly-coupled superconductor-insulator-superconductor (SIS) junction arrays are formed in
this system. The superconducting properties of these 5 nm Pb nanowire arrays were studied in
detail by means of bulk DC magnetization, specific heat and electrical transport measurements.
The experimental results indicate that the superconducting fluctuations survive up to 10~11 K,
which is 3~4 K above the bulk critical temperature of 7.2 K of Pb. Zero resistance is reached
below 2 K. More interestingly, the upper critical field is observed to be ~15 T and is enhanced by
nearly 200 times when compared to the bulk Pb‘s small critical field of 0.08 T. The high onset
temperature may originate from the surface contribution, as the aspect ratio is large in a 5 nm
nanowire. The great enhancement of the upper critical field is interpreted as the replacement of
the orbital limit for superconductivity by the Pauli limit. These remarkable features observed in 5
nm Pb nanowire arrays demonstrate that the properties of a superconductor can be largely
modified by nano-structuring.

For the quasi-1D carbide superconductor Sc

_{3}CoC

_{4}, 1D [CoC

_{4}]

_{∞} ribbons embedded in a Sc
matrix are weakly coupled when the coherence length exceeds the interribbon distance at low
temperature. We have measured the transport properties of a single crystalline sample. The
sample was synthetized by Dr. Ernst-Wilhelm Scheidt, Dr. Georg Eickerling and Prof. Wolfgang
Scherer. A very broad transition starts at T

_{c}^{onset}=4.5 K and zero resistivity is reached below 1.2 K,
which confirms the 1D nature of [CoC

_{4}]

_{∞} ribbons. The resistivity approaches zero in two-steps,
where the first drop below the onset temperature is due to superconducting fluctuations in
individual [CoC

_{4}]

_{∞} ribbons and the coupling between neighboring [CoC

_{4}]

_{∞} ribbons causes the
second drop below 2 K. Similar to the quasi-1D superconductor Tl

_{2}Mo

_{6}Se

_{6}, solid evidence of a
BKT transition is also found in Sc

_{3}CoC

_{4}. The resistance above T

_{BKT} matches the theoretical
prediction extremely well with T

_{BKT} determined as 1.55 (± 0.1) K. Moreover, the conversion
from linear I-V characteristics above T

_{BKT} to a power law dependence V ∝ I

^{α(T)} below T

_{BKT} is
clearly observed. This is in perfect agreement with a determination of T

_{BKT}= 1.55 (± 0.05) K from the temperature where the exponent α(T

_{BKT})=3. Our experimental results of 5 nm Pb
nanowire arrays and the quasi-1D carbide superconductor Sc

_{3}CoC

_{4} indicate that the
superconducting transition in these arrays of weakly-coupled 1D superconductors undergoes a
crossover from a 1D fluctuating superconducting state at high temperatures towards a 3D bulk
phase-coherent superconducting state in the low-temperature regime, induced by the lateral
coupling via the Josephson or proximity effect.

Our collaborator Mr. Qinglin He and Prof. Iam Keong Sou fabricated a topological insulator
Bi

_{2}Te

_{3} on top of non-superconducting FeTe by van der Waals epitaxy with Molecular Beam
Epitaxy (MBE). Interestingly, the as-grown Bi

_{2}Te

_{3}/FeTe heterostructure becomes
superconducting with critical temperature depending on the thickness of the Bi

_{2}Te

_{3} layer. The
superconducting transition shows a pronounced 2D behavior with a BKT transition clearly
identified. In this thesis, I will present point contact spectroscopy data obtained on a
Bi

_{2}Te

_{3}(9QL)/FeTe sample of critical temperature T

_{c} ~ 13 K. The point contact was fabricated on
the edge of the heterostructure to provide tunneling into the edge of the interface. Three unusual
main features are observed for this new superconductor. An unusual zero bias conductance peak
(ZBCP) appears below 8 K that coincides with the establishment of the zero resistance
superconducting state. The height of the peak increases with decreasing temperature but the
width remains at a constant value of ~3.8 meV. The peak is rather robust against high magnetic
fields and no splitting is observed with the magnetic field applied along the crystalline a,b and c
directions. Interstitial excess iron, which is inevitably always present it FeTe, is discussed as
possible origin of the ZBCP, although more exotic states such as Majorana flat bands at the
interface edge cannot be fully excluded. Furthermore, the measured superconducting gap shows
a pronounced double-gap structure with Δ

_{1} ~ 4.7 meV and Δ

_{2} ~ 9.5 meV in the superconducting
state, respectively. The extremely large gaps are unexpected, since bulk FeSe or FeSe

_{1-x}Te

_{x} show
small superconducting gaps of ~2 – 3 meV with a comparable critical temperature. Our point
contact spectroscopy data also suggests that a pseudogap opens below 40 K and gradually
evolves into the superconducting gap below 15 K. This behavior is very similar to the high T

_{c}
cuprates in which a pseudogap appears well above the critical temperature. The energy-resolved
information obtained by point-contact spectroscopy demonstrates that this new interfacial
superconductor Bi

_{2}Te

_{3}(9QL)/FeTe has potential to be a high T

_{c} superconductor and a wealth of
exotic properties could exist.

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