ABSTRACT - DRUM - University of Maryland

List of Figures
1.1 Braiding of Majorana fermions bound to vortices. . . . . . . . . . . . 15
1.2 Illustrations of the two heterostructure that support Majorana excitations:
(a) a superconductor-topological insulator heterostructure,
(b) a superconductor-semiconductor-magnetic insulator heterostructure.
Reproduced from Bonderson, Das Sarma, Freedman and Nayak,
arXiv:1003.2856 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1 The phase diagram for fermions on a square lattice with nearestneighbor
hoppings and attraction (g/t=1). The phase boundary separates
a normal metal and a topological (p x +ip y )-wave SC. The insets
display FSs for µ < 0 (left) and µ > 0 (right). . . . . . . . . . . . . . 39
2.2 The phase diagram for spinless fermions on a triangular lattice with
nearest-neighbor hoppings and attraction (g/t=1). The bottom of
the band is located at µ = −6t and the top is at µ = 3t; µ ∗ = 2t
corresponds to a van Hove singularity. Two SC phases, with (p x +ip y )-
and f-wave symmetries are present. They are separated by a firstorder
phase transition at µ cr /t ≈ 1.057. The insets (left to right) are
the FSs for µ < µ ∗ , µ µ ∗ , and µ > µ ∗ and the dashed lines indicate
the nodal directions of the f-wave SC. . . . . . . . . . . . . . . . . . 45
5.1 Mach-Zehnder interferometer proposed in Ref. [122] for topological
qubit detection. Due to the Aharonov-Casher effect, the vortex
current is sensitive to the charge enclosed. Long Josephson junction
between two topological superconductors carries allows for Josephson
vortices (fluxons) that carry Majorana zero-energy modes. . . . . . . 84
5.2 Schematic illustration of the topological qubit coupled to thermal
bath, modeled by a collection of harmonic oscillators. . . . . . . . . . 94
7.1 Schematic view of the two chains coupled by pair tunneling(denoted
by dashed lines). The chains are bended near the two ends to avoid
the single-particle tunneling. . . . . . . . . . . . . . . . . . . . . . . . 136
vi