- Page 1 and 2: ABSTRACT Title of dissertation: MAJ
- Page 3 and 4: MAJORANA QUBITS IN NON-ABELIAN TOPO
- Page 5 and 6: Acknowledgments First and foremost,
- Page 7 and 8: Table of Contents List of Figures L
- Page 9 and 10: List of Figures 1.1 Braiding of Maj
- Page 11 and 12: Chapter 1 Introduction The subject
- Page 13 and 14: closed throughout the path. If one
- Page 15 and 16: its original configuration, we requ
- Page 17 and 18: mathematics. It is easy to check th
- Page 19 and 20: Here τ x is the Pauli matrix actin
- Page 21 and 22: y constructing the ground state pro
- Page 23 and 24: here and leaves its proof to Append
- Page 25 and 26: the zero mode (see Chapter 3 for de
- Page 27 and 28: In the case of Ising anyons, 2N vor
- Page 29 and 30: find a realistic material in nature
- Page 31: states near the Fermi circle. We fi
- Page 35 and 36: dimensional non-chiral Majorana mod
- Page 37 and 38: is formed out of two fermions, does
- Page 39 and 40: gapless and should not be neglected
- Page 41 and 42: zero modes. We study a one-dimensio
- Page 43 and 44: of possible paired states which is
- Page 45 and 46: where d ≡ (d 1 , d 2 , d 3 ) = (R
- Page 47 and 48: If the order parameter is proportio
- Page 49 and 50: 0.015 T/t 0.01 Normal p x + ip y 0.
- Page 51 and 52: trivial p x - and p y -states lead
- Page 53 and 54: with the gap operator being ˆ∆ =
- Page 55 and 56: 0.2 T/t 0.1 Normal f p x + ip y µ
- Page 57 and 58: 2.3 Discussion and Conclusions In c
- Page 59 and 60: Chapter 3 Majorana Bound States in
- Page 61 and 62: satisfied for m = 0. The singlevalu
- Page 63 and 64: We summarize this section by provid
- Page 65 and 66: Here γ a and Γ a are 4 × 4 Dirac
- Page 67 and 68: with λ = µξ/v. It has the follow
- Page 69 and 70: where n = (R∆, −I∆) field des
- Page 71 and 72: Chapter 4 Topological Degeneracy Sp
- Page 73 and 74: ound states are usually splitted an
- Page 75 and 76: sponding quasiparticle operator can
- Page 77 and 78: Of particular importance is the sig
- Page 79 and 80: [61]. Although analytical expressio
- Page 81 and 82: eyond perturbation theory and the r
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eaks down in this regime and one sh
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4.3 Conclusions In this chapter, we
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the fermion bath, and consequently
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tion for the reduced density matrix
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like phonons. However, such process
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We also notice that in this formula
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etween two topological p x + ip y s
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neglect the AC phase. The Hamiltoni
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which in principle lead to a strong
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We conclude that the geometric phas
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The first-order term vanishes due t
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apply to any realistic system where
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ound states are typically close to
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Chapter 6 Non-adiabaticity in the B
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minor modifications in the details,
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{α(T )} to {α(0)}: |α(T )〉 =
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educed to 2 N−1 by fermion parity
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Berry connection of this state then
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wavefunction is u n (r), v n (r). W
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asis. The most general form of BdG
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6.2.1 Effect of Tunneling Splitting
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Because E + ∼ ∆ 0 e −R/ξ , |
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tunneling amplitudes between them a
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ˆΓ i = iˆγ i ˆξiˆη i , i =
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considerations, we should have β 1
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states: ν(ε) = 2ν 0 ε √ ε2
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necessary as a matter of principle
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Chapter 7 Majorana Zero Modes Beyon
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We then demonstrate that in a finit
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The standard Abelian bosonization r
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and define the chiral fields by ˜
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of (7.2) has a product of the Klein
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7.3 Stability of the Degeneracy We
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quence. The splitting is then propo
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where α = 1 2 (K + K−1 − 2). A
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effect of quasiparticle tunneling o
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Appendix A Derivation of the Pfaffi
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which allows further simplification
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List of Publications Publications t
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Bibliography [1] K. von Klitzing, G
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[46] S. Das Sarma, C. Nayak, and S.
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[92] A. W. W. Ludwig, D. Poilblanc,
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[133] M. V. Berry, Proc. R. Soc. Lo