ABSTRACT - DRUM - University of Maryland

More documents

Recommendations

Info

[67] M. T. Deng et al., arXiv:1204.4130. [68] L. P. Rokhinson, X. Liu, and J. K. Furdyna, Nat. Phys. (2012). [69] P. W. Anderson, Phys. Rev. 130, 439 (1963). [70] G. E. Volovik, Sov. Phys. JETP 67, 1804 (1988). [71] F. D. M. Haldane, Phys. Rev. Lett. 93, 206602 (2004). [72] W. Kohn and J. H. Luttinger, Phys. Rev. Lett. 15, 524 (1965). [73] A. V. Chubukov, Phys. Rev. B 48, 1097 (1993). [74] V. M. Galitski and S. Das Sarma, Phys. Rev. B 67, 144520 (2003). [75] V. M. Galitski, Phys. Rev. B 77, 100502R (2008). [76] V. Gurarie and L. Radzihovsky, Phys. Rev. B 75, 212509 (2007). [77] M. Stone and R. Roy, Phys. Rev. B 69, 184511 (2004). [78] A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975). [79] G. Volovik, JETP Lett. 70, 609 (1999). [80] S. Tewari, S. D. Sarma, and D.-H. Lee, Phys. Rev. Lett. 99, 037001 (2007). [81] T. Mizushima and K. Machida, Phys. Rev. A 81, 053605 (2010). [82] R. Jackiw and P. Rossi, Nucl. Phys. B 190, 681 (1981). [83] T. D. Stanescu, J. D. Sau, R. M. Lutchyn, and S. Das Sarma, Phys. Rev. B 81, 241310 (2010). [84] E. J. Weinberg, Phys. Rev. D 24, 2669 (1981). [85] T. Fukui and T. Fujiwara, J. Phys. Soc. Jpn. 79, 033701 (2010). [86] P. Bonderson, Phys. Rev. Lett. 103, 110403 (2009). [87] Y. Tserkovnyak and S. H. Simon, Phys. Rev. Lett. 90, 016802 (2003). [88] M. Baraban, G. Zikos, N. Bonesteel, and S. H. Simon, Phys. Rev. Lett. 103, 076801 (2009). [89] Y. E. Kraus, A. Auerbach, H. A. Fertig, and S. H. Simon, Phys. Rev. B 79, 134515 (2009). [90] V. Lahtinen et al., Ann. Phys.(N.Y.) 323, 2286 (2008). [91] M. Cheng, R. M. Lutchyn, V. Galitski, and S. Das Sarma, Phys. Rev. Lett. 103, 107001 (2009). 154
[92] A. W. W. Ludwig, D. Poilblanc, S. Trebst, and M. Troyer, New J. Phys. 13, 045014 (2011). [93] L. Landau and E. LifshitzQuantum Mechanics (Course of Theoretical Physics) Vol. 3, 2 ed. (Pergamon Press, 1984). [94] V. M. Galitski and D. D. Sokoloff, Geophys. Astrophys. Fluid Dynamics 91, 147 (1999); V. M. Galitski, K. M. Kuzanyan, and D. D. Sokoloff, Astron.Rep. 49, 337 (2005). [95] J. Nilsson, A. R. Akhmerov, and C. W. J. Beenakker, Phys. Rev. Lett. 101, 120403 (2008). [96] C. Chamon, R. Jackiw, Y. Nishida, S.-Y. Pi, and L. Santos, Phys. Rev. B 81, 224515 (2010). [97] E. Grosfeld and A. Stern, Phys. Rev. B 73, 201303 (2006). [98] A. Feiguin et al., Phys. Rev. Lett. 98, 160409 (2007). [99] C. Gils et al., Phys. Rev. Lett. 103, 070401 (2009). [100] C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008). [101] P. Bonderson and J. K. Slingerland, Phys. Rev. B 78, 125323 (2008). [102] M. Levin and B. I. Halperin, Phys. Rev. B 79, 205301 (2009). [103] M. Hermanns, Phys. Rev. Lett. 104, 056803 (2010). [104] N. Read and A. W. W. Ludwig, Phys. Rev. B 63, 024404 (2000). [105] A. Zyuzin and B. Z. Spivak, Pisma Zh. Eksp. Teor. Fiz. 43, 185 (1986) [JETP Lett. 43, 234 (1986)]; V. M. Galitski, M. G. Vavilov, and L. I. Glazman, Phys. Rev. Lett 94, 096602 (2005); V. M. Galitski and A. I. Larkin, Phys. Rev. B 66, 064526 (2002). [106] M. Cheng, R. M. Lutchyn, V. Galitski, and S. Das Sarma, Phys. Rev. B 82, 094504 (2010). [107] J. D. Sau, C. H. Lin, H.-Y. Hui, and S. Das Sarma, Phys. Rev. Lett. 108, 067001 (2012). [108] J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Phys. Rev. B 82, 094522 (2010). [109] L. Mao and C. Zhang, Phys. Rev. B 82, 174506 (2010). [110] G. Goldstein and C. Chamon, Phys. Rev. B 85, 205109 (2011). 155
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 and 32:
states near the Fermi circle. We fi
Page 33 and 34:
pairing: ( ) p H = ψ † 2 2m −
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
Page 83 and 84:
eaks down in this regime and one sh
Page 85 and 86:
4.3 Conclusions In this chapter, we
Page 87 and 88:
the fermion bath, and consequently
Page 89 and 90:
tion for the reduced density matrix
Page 91 and 92:
like phonons. However, such process
Page 93 and 94:
We also notice that in this formula
Page 95 and 96:
etween two topological p x + ip y s
Page 97 and 98:
neglect the AC phase. The Hamiltoni
Page 99 and 100:
which in principle lead to a strong
Page 101 and 102:
We conclude that the geometric phas
Page 103 and 104:
The first-order term vanishes due t
Page 105 and 106:
apply to any realistic system where
Page 107 and 108:
ound states are typically close to
Page 109 and 110:
Chapter 6 Non-adiabaticity in the B
Page 111 and 112:
minor modifications in the details,
Page 113 and 114: {α(T )} to {α(0)}: |α(T )〉 =
Page 115 and 116: educed to 2 N−1 by fermion parity
Page 117 and 118: Berry connection of this state then
Page 119 and 120: wavefunction is u n (r), v n (r). W
Page 121 and 122: asis. The most general form of BdG
Page 123 and 124: 6.2.1 Effect of Tunneling Splitting
Page 125 and 126: Because E + ∼ ∆ 0 e −R/ξ , |
Page 127 and 128: tunneling amplitudes between them a
Page 129 and 130: ˆΓ i = iˆγ i ˆξiˆη i , i =
Page 131 and 132: considerations, we should have β 1
Page 133 and 134: states: ν(ε) = 2ν 0 ε √ ε2
Page 135 and 136: necessary as a matter of principle
Page 137 and 138: Chapter 7 Majorana Zero Modes Beyon
Page 139 and 140: We then demonstrate that in a finit
Page 141 and 142: The standard Abelian bosonization r
Page 143 and 144: and define the chiral fields by ˜
Page 145 and 146: of (7.2) has a product of the Klein
Page 147 and 148: 7.3 Stability of the Degeneracy We
Page 149 and 150: quence. The splitting is then propo
Page 151 and 152: where α = 1 2 (K + K−1 − 2). A
Page 153 and 154: effect of quasiparticle tunneling o
Page 155 and 156: Appendix A Derivation of the Pfaffi
Page 157 and 158: which allows further simplification
Page 159 and 160: List of Publications Publications t
Page 161 and 162: Bibliography [1] K. von Klitzing, G
Page 163: [46] S. Das Sarma, C. Nayak, and S.
Page 167 and 168: [133] M. V. Berry, Proc. R. Soc. Lo
show all

ABSTRACT - DRUM - University of Maryland

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?