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Volumn 87, Issue 11, 2013, Pages

Unpaired Floquet Majorana fermions without magnetic fields

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EID: 84875345764     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.115420     Document Type: Article
Times cited : (104)

References (76)
  • 1
    • 84875354437 scopus 로고    scopus 로고
    • APS March Meeting, BAPS.2012.MAR.D44.3 (APS
    • L. Kouwenhoven, APS March Meeting, BAPS.2012.MAR.D44.3 (APS, 2012);
    • (2012)
    • Kouwenhoven, L.1
  • 2
    • 79961219734 scopus 로고    scopus 로고
    • SCIEAS 0036-8075 10.1126/science.332.6026.193
    • R. F. Service, Science SCIEAS 0036-8075 10.1126/science.332.6026.193 332, 193 (2011);
    • (2011) Science , vol.332 , pp. 193
    • Service, R.F.1
  • 3
    • 77955595279 scopus 로고    scopus 로고
    • 1943-2879 10.1103/Physics.3.24
    • M. Franz, Physics 1943-2879 10.1103/Physics.3.24 3, 24 (2010).
    • (2010) Physics , vol.3 , pp. 24
    • Franz, M.1
  • 7
    • 40849098643 scopus 로고    scopus 로고
    • Superconducting proximity effect and majorana fermions at the surface of a topological insulator
    • DOI 10.1103/PhysRevLett.100.096407
    • L. Fu and C. L. Kane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.096407 100, 096407 (2008). (Pubitemid 351399080)
    • (2008) Physical Review Letters , vol.100 , Issue.9 , pp. 096407
    • Fu, L.1    Kane, C.L.2
  • 8
    • 28844477210 scopus 로고    scopus 로고
    • Z2 topological order and the quantum spin hall effect
    • DOI 10.1103/PhysRevLett.95.146802, 146802
    • The existence of helical edge modes in the topological insulating phase requires the presence of SOC in the bulk. See, for example, C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005). (Pubitemid 41777602)
    • (2005) Physical Review Letters , vol.95 , Issue.14 , pp. 1-4
    • Kane, C.L.1    Mele, E.J.2
  • 10
    • 68649109866 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.103.020401
    • M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.020401 103, 020401 (2009).
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 020401
    • Sato, M.1    Takahashi, Y.2    Fujimoto, S.3
  • 13
    • 77954945903 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.125318
    • J. Alicea, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.125318 81, 125318 (2010);
    • (2010) Phys. Rev. B , vol.81 , pp. 125318
    • Alicea, J.1
  • 14
    • 77958138382 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.105.177002
    • Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.177002 105, 177002 (2010).
    • (2010) Phys. Rev. Lett. , vol.105 , pp. 177002
    • Oreg, Y.1    Refael, G.2    Von Oppen, F.3
  • 15
    • 78649365559 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.105.227003
    • A. C. Potter and P. A. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.227003 105, 227003 (2010).
    • (2010) Phys. Rev. Lett. , vol.105 , pp. 227003
    • Potter, A.C.1    Lee, P.A.2
  • 16
    • 84875308137 scopus 로고    scopus 로고
    • The term unpaired in this paper refers to single Majorana states which do not appear degenerated - in energy for static systems or in Floquet quasienergy for time-periodic Hamiltonians - with other Majorana states localized at the same region.
    • The term unpaired in this paper refers to single Majorana states which do not appear degenerated - in energy for static systems or in Floquet quasienergy for time-periodic Hamiltonians - with other Majorana states localized at the same region.
  • 17
    • 0000049832 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.61.10267
    • N. Read and D. Green, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.61. 10267 61, 10267 (2000).
    • (2000) Phys. Rev. B , vol.61 , pp. 10267
    • Read, N.1    Green, D.2
  • 18
    • 55049105990 scopus 로고    scopus 로고
    • PHUSEY 1063-7869 10.1070/1063-7869/44/10S/S29
    • A. Y. Kitaev, Phys. Usp. PHUSEY 1063-7869 10.1070/1063-7869/44/10S/S29 44, 131 (2001).
    • (2001) Phys. Usp. , vol.44 , pp. 131
    • Kitaev, A.Y.1
  • 20
    • 0035129985 scopus 로고    scopus 로고
    • Non-Abelian statistics of half-quantum vortices in p-wave superconductors
    • DOI 10.1103/PhysRevLett.86.268
    • D. A. Ivanov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86. 268 86, 268 (2001). (Pubitemid 32131693)
    • (2001) Physical Review Letters , vol.86 , Issue.2 , pp. 268-271
    • Ivanov, D.A.1
  • 24
    • 78650821791 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.82.235114
    • T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.235114 82, 235114 (2010).
    • (2010) Phys. Rev. B , vol.82 , pp. 235114
    • Kitagawa, T.1    Berg, E.2    Rudner, M.3    Demler, E.4
  • 25
    • 62149095055 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.79.081406
    • T. Oka and H. Aoki, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79. 081406 79, 081406 (2009).
    • (2009) Phys. Rev. B , vol.79 , pp. 081406
    • Oka, T.1    Aoki, H.2
  • 26
    • 66849089615 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.79.205406
    • P. H. Rivera, A. L. C. Pereira, and P. A. Schulz, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.205406 79, 205406 (2009).
    • (2009) Phys. Rev. B , vol.79 , pp. 205406
    • Rivera, P.H.1    Pereira, A.L.C.2    Schulz, P.A.3
  • 28
    • 84856534542 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.83.245436
    • Y. Zhou and M. W. Wu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83. 245436 83, 245436 (2011).
    • (2011) Phys. Rev. B , vol.83 , pp. 245436
    • Zhou, Y.1    Wu, M.W.2
  • 29
    • 84860477459 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.155449
    • M. Busl, G. Platero, and A.-P. Jauho, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.155449 85, 155449 (2012).
    • (2012) Phys. Rev. B , vol.85 , pp. 155449
    • Busl, M.1    Platero, G.2    Jauho, A.-P.3
  • 32
  • 34
    • 84875298884 scopus 로고    scopus 로고
    • More work for this type of FMFs has appeared during the reviewing period of this paper, namely arXiv: 1301.4433;
    • More work for this type of FMFs has appeared during the reviewing period of this paper, namely, A. Kundu and B. Seradjeh, arXiv: 1301.4433;
    • Kundu, A.1    Seradjeh, B.2
  • 36
    • 84864484134 scopus 로고    scopus 로고
    • 1050-2947 10.1103/PhysRevA.86.013639
    • G. Liu, N. Hao, S.-L. Zhu, and W. M. Liu, Phys. Rev. A 1050-2947 10.1103/PhysRevA.86.013639 86, 013639 (2012).
    • (2012) Phys. Rev. A , vol.86 , pp. 013639
    • Liu, G.1    Hao, N.2    Zhu, S.-L.3    Liu, W.M.4
  • 37
    • 84875336667 scopus 로고    scopus 로고
    • For time-independent unitary transformations the topological properties are common to the two linked Hamiltonians. For time-dependent unitary transformations the topological properties are preserved only in very specific cases.
    • For time-independent unitary transformations the topological properties are common to the two linked Hamiltonians. For time-dependent unitary transformations the topological properties are preserved only in very specific cases.
  • 39
    • 84856509567 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.020503
    • M. Kjaergaard, K. Wölms, and K. Flensberg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.020503 85, 020503 (2012).
    • (2012) Phys. Rev. B , vol.85 , pp. 020503
    • Kjaergaard, M.1    Wölms, K.2    Flensberg, K.3
  • 40
    • 3042690839 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/5/1/356
    • D. Jaksch and P. Zoller, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/356 5, 56 (2003).
    • (2003) New J. Phys. , vol.5 , pp. 56
    • Jaksch, D.1    Zoller, P.2
  • 41
    • 19744382564 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.70.041603
    • E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.041603 70, 041603 (2004).
    • (2004) Phys. Rev. A , vol.70 , pp. 041603
    • Mueller, E.J.1
  • 42
    • 18144398571 scopus 로고    scopus 로고
    • Fractional quantum hall states of atoms in optical lattices
    • DOI 10.1103/PhysRevLett.94.086803, 086803
    • A. S. Sørensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.086803 94, 086803 (2005). (Pubitemid 40620676)
    • (2005) Physical Review Letters , vol.94 , Issue.8 , pp. 1-4
    • Sorensen, A.S.1    Demler, E.2    Lukin, M.D.3
  • 44
    • 34548202482 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.51.652
    • I. I. Rabi, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.51.652 51, 652 (1937).
    • (1937) Phys. Rev. , vol.51 , pp. 652
    • Rabi, I.I.1
  • 46
    • 84875329283 scopus 로고    scopus 로고
    • c/2.
    • c / 2.
  • 48
  • 50
    • 80054934761 scopus 로고    scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.83.1057
    • X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.83.1057 83, 1057 (2011).
    • (2011) Rev. Mod. Phys. , vol.83 , pp. 1057
    • Qi, X.-L.1    Zhang, S.-C.2
  • 51
    • 33748975638 scopus 로고
    • PRVDAQ 1550-7998 10.1103/PhysRevD.13.3398
    • R. Jackiw and C. Rebbi, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.13.3398 13, 3398 (1976).
    • (1976) Phys. Rev. D , vol.13 , pp. 3398
    • Jackiw, R.1    Rebbi, C.2
  • 52
    • 84870266432 scopus 로고    scopus 로고
    • SSTEET 0268-1242 10.1088/0268-1242/27/12/124003
    • M. Leijnse and K. Flensberg, Semicond. Sci. Technol. SSTEET 0268-1242 10.1088/0268-1242/27/12/124003 27, 124003 (2012).
    • (2012) Semicond. Sci. Technol. , vol.27 , pp. 124003
    • Leijnse, M.1    Flensberg, K.2
  • 53
    • 84875323504 scopus 로고    scopus 로고
    • Such breaking can be simple (e.g., induced by an external magnetic field) or may spontaneously develop due to interactions.
    • Such breaking can be simple (e.g., induced by an external magnetic field) or may spontaneously develop due to interactions.
  • 54
    • 45849155677 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.87.256801
    • I. L. Aleiner and V. I. Fal'ko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.256801 87, 256801 (2001).
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 256801
    • Aleiner, I.L.1    Fal'Ko, V.I.2
  • 55
    • 0035615116 scopus 로고    scopus 로고
    • FNDPA4 0015-9018 10.1023/A:1017550822221
    • D. Frustaglia and K. Richter, Found. Phys. FNDPA4 0015-9018 10.1023/A:1017550822221 31, 399 (2001).
    • (2001) Found. Phys. , vol.31 , pp. 399
    • Frustaglia, D.1    Richter, K.2
  • 56
    • 0042839687 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.68.041303
    • M. Popp, D. Frustaglia, and K. Richter, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.041303 68, 041303 (2003).
    • (2003) Phys. Rev. B , vol.68 , pp. 041303
    • Popp, M.1    Frustaglia, D.2    Richter, K.3
  • 58
    • 84875357307 scopus 로고    scopus 로고
    • z in the latter eigenstate.
    • z in the latter eigenstate.
  • 59
    • 5344247998 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.56.748
    • F. H. M. Faisal and J. Z. Kamiński, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.748 56, 748 (1997).
    • (1997) Phys. Rev. A , vol.56 , pp. 748
    • Faisal, F.H.M.1    Kamiński, J.Z.2
  • 60
    • 33748713280 scopus 로고    scopus 로고
    • Floquet-Bloch states, quasienergy bands, and high-order harmonic generation for single-walled carbon nanotubes under intense laser fields
    • DOI 10.1103/PhysRevB.74.115406
    • H. Hsu and L. E. Reichl, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.115406 74, 115406 (2006). (Pubitemid 44396728)
    • (2006) Physical Review B - Condensed Matter and Materials Physics , vol.74 , Issue.11 , pp. 115406
    • Hsu, H.1    Reichl, L.E.2
  • 61
    • 84875283865 scopus 로고    scopus 로고
    • An extra phase factor might be needed to decouple the two solutions; this depends on the direction of the SOC at t=0 and/or on the arbitrary phases accompanying each of the computed eigenvectors.
    • An extra phase factor might be needed to decouple the two solutions; this depends on the direction of the SOC at t = 0 and/or on the arbitrary phases accompanying each of the computed eigenvectors.
  • 62
    • 84857820769 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.108.096802
    • D. Sticlet, C. Bena, and P. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.096802 108, 096802 (2012).
    • (2012) Phys. Rev. Lett. , vol.108 , pp. 096802
    • Sticlet, D.1    Bena, C.2    Simon, P.3
  • 63
    • 84875317021 scopus 로고    scopus 로고
    • Not only physical quantum wires but also quasi-1D-electron gases realized in gate-tunable quantum-well heterostructures.
    • Not only physical quantum wires but also quasi-1D-electron gases realized in gate-tunable quantum-well heterostructures.
  • 64
    • 77956302422 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.82.021607
    • C. Zhang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.021607 82, 021607 (2010).
    • (2010) Phys. Rev. A , vol.82 , pp. 021607
    • Zhang, C.1
  • 65
    • 84875359476 scopus 로고    scopus 로고
    • ̃so/âΩ.
    • ̃so / â Ω.
  • 66
    • 0037113414 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.66.205320
    • M. Moskalets and M. Büttiker, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.66.205320 66, 205320 (2002).
    • (2002) Phys. Rev. B , vol.66 , pp. 205320
    • Moskalets, M.1    Büttiker, M.2
  • 67
    • 19544378494 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.93.087201
    • A. Brataas and Y. Tserkovnyak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.087201 93, 087201 (2004).
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 087201
    • Brataas, A.1    Tserkovnyak, Y.2
  • 70
    • 84875338651 scopus 로고    scopus 로고
    • Notice that in this work we have applied the time-dependent unitary transformation of Eq. to the states as a mathematical tool to obtain the solutions of the time-dependent BdG-Schrödinger equation dictated by Hî(t). In such mathematical framework the chemical potential μ appearing in Hî(t) is not modified at all when applying the transformation to the states.
    • Notice that in this work we have applied the time-dependent unitary transformation of Eq. to the states as a mathematical tool to obtain the solutions of the time-dependent BdG-Schrödinger equation dictated by H î (t). In such mathematical framework the chemical potential μ appearing in H î (t) is not modified at all when applying the transformation to the states.
  • 71
    • 13544268696 scopus 로고    scopus 로고
    • Driven quantum transport on the nanoscale
    • DOI 10.1016/j.physrep.2004.11.002, PII S0370157304005071
    • S. Kohler, J. Lehmann, and P. Hänggi, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2004.11.002 406, 379 (2005). (Pubitemid 40224317)
    • (2005) Physics Reports , vol.406 , Issue.6 , pp. 379-443
    • Kohler, S.1    Lehmann, J.2    Hanggi, P.3
  • 73
    • 67650935000 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.79.051129
    • D. W. Hone, R. Ketzmerick, and W. Kohn, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.051129 79, 051129 (2009).
    • (2009) Phys. Rev. e , vol.79 , pp. 051129
    • Hone, D.W.1    Ketzmerick, R.2    Kohn, W.3
  • 74
    • 77955594028 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.82.021114
    • R. Ketzmerick and W. Wustmann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.021114 82, 021114 (2010).
    • (2010) Phys. Rev. e , vol.82 , pp. 021114
    • Ketzmerick, R.1    Wustmann, W.2
  • 75
    • 0000784603 scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.40.5325
    • T. Ando, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.5325 40, 5325 (1989).
    • (1989) Phys. Rev. B , vol.40 , pp. 5325
    • Ando, T.1


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