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The stability of Majorana fermion in correlated quantum wire |
| Zhang De-Ping (张德平), Tian Guang-Shan (田光善) |
| School of Physics, Peking University, Beijing 100871, China |
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Abstract In this paper, we investigate the effect of the Coulomb interaction between electrons on the stability of Majorana fermion in a heterostructure of s-wave superconductor and quantum wire. In particular, by using the bosonization method and the renormalization group technique, we show that interplay between the so-called umklapp electron–electron scattering process and the superconducting proximity effect plays an extremely important role in determining the phase diagram of the system. We find that, at half-filling, the strong umklapp scattering process suppresses not only the superconducting pairing interaction and hence, destabilizes Majorana fermion in the quantum wire, but aslo results in a Mott insulating state. However, if the proximity effect is sufficiently strong, the topological superconducting phase can still survive and support Majorana fermion in the heterostructure. Furthermore, the existence of a critical Luttinger liquid phase is also found in a narrow region of parameters.
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Received: 17 September 2014
Revised: 11 February 2015
Accepted manuscript online:
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PACS:
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04.50.-h
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(Higher-dimensional gravity and other theories of gravity)
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74.45.+c
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(Proximity effects; Andreev reflection; SN and SNS junctions)
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74.20.Rp
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(Pairing symmetries (other than s-wave))
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79.60.Jv
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(Interfaces; heterostructures; nanostructures)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11374017). |
Corresponding Authors:
Tian Guang-Shan
E-mail: tiangs@pku.edu.cn
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Cite this article:
Zhang De-Ping (张德平), Tian Guang-Shan (田光善) The stability of Majorana fermion in correlated quantum wire 2015 Chin. Phys. B 24 080401
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| [1] |
Majorana E 1937 Nuovo Cimento 14 171
|
| [2] |
Abrikosov A A, Gorkov L P and Dzyaloshinski I E 1963 Methods of Quantum Field Theory in Statistical Physics (New York: Dover Publications)
|
| [3] |
Ivanov D A Phys. Rev. Lett. 2001 86 268
|
| [4] |
Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
|
| [5] |
Qi X L and S C Zhang 2011 Rev. Mod. Phys. 83 1057
|
| [6] |
Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98 106803
|
| [7] |
Abrikosov A A 1988 Fundamentals of the Theory of Metals (Amsterdam: North-Holland) p. 483
|
| [8] |
Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
|
| [9] |
Fu L and Kane C L 2009 Phys. Rev. Lett. 102 216403
|
| [10] |
Sau J D and Tewari S 2013 Phys. Rev. B 88 054503
|
| [11] |
Klinovaja J, Gangadharaiah S and Loss D 2012 Phys. Rev. Lett. 108 196804
|
| [12] |
Klinovaja J, Ferreira G J and Loss D 2012 Phys. Rev. B 86 235416
|
| [13] |
Nadj-Perge S, Drozdov I K, Bernevig B A and Yazdani A 2013 Phys. Rev. B 88 020407
|
| [14] |
Sau J D, Lutchyn R M, Tewari S and Das Sarma S 2010 Phys. Rev. Lett. 104 040502
|
| [15] |
Sau J D, Tewari S, Lutchyn R M, Stanescu T D and Das Sarma S 2010 Phys. Rev. B 82 214509
|
| [16] |
Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Rev. Lett. 105 077001
|
| [17] |
Oreg Y, Refael G and von Oppen F 2010 Phys. Rev. Lett. 105 177002
|
| [18] |
Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M and Kouwenhoven L P 2012 Science 336 1003
|
| [19] |
Das A, Ronen Y, Most Y, Oreg Y, Heiblum M and Shtrikman H 2012 Nat. Phys. 8 887
|
| [20] |
Rokhinson L P, Liu X Y and Furdyna J K 2012 Nat. Phys. 8 795
|
| [21] |
Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P and Xu H Q 2012 Nano Lett. 12 6414
|
| [22] |
Churchill H O H, Fatemi V, Grove-Rasmussen K, Deng M T, Caroff P, Xu H Q and Marcus C M 2013 Phys. Rev. B 87 241401
|
| [23] |
Finck A D K, Van Harlingen D J, Mohseni P K, Jung K and Li X 2013 Phys. Rev. Lett. 110 126406
|
| [24] |
Lieb E and Mattis D 1965 Math. Phys. 6 304
|
| [25] |
Giamarchi T 2004 Quantum Physics in One Dimension (Oxford: Oxford University Press)
|
| [26] |
Lutchyn R M and Fisher M P A 2011 Phys. Rev. B 84 214528
|
| [27] |
Gangadharaiah S, Braunecker B, Simon P and Loss D 2011 Phys. Rev. Lett. 107 036801
|
| [28] |
Sela E, Altland A and Rosch A 2011 Phys. Rev. B 84 085114
|
| [29] |
Stoudenmire E M, Alicea J, Starykh O A and Fisher M P A 2011 Phys. Rev. B 84 014503
|
| [30] |
Gogolin A O, Nersesyan A A and Tsvelik A M 1998 Bosonization and Strongly Correlated Systems (Cambridge: Cambridge University Press)
|
| [31] |
Kitaev A Y 2001 Phys. Usp. 44 131
|
| [32] |
Amit D J 1984 Field Theory, the Renormalization Group and Critical Phenomena (Singpore: World Scientific)
|
| [33] |
Fradkin E 2013 Field Theories of Condensed Matter Physics (Cambridge: Cambridge University Press)
|
| [34] |
Anderson P W 1984 Basic Notions of Condensed Matter Physics (California: Benjamin Cummings)
|
| [35] |
Shi D, Wen R, Liu G H and Tian G S 2010 Chin. Phys. B 19 077503
|
| [36] |
Wen R, Liu G H and Tian G S 2011 Commun. Theor. Phys. 55 1102
|
| [37] |
He P S, Oh S J, Chen Y and Tian G S 2010 Commun. Theor. Phys. 54 897
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