Impurity- and magnetic-field-induced quasiparticle states in chiral p-wave superconductors

Abstract

Both impurity- and magnetic-field-induced quasiparticle states in chiral p-wave superconductors are investigated theoretically by solving the Bogoliubov–de Gennes equations self-consistently. At the strong scattering limit, we find that a universal state bound to the impurity can be induced for both a single nonmagnetic impurity and a single magnetic impurity. Furthermore, we find that different chiral order parameters and the corresponding supercurrents have uniform distributions around linear impurities. Calculations of the local density of states in the presence of an external magnetic field show that the intensity peak of the zero-energy Majorana mode in the vortex core can be enhanced dramatically by tuning the strength of the external magnetic field or pairing interaction.

Keywords

nonmagnetic/magnetic impurity / chiral p-wave superconductor / vortex state / Majorana mode

References

[1] X. G.Wen and Q.Niu, Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces, Phys. Rev. B41(13), 9377 (1990)

[2] C.Nayakand F.Wilczek, 2n-quasihole states realize 2ⁿ⁻¹-dimensional spinor braiding statistics in paired quantum Hall states, Nucl. Phys. B479(3), 529(1996)

[3] S.Murakami, N.Nagaosa, and S. C.Zhang, Spin-Hall insulator, Phys. Rev. Lett.93(15), 156804(2004)

[4] C. L.Kaneand E. J.Mele, Z₂ topological order and the quantum spin Hall effect, Phys. Rev. Lett.95(14), 146802(2005)

[5] A.Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321(1), 2 (2006)

[6] D. H.Lee, G. M.Zhang, and T.Xiang, Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions, Phys. Rev. Lett.99(19), 196805(2007)

[7] R. E.Prangeand S. M.Girvin, The Quantum Hall Effect, Berlin: Springer-Verlag, 1987

[8] D. J.Thouless, M.Kohmoto, M. P.Nightingale, and M.denNijs, Quantized Hall conductance in a twodimensional periodic potential, Phys. Rev. Lett. 49(6), 405(1982)

[9] V.Gurarie, L.Radzihovsky, and A. V.Andreev, Quantum phase transitions across a p-wave Feshbach resonance, Phys. Rev. Lett. 94(23), 230403(2005)

[10] S.Tewari, S.Das Sarma, C.Nayak, C.Zhang, and P.Zoller, Quantum computation using vortices and Majorana zero modes of a p_x+ ip_ysuperfluid of fermionic cold atoms, Phys. Rev. Lett.98(1), 010506(2007)

[11] M. Z.Hasanand C. L.Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045(2010)

[12] X. L.Qiand S. C.Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057(2011)

[13] G. E.Volovik, The Universe in a Helium Droplet, New York: Oxford Science Publications, 2003

[14] A. P.Machenzieand Y.Maeno, The superconductivity of Sr₂RuO₄ and the physics of spin-triplet pairing, Rev. Mod. Phys. 75(657), 2003(2003)

[15] E.Majorana, Teoria simmetrica dell’elettrone e del positrone, Nuovo Cim. 14(4), 171(1937)

[16] N.Readand D.Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B61(15), 10267(2000)

[17] T.Mizushima, M.Ichioka, and K.Machida, Role of the Majorana fermion and the edge mode in chiral superfluidity near a p-wave Feshbach resonance, Phys. Rev. Lett. 101(15), 150409(2008)

[18] G.Mooreand N.Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B360(2–3), 362(1991)

[19] M.Greiter, X. G.Wen, and F.Wilczek, Paired Hall states, Nucl. Phys. B374(3), 567(1992)

[20] L.Fuand C. L.Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett.100(9), 096407(2008)

[21] J. D.Sau, R. M.Lutchyn, S.Tewari, and S.Das Sarma, Generic new platform for topological quantum computation using semiconductor heterostructures, Phys. Rev. Lett. 104(4), 040502(2010)

[22] J.Alicea, Majorana fermions in a tunable semiconductor device, Phys. Rev. B81(12), 125318(2010)

[23] M.Matsumotoand R.Heeb, Vortex charging effect in a chiral p_x±ip_y-wave superconductor, Phys. Rev. B65(1), 014504(2001)

[24] L.Yu,Bound state in superconductors with paramagnetic impurities, Acta. Phys. Sin. 21, 75(1965)

[25] H.Shiba, Classical spins in superconductors, Prog. Theor. Phys. 40(3), 435(1968)

[26] A. V.Balatsky, I.Vekhter, and J. X.Zhu, Impurityinduced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373(2006)

[27] Y.Chenand C. S.Ting, States of local moment induced by nonmagnetic impurities in cuprate superconductors, Phys. Rev. Lett. 92(7), 077203(2004)

[28] M.Takigawa, M.Ichioka, K.Kuroki, and Y.Tanaka, Electronic structure and spontaneous internal field around nonmagnetic impurities in spin-triplet chiral p- wave superconductors, Phys. Rev. B72(22), 224501(2005)

[29] H.Hu, L.Jiang, H.Pu, Y.Chen, and X. J.Liu, Universal impurity-induced bound state in topological superfluids, Phys. Rev. Lett. 110(2), 020401(2013)

[30] Y.Tanuma,N.Hayashi, Y.Tanaka, and A. A.Golubov, Model for vortex-core tunneling spectroscopy of chiral p- wave superconductors via odd-frequency pairing states, Phys. Rev. Lett.102(11), 117003 (2009)

[31] Q.Han, Z. D.Wang, Q. H.Wang, and T.Xia, Vortex state in Na_xCoO₂·yH₂O: p_x±ip_y-wave versus d_x2−y2±id_xy-wave pairing, Phys. Rev. Lett.92(2), 027004(2004)

[32] C.Caroli, P. G.de Gennes, and J.Matricon, Bound Fermion states on a vortex line in a type II superconductor, Phys. Lett.9(4), 307(1964)

[33] G. E.Volovik, Superconductivity with lines of gap nodes: Density of states in the vortex, Pis’ma ZhETF58, 457(1993) [JETP Lett. 58, 469(1993)]

[34] Y.Chenand C. S.Ting, Magnetic-field-induced spindensity wave in high-temperature superconductors, Phys. Rev. B65(18), 180513(2002)

[35] G.Volovik, Fermion zero modes on vortices in chiral superconductors, JETP Lett.70(9), 609(1999)

[36] D. A.Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett.86(2), 268(2001)

[37] A. S.Mel’nikov, D. A.Ryzhov, and M. A.Silaev, Electronic structure and heat transport of multi-vortex configurations in mesoscopic superconductors, Phys. Rev. B78(6), 064513(2008)

[38] A. S.Mel’nikovand M. A.Silaev, Inter-vortex quasiparticle tunneling and the electronic structure of multivortex configurations in type-II superconductors, JETP Lett. 83(12), 578(2006)

[39] Y.Wangand A. H.MacDonald, Mixed-state quasiparticle spectrum for d-wave superconductors, Phys. Rev. B52(6), R3876(1995)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg