Impurity- and magnetic-field-induced quasiparticle states in chiral p-wave superconductors
Yao-Wu Guo1, Wei Li2,3(), Yan Chen1,4()
1. Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China 2. State Key Laboratory of Functional Materials for Informatics and Shanghai Center for Superconductivity, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 3. CAS Center for Excellence in Superconducting Electronics, Shanghai 200050, China 4. Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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.
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) https://doi.org/10.1103/PhysRevB.41.9377
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) https://doi.org/10.1016/0550-3213(96)00430-0
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) https://doi.org/10.1103/PhysRevLett.99.196805
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) https://doi.org/10.1103/PhysRevLett.49.405
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) https://doi.org/10.1103/PhysRevLett.94.230403
10
S.Tewari, S.Das Sarma, C.Nayak, C.Zhang, and P.Zoller, Quantum computation using vortices and Majorana zero modes of a px+ ipysuperfluid of fermionic cold atoms, Phys. Rev. Lett.98(1), 010506(2007) https://doi.org/10.1103/PhysRevLett.98.010506
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) https://doi.org/10.1103/PhysRevB.61.10267
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) https://doi.org/10.1103/PhysRevLett.101.150409
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) https://doi.org/10.1103/PhysRevLett.100.096407
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) https://doi.org/10.1103/PhysRevLett.104.040502
A. V.Balatsky, I.Vekhter, and J. X.Zhu, Impurityinduced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373(2006) https://doi.org/10.1103/RevModPhys.78.373
27
Y.Chenand C. S.Ting, States of local moment induced by nonmagnetic impurities in cuprate superconductors, Phys. Rev. Lett. 92(7), 077203(2004) https://doi.org/10.1103/PhysRevLett.92.077203
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) https://doi.org/10.1103/PhysRevB.72.224501
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) https://doi.org/10.1103/PhysRevLett.110.020401
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) https://doi.org/10.1103/PhysRevLett.102.117003
31
Q.Han, Z. D.Wang, Q. H.Wang, and T.Xia, Vortex state in NaxCoO2·yH2O: px±ipy-wave versus dx2−y2±idxy-wave pairing, Phys. Rev. Lett.92(2), 027004(2004) https://doi.org/10.1103/PhysRevLett.92.027004
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) https://doi.org/10.1016/0031-9163(64)90375-0
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) https://doi.org/10.1103/PhysRevB.65.180513
35
G.Volovik, Fermion zero modes on vortices in chiral superconductors, JETP Lett.70(9), 609(1999) https://doi.org/10.1134/1.568223
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) https://doi.org/10.1103/PhysRevB.78.064513
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) https://doi.org/10.1134/S0021364006120113