|
|
Spatial modulation of unitary impurity-induced resonances in superconducting CeCoIn5 |
Ge Zhang1,Bin Liu1,*( ),Yi-Feng Yang2,3,Shiping Feng4 |
1 Department of Physics, Beijing Jiaotong University, Beijing 100044, China 2 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3 Collaborative Innovation Center of Quantum Matter, Beijing 100190, China 4 Department of Physics, Beijing Normal University, Beijing 100875, China |
|
|
Abstract Motivated by recent experimental progress in high-resolution scanning tunneling microscopy (STM) techniques, we investigate the local quasiparticle density of states around a unitary impurity in the heavy-fermion superconductor CeCoIn5. Based on the T -matrix approach we obtain a sharp nearly zero-energy resonance state in the strong impurity potential scattering localized around the impurity and find qualitative differences in the spatial pattern of the tunneling conductance modulated by the nodal structure of the superconducting gap. These unique features may be used as a probe of the superconducting gap symmetry and, in combination with further STM measurements, may help to confirm the dx2−y2 pairing in CeCoIn5 at ambient pressure.
|
Keywords
pairing symmetries
effects of disorder
tunneling phenomena
|
Corresponding Author(s):
Bin Liu
|
Online First Date: 01 February 2016
Issue Date: 08 June 2016
|
|
1 |
D. J. Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys. 84(4), 1383 (2012)
https://doi.org/10.1103/RevModPhys.84.1383
|
2 |
Ø. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Scanning tunneling spectroscopy of high-temperature superconductors, Rev. Mod. Phys. 79(1), 353 (2007)
https://doi.org/10.1103/RevModPhys.79.353
|
3 |
B. D. White, J. D. Thompson, and M. B. Maple, Unconventional superconductivity in heavy-fermion compounds, Physica C 514, 246 (2015)
https://doi.org/10.1016/j.physc.2015.02.044
|
4 |
G. Knebel, D. Aoki, and J. Flouquet, Antiferromagnetism and superconductivity in cerium based heavy-fermion compounds, C. R. Phys. 12(5-6), 542 (2011)
https://doi.org/10.1016/j.crhy.2011.05.002
|
5 |
G. Stewart, Non-Fermi-liquid behavior in d- and f- electron metals, Rev. Mod. Phys. 73(4), 797 (2001)
https://doi.org/10.1103/RevModPhys.73.797
|
6 |
G. Stewart, Heavy-fermion systems, Rev. Mod. Phys. 56(4), 755 (1984)
https://doi.org/10.1103/RevModPhys.56.755
|
7 |
F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schafer, Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2, Phys. Rev. Lett. 43(25), 1892 (1979)
https://doi.org/10.1103/PhysRevLett.43.1892
|
8 |
S. Kittaka, Y. Aoki, Y. Shimura, T. Sakakibara, S. Seiro, C. Geibel, F. Steglich, H. Ikeda, and K. Machida, Multiband superconductivity with unexpected deficiency of nodal quasiparticles in CeCu2Si2, Phys. Rev. Lett. 112(6), 067002 (2014)
https://doi.org/10.1103/PhysRevLett.112.067002
|
9 |
H. Ikeda, M. Suzuki, and R. Arita, Emergent loop-nodal s±-wave superconductivity in CeCu2Si2: Similarities to the iron-based superconductors, Phys. Rev. Lett. 114(14), 147003 (2015)
https://doi.org/10.1103/PhysRevLett.114.147003
|
10 |
H. Hegger, C. Petrovic, E. G. Moshopoulou, M. F. Hundley, J. L. Sarrao, Z. Fisk, and J. D. Thompson, Pressure-induced superconductivity in Quasi-2D CeRhIn5, Phys. Rev. Lett. 84(21), 4986 (2000)
https://doi.org/10.1103/PhysRevLett.84.4986
|
11 |
C. Petrovic, P. G. Pagliuso, M. F. Hundley, R. Movshovich, J. L. Sarrao, J. D. Thompson, Z. Fisk, and P. Monthoux, Heavy-fermion superconductivity in CeCoIn5 at 2.3 K, J. Phys.: Condens. Matter 13(17), L337 (2001)
https://doi.org/10.1088/0953-8984/13/17/103
|
12 |
C. Petrovic, R. Movshovich, M. Jaime, P. G. Pagliuso, M. F. Hundley, J. L. Sarrao, Z. Fisk, and J. D. Thompson, A new heavy-fermion superconductor CeIrIn5: Relative of the cuprates? Europhys. Lett. 53(3), 354 (2001)
https://doi.org/10.1209/epl/i2001-00161-8
|
13 |
A. McCollam, S. R. Julian, P. M. C. Rourke, D. Aoki, and J. Flouquet, Anomalous de Haas–van Alphen Oscillations in CeCoIn5, Phys. Rev. Lett. 94(18), 186401 (2005)
https://doi.org/10.1103/PhysRevLett.94.186401
|
14 |
T. Shang, R. E. Baumbach, K. Gofryk, F. Ronning, Z. F. Weng, J. L. Zhang, X. Lu, E. D. Bauer, J. D. Thompson, and H. Q. Yuan, CeIrIn5: Superconductivity on a magnetic instability, Phys. Rev. B 89(4), 041101 (2014)
https://doi.org/10.1103/PhysRevB.89.041101
|
15 |
J. S. van Dyke, F. Massee, M. P. Allan, J. C. S. Davisb, C. Petrovic, and D. K. Morr, Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5, Proc. Natl. Acad. Sci. USA 111(32), 11663 (2014)
https://doi.org/10.1073/pnas.1409444111
|
16 |
M. P. Allan, F. Massee, D. K. Morr, J. van Dyke, A. W. Rost, A. P. Mackenzie, C. Petrovic, and J. C. Davis, Imaging Cooper pairing of heavy fermions in CeCoIn5, Nat. Phys. 9(8), 468 (2013)
https://doi.org/10.1038/nphys2671
|
17 |
B. B. Zhou, S. Misra, E. H. da Silva Neto, P. Aynajian, R. E. Baumbach, J. D. Thompson, E. D. Bauer, and A. Yazdani, Visualizing nodal heavy fermion superconductivity in CeCoIn5, Nat. Phys. 9(8), 474 (2013)
https://doi.org/10.1038/nphys2672
|
18 |
T. Hu, H. Xiao, T. A. Sayles, M. Dzero, M. B. Maple, and C. C. Almasan, Strong magnetic fluctuations in a superconducting state of CeCoIn5, Phys. Rev. Lett. 108(5), 056401 (2012)
https://doi.org/10.1103/PhysRevLett.108.056401
|
19 |
M. Kenzelmann, S. Gerber, N. Egetenmeyer, J. L. Gavilano, Th. Strässle, A. D. Bianchi, E. Ressouche, R. Movshovich, E. D. Bauer, J. L. Sarrao, and J. D. Thompson, Evidence for a magnetically driven superconducting Qphase of CeCoIn5, Phys. Rev. Lett. 104(12), 127001 (2010)
https://doi.org/10.1103/PhysRevLett.104.127001
|
20 |
X. Lu, H. Lee, T. Park, F. Ronning, E. D. Bauer, and J. D. Thompson, Heat-capacity measurements of energy-gap nodes of the heavy-fermion superconductor CeIrIn5 deep inside the pressure-dependent dome structure of its superconducting phase diagram, Phys. Rev. Lett. 108(2), 027001 (2012)
https://doi.org/10.1103/PhysRevLett.108.027001
|
21 |
T. Park, H. Lee, I. Martin, X. Lu, V. A. Sidorov, K. Gofryk, F. Ronning, E. D. Bauer, and J. D. Thompson, Textured superconducting phase in the heavy fermion CeRhIn5, Phys. Rev. Lett. 108(7), 077003 (2012)
https://doi.org/10.1103/PhysRevLett.108.077003
|
22 |
Y. Kohori, Y. Yamato, Y. Iwamoto, T. Kohara, E. D. Bauer, M. B. Maple, and J. L. Sarrao, NMR and NQR studies of the heavy fermion superconductors CeTIn5 (T= Co and Ir), Phys. Rev. B 64(13), 134526 (2001)
https://doi.org/10.1103/PhysRevB.64.134526
|
23 |
Y. Matsuda and K. Izawa, Determination of the directions of gap nodes in exotic superconductors, Physica C388–389, 487 (2003)
https://doi.org/10.1016/S0921-4534(02)02389-4
|
24 |
K. Izawa and Y. Matsuda, Nodal structure of unconventional superconductors determined by thermal conductivity, J. Low Temp. Phys. 131, 429 (2003)
https://doi.org/10.1023/A:1022982715521
|
25 |
K. Izawa, H. Yamaguchi, Y. Matsuda, H. Shishido, R. Settai, and Y. Onuki, Angular position of nodes in the superconducting gap of quasi-2D heavy-fermion superconductor CeCoIn5, Phys. Rev. Lett. 87(5), 057002 (2001)
https://doi.org/10.1103/PhysRevLett.87.057002
|
26 |
H. Aoki, T. Sakakibara, H. Shishido, R. Settai, Y. nuki, P. Miranovi, and K. Machida, Field-angle dependence of the zero-energy density of states in the unconventional heavy-fermion superconductor CeCoIn5, J. Phys.: Condens. Matter 16(3), L13 (2004)
https://doi.org/10.1088/0953-8984/16/3/L02
|
27 |
K. An, T. Sakakibara, R. Settai, Y. Onuki, M. Hiragi, M. Ichioka, and K. Machida, Sign reversal of field-angle resolved heat capacity oscillations in a heavy fermion superconductor CeCoIn5 and dx2−y2 pairing symmetry, Phys. Rev. Lett. 104(3), 037002 (2010)
https://doi.org/10.1103/PhysRevLett.104.037002
|
28 |
R. Ikeda and H. Adachi, Modulated vortex lattice in high fields and gap nodes, Phys. Rev. B 69(21), 212506 (2004)
https://doi.org/10.1103/PhysRevB.69.212506
|
29 |
C. Stock, C. Broholm, J. Hudis, H. J. Kang, and C. Petrovic, Spin resonance in the d-wave superconductor CeCoIn5, Phys. Rev. Lett. 100(8), 087001 (2008)
https://doi.org/10.1103/PhysRevLett.100.087001
|
30 |
I. Eremin, G. Zwicknagl, P. Thalmeier, and P. Fulde, Feedback spin resonance in superconducting CeCu2Si2 and CeCoIn5, Phys. Rev. Lett. 101(18), 187001 (2008)
https://doi.org/10.1103/PhysRevLett.101.187001
|
31 |
N. Hiasa and R. Ikeda, Instability of square vortex lattice in d-wave superconductors is due to paramagnetic depairing, Phys. Rev. Lett. 101(2), 027001 (2008)
https://doi.org/10.1103/PhysRevLett.101.027001
|
32 |
W. K. Park, J. L. Sarrao, J. D. Thompson, and L. H. Greene, Andreev reflection in heavy-fermion superconductors and order parameter symmetry in CeCoIn5, Phys. Rev. Lett. 100(17), 177001 (2008)
https://doi.org/10.1103/PhysRevLett.100.177001
|
33 |
A. Vorontsov and I. Vekhter, Nodal structure of quasi-two-dimensional superconductors probed by a magnetic field, Phys. Rev. Lett. 96(23), 237001 (2006)
https://doi.org/10.1103/PhysRevLett.96.237001
|
34 |
A. Vorontsov and I. Vekhter, Unconventional superconductors under a rotating magnetic field (I): Density of states and specific heat, Phys. Rev. B 75(22), 224501 (2007)
https://doi.org/10.1103/PhysRevB.75.224501
|
35 |
F. Ronning, J. X. Zhu, T. Das, M. J. Graf, R. C. Albers, H. B. Rhee, and W. E. Pickett, Superconducting gap structure of the 115s revisited, J. Phys.: Condens. Matter 24(29), 294206 (2012)
https://doi.org/10.1088/0953-8984/24/29/294206
|
36 |
T. Das, A. B. Vorontsov, I. Vekhter, and M. J. Graf, Field-angle-resolved anisotropy in superconducting CeCoIn5 using realistic Fermi surfaces, Phys. Rev. B 87(17), 174514 (2013)
https://doi.org/10.1103/PhysRevB.87.174514
|
37 |
B. Liu, Nonmagnetic impurity resonance states as a test of superconducting pairing symmetry in CeCoIn5, Phys. Rev. B 88(24), 245127 (2013)
https://doi.org/10.1103/PhysRevB.88.245127
|
38 |
A. Koitzsch, I. Opahle, S. Elgazzar, S. V. Borisenko, J. Geck, V. B. Zabolotnyy, D. Inosov, H. Shiozawa, M. Richter, M. Knupfer, J. Fink, B. Büchner, E. D. Bauer, J. L. Sarrao, and R. Follath, Electronic structure of CeCoIn5 from angle-resolved photoemission spectroscopy, Phys. Rev. B 79(7), 075104 (2009)
https://doi.org/10.1103/PhysRevB.79.075104
|
39 |
P. Aynajian, E. H. da Silva Neto, A. Gyenis, R. E. Baumbach, J. D. Thompson, Z. Fisk, E. D. Bauer, and A. Yazdani, Visualizing heavy fermions emerging in a quantum critical Kondo lattice, Nature 486(7402), 201 (2012)
https://doi.org/10.1038/nature11204
|
40 |
S. Ernst, S. Wirth, F. Steglich, Z. Fisk, J. L. Sarrao, and J. D. Thompson, Scanning tunneling microscopy studies on CeCoIn5 and CeIrIn5, Phys. Status Solidi 247(3), 624 (2010)
https://doi.org/10.1002/pssb.200983035
|
41 |
A. V. Balatsky, I. Vekhter, and J. X. Zhu, Impurity-induced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373 (2006)
https://doi.org/10.1103/RevModPhys.78.373
|
42 |
T. Maehira, T. Hotta, K. Ueda, and A. Hasegawa, Relativistic band-structure calculations for CeTIn5 (T= Ir and Co) and analysis of the energy bands by using tight-binding method, J. Phys. Soc. Jpn. 72(4), 854 (2003)
https://doi.org/10.1143/JPSJ.72.854
|
43 |
Y. Ōnuki, R. Settai, K. Sugiyama, T. Takeuchi, T. C. Kobayashi, Y. Haga, and E. Yamamoto, Recent advances in the magnetism and superconductivity of heavy fermion systems, J. Phys. Soc. Jpn. 73(4), 769 (2004)
https://doi.org/10.1143/JPSJ.73.769
|
44 |
Y. Haga, Y. Inada, H. Harima, K. Oikawa, M. Murakawa, H. Nakawaki, Y. Tokiwa, D. Aoki, H. Shishido, S. Ikeda, N. Watanabe, and Y. Onuki, Quasi-two-dimensional Fermi surfaces of the heavy fermion superconductor CeIrIn5, Phys. Rev. B 63(6), 060503 (2001)
https://doi.org/10.1103/PhysRevB.63.060503
|
45 |
D. Hall, E. C. Palm, T. P. Murphy, S. W. Tozer, C. Petrovic, E. Miller-Ricci, L. Peabody, C. Li, U. Alver, R. G. Goodrich, J. L. Sarrao, P. G. Pagliuso, J. M. Wills, and Z. Fisk, Electronic structure of CeRhIn5: de Haas–van Alphen and energy band calculations, Phys. Rev. B 64(6), 064506 (2001)
https://doi.org/10.1103/PhysRevB.64.064506
|
46 |
H. Shishido, T. Ueda, S. Hashimoto, T. Kubo, R. Settai, H. Harima, and Y. Onuki, A de Haas–van Alphen experiment under pressure on CeCoIn5: Deviation from the quantum critical region, J. Phys.: Condens. Matter 15(32), L499 (2003)
https://doi.org/10.1088/0953-8984/15/32/101
|
47 |
L. Dudy, J. D. Denlinger, L. Shu, M. Janoschek, J. W. Allen, and M. B. Maple, Yb valence change in Ce1–xYbxCoIn5 from spectroscopy and bulk properties, Phys. Rev. B 88(16), 165118 (2013)
https://doi.org/10.1103/PhysRevB.88.165118
|
48 |
K. Tanaka, H. Ikeda, Y. Nisikawa, and K. Yamada, Theory of superconductivity in CeMIn5 (M=Co, Rh, Ir) on the basis of the three dimensional periodic Anderson model, J. Phys. Soc. Jpn. 75(2), 024713 (2006)
https://doi.org/10.1143/JPSJ.75.024713
|
49 |
S. H. Pan, E. W. Hudson, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403(6769), 746 (2000)
https://doi.org/10.1038/35000514
|
50 |
S. H. Pan, J. P. O’Neal, R. L. Badzey, C. Chamon, H. Ding, J. R. Engelbrecht, Z. Wang, H. Eisaki, S. Uchida, A. K. Gupta, K.W. Ng, E. W. Hudson, K. M. Lang, and J. C. Davis, Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x, Nature 413(6853), 282 (2001)
https://doi.org/10.1038/35095012
|
51 |
E. W. Hudson, K. M. Lang, V. Madhavan, S. H. Pan, H. Eisaki, S. Uchida, and J. C. Davis, Interplay of magnetism and high-Tcsuperconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+d, Nature 411(6840), 920 (2001)
https://doi.org/10.1038/35082019
|
52 |
S. Haas and K. Maki, Quasiparticle bound states around impurities in dx2−y2-wave superconductors, Phys. Rev. Lett. 85(10), 2172 (2000)
https://doi.org/10.1103/PhysRevLett.85.2172
|
53 |
A. Yazdani, B. A. Jones, C. P. Lutz, M. F. Crommie, and D. M. Eigler, Probing the local effects of magnetic impurities on superconductivity, Science 275(5307), 1767 (1997)
https://doi.org/10.1126/science.275.5307.1767
|
54 |
M. I. Salkola, A. V. Balatsky, and J. R. Schrieffer, Spectral properties of quasiparticle excitations induced by magnetic moments in superconductors, Phys. Rev. B 55(18), 12648 (1997)
https://doi.org/10.1103/PhysRevB.55.12648
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|