2D materials; charge density wave; transition-metal dichalcogenide
Abstract :
[en] Despite intense efforts on all known quasi-two-dimensional superconductors, the origin and exact boundary of the electronic orderings, particularly charge density waves and superconductivity, are still attractive problems with several open questions. Here, in order to reveal how the superconducting gap evolves, we report on high quality complementary measurements of magneto-optical imaging, specific heat, magnetic susceptibility, resistivity measurements, Andreev spectroscopy, and London penetration depth λab(T) measurements supplemented with theoretical calculations for 2H-NbSe2 and 2H-NbS2 single crystals. The temperature dependence of λab(T)calculated from the lower critical field and Andreev spectroscopy can be well described by using a two-band model with s-wave-like gaps. The effect of pressure on the superconducting gap of both systems illustrates that both bands are practically affected. Upon compression, the Fermi surfaces do not change significantly, and the nesting remains almost unaffected compared to that at ambient condition. However, a strong bending in the upper critical fields (Hc2) curves is obtained under pressure and support the presence of a strong Pauli paramagnetic effect. In NbSe2, using a two-band model with s-wave-like gaps, the temperature dependence Hc2 (T) can be properly described. In contrast to that, the behavior of Hc2 for NbS2 is ruled by the spin paramagnetic effect. The estimated values of the penetration depth at T = 0 K confirm that NbSe2 and NbS2 superconductors depart from a Uemura-style relationship between Tc with 1/λab^2, the in-plane superconducting penetration depth.
Disciplines :
Physics
Author, co-author :
Majumdar, Arnab; Uppsala University, Sweden
VanGennep, Derrick; Harvard University, Cambridge, Massachusetts 02138, USA
Brisbois, Jérémy ; Université de Liège - ULiège > CSL (Centre Spatial de Liège)
Chareev, Dmitriy; Institute of Experimental Mineralogy, Russian Academy of Sciences, 142432, Chernogolovka, Moscow District, Russia
Sadakov, A.D.; 4Institute of Experimental Mineralogy, Russian Academy of Sciences, 142432, Chernogolovka, Moscow District, Russia
Usoltsev, A.S.; 4Institute of Experimental Mineralogy, Russian Academy of Sciences, 142432, Chernogolovka, Moscow District, Russia
Mito, Masaki; Kyushu Institute of Technology, Fukuoka 804–8550, Japan
Silhanek, Alejandro ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés
Sarkar, Tapati; Department of Materials Science and Engineering, Uppsala University, Box 534, SE-75121, Sweden
M. B. Maple, in Magnetism and Magnetic Materials-1976: Proceedings of the First Joint MMM-Intermag Conference, edited by H. C. Wolfe, J. J. Becker, and G. H. Lander, AIP Conf. Proc. No. 34 (AIP, New York, 1976), p. 71.
P. C. Canfield, P. L. Gammel, and D. J. Bishop, New magnetic superconductors: A toy box for solid-state physicists, Physics Today 51 (10), 40 (1998) 10.1063/1.882396.
M. D. Johannes and I. I. Mazin, Phys. Rev. B 77, 165135 (2008) 10.1103/PhysRevB.77.165135.
J. J. Hamlin, D. A. Zocco, T. A. Sayles, and M. B. Maple, Phys. Rev. Lett. 102, 177002 (2009) 10.1103/PhysRevLett.102.177002.
D. A. Zocco, J. J. Hamlin, K. Grube, J. Chu, H. Kuo, I. R. Fisher, and M. B. Maple, Phys. Rev. B 91, 205114 (2015) 10.1103/PhysRevB.91.205114.
Q. H. Wang, K. Kalantar-zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Nat. Nanotechnol. 7, 699 (2012) 10.1038/nnano.2012.193.
A. K. Geim and I. V Grigorieva, Nature (London) 499, 419 (2013) 10.1038/nature12385.
E. Revolinsky, E. P. Lautenschlager, and C. H. Armitage, Solid State Commun. 1, 59 (1963) 10.1016/0038-1098(63)90358-2.
I. Guillamon, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodiere, Phys. Rev. Lett. 101, 166407 (2008) 10.1103/PhysRevLett.101.166407.
H. N. S. Lee, H. McKinzie, D. S. Tannhauser, and A. Wold, J. Appl. Phys. 40, 602 (1969) 10.1063/1.1657440.
R. Grasset, T. Cea, Y. Gallais, M. Cazayous, A. Sacuto, L. Cario, L. Benfatto, and M. Méasson, Phys. Rev. B 97, 094502 (2018) 10.1103/PhysRevB.97.094502.
M. Leroux, M. Le Tacon, M. Calandra, L. Cario, M.-A. Measson, P. Diener, E. Borrissenko, A. Bosak, and P. Rodiere, Phys. Rev. B 86, 155125 (2012) 10.1103/PhysRevB.86.155125.
F. Flicker and J. Van Wezel, Nat. Commun. 6, 7034 (2015) 10.1038/ncomms8034.
Z. Liu, L. Cai, and X. Zhang, J. Alloys Compd. 610, 472 (2014) 10.1016/j.jallcom.2014.05.013.
E. Boaknin, M. A. Tanatar, J. Paglione, D. Hawthorn, F. Ronning, R. W. Hill, M. Sutherland, L. Taillefer, J. Sonier, S. M. Hayden, and J. W. Brill, Phys. Rev. Lett. 90, 117003 (2003) 10.1103/PhysRevLett.90.117003.
H. F. Hess, R. B. Robinson, and J. V Waszczak, Phys. Rev. Lett. 64, 2711 (2000) 10.1103/PhysRevLett.64.2711.
C. L. Huang, J. Lin, Y. T. Chang, C. P. Sun, H. Y. Shen, C. C. Chou, H. Berger, T. K. Lee, and H. D. Yang, Phys. Rev. B 76, 212504 (2007) 10.1103/PhysRevB.76.212504.
A. Bussmann-Holder, R. Micnas, and A. R. Bishop, Eur. Phys. J. B 37, 345 (2004) 10.1140/epjb/e2004-00065-5.
S. Fiechter and H.-M. Kuhne, J. Crystallogr. Growth 83, 517 (1987) 10.1016/0022-0248(87)90246-6.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevMaterials.4.084005 for more details on the sample preparation, crystal structure, temperature dependence of the resistivity, and atomic distances under pressure, and superconducting parameters at ambient pressure.
M. Mito, M. Hitaka, T. Kawae, K. Takeda, T. Kitai, and N. Toyoshima, Jpn. J. Appl. Phys. 40, 6641 (2001) 10.1143/JJAP.40.6641.
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, J. Phys. Condens. Matter 21, 395502 (2009) 10.1088/0953-8984/21/39/395502.
J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) 10.1103/PhysRevLett.77.3865.
H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976) 10.1103/PhysRevB.13.5188.
C. Jooss, J. Albrecht, H. Kuhn, S. Leonhardt, and H. Kronmuller, Rep. Prog. Phys. 65, 651 (2002) 10.1088/0034-4885/65/5/202.
G. Shaw, J. Brisbois, L. B. G. L. Pinheiro, J. Müller, S. B. Alvarez, T. Devillers, N. M. Dempsey, J. E. Scheerder, J. Van de Vondel, S. Melinte, P. Vanderbemden, M. Motta, W. A. Ortiz, K. Hasselbach, R. B. G. Kramer, and A V Silhanek, Rev. Sci. Instrum. 89, 023705 (2018) 10.1063/1.5016293.
T. Valla, A. V Fedorov, P. D. Johnson, P.-A. Glans, C. McGuinness, K. E. Smith, E. Y. Andrei, and H. Berger, Phys. Rev. Lett. 92, 086401 (2004) 10.1103/PhysRevLett.92.086401.
X. Xi, L. Zhao, Z. Wang, H. Berger, L. Forró, J. Shan, and K. F. Mak, Nat. Nanotechnol. 10, 765 (2015) 10.1038/nnano.2015.143.
M. M. Ugeda, A. J. Bradley, Y. Zhang, S. Onishi, Y. Chen, W. Ruan, C. Ojeda-aristizabal, H. Ryu, M. T. Edmonds, H. Tsai, A. Riss, S. Mo, D. Lee, A. Zettl, Z. Hussain, Z. Shen, and M. F. Crommie, Nat. Phys. 12, 92 (2016) 10.1038/nphys3527.
M. D. Johannes, I. I. Mazin, and C. A. Howells, Phys. Rev. B 73, 205102 (2006) 10.1103/PhysRevB.73.205102.
T. Giamarchi and S. Bhattacharya, in High Magnetic Fields, edited by C. Berthier, L. P. Levy, and G. Martinez, 1st ed. (Springer-Verlag, Berlin, 2001), pp. 314-360.
V. G. Tissen, M. R. Osorio, J. P. Brison, N. M. Nemes, M. Garcia-Hernandez, L. Cario, P. Rodiere, S. Vieira, and H. Suderow, Phys. Rev. B 87, 134502 (2013) 10.1103/PhysRevB.87.134502.
M. Leroux, I. Errea, M. Le Tacon, S. Souliou, G. Garbarino, L. Cario, A. Bosak, F. Mauri, M. Calandra, and P. Rodiere, Phys. Rev. B 92, 140303 (2015) 10.1103/PhysRevB.92.140303.
R. Kummel, U. Gunsenheimer, and R. Nicolsky, Phys. Rev. B 42, 3992 (1990) 10.1103/PhysRevB.42.3992.
M. Abdel-Hafiez, P. J. Pereira, S. A. Kuzmichev, T. E. Kuzmicheva, V. M. Pudalov, L. Harnagea, A. A. Kordyuk, A. V. Silhanek, V. V. Moshchalkov, B. Shen, Hai-Hu Wen, A. N. Vasiliev, and Xiao-Jia Chen, Phys. Rev. B 90, 054524 (2014) 10.1103/PhysRevB.90.054524.
S. V. Borisenko, A. A. Kordyuk, V. B. Zabolotnyy, D. S. Inosov, D. Evtushinsky, B. Buechner, A. N. Yaresko, A. Varykhalov, R. Follath, W. Eberhardt, L. Patthey, and H. Berger, Phys. Rev. Lett. 102, 166402 (2009) 10.1103/PhysRevLett.102.166402.
J. A. Wilson, F. J. Di Salvo, and S. Mahajan, Phys. Rev. Lett. 32, 882 (1974) 10.1103/PhysRevLett.32.882.
L. F. Mattheiss, Phys. Rev. Lett. 30, 784 (1973) 10.1103/PhysRevLett.30.784.
M.-H. Whangbo and E. Canadell, J. Am. Chem. Soc. 114, 9587 (1992) 10.1021/ja00050a044.
A. Bianconi and T. Jarlborg, Nov. Supercond. Mater. 1, 37 (2015).
A. M. Clogston, Phys. Rev. Lett. 9, 266 (1962) 10.1103/PhysRevLett.9.266.
N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Phys. Rev. 147, 295 (1966) 10.1103/PhysRev.147.295.
A. Gurevich, Phys. Rev. B 67, 184515 (2003) 10.1103/PhysRevB.67.184515.
M. Abdel-Hafiez, J. Ge, A. N. Vasiliev, D. A. Chareev, J. Van de Vondel, and A. V. Silhanek, Phys. Rev. B, 88, 174512 (2013) 10.1103/PhysRevB.88.174512.
M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kazakov, J. Karpinski, J. Roos, and H. Keller, Phys. Rev. Lett. 88, 167004 (2002) 10.1103/PhysRevLett.88.167004.
E. H. Brandt, Phys. Rev. B 60, 11939 (1999) 10.1103/PhysRevB.60.11939.
A. Carrington and F. Manzano, Phys. C 385, 205 (2003) 10.1016/S0921-4534(02)02319-5.
T. Saito, S. Onari, and H. Kontani, Phys. Rev. B 88, 045115 (2013) 10.1103/PhysRevB.88.045115.
D. C. Johnston, Supercond. Sci. Technol. 26, 115011 (2013) 10.1088/0953-2048/26/11/115011.
K. Rossnagel, O. Seifarth, L. Kipp, M. Skibowski, D. Vob, P. Kruger, A. Mazur, and J. Pollman, Phys. Rev. B 64, 235119 (2001) 10.1103/PhysRevB.64.235119.
T. Klein, L. Lyard, J. Marcus, C. Marcenat, P. Szabó, Z. Hol, P. Samuely, B. W. Kang, H. Kim, H. Lee, H. Lee, and S. Lee, Phys. Rev. B 73, 224528 (2006) 10.1103/PhysRevB.73.224528.
T. Yokoya, T. Kiss, A. Chainani, S. Shin, M. Nohara, and H. Takagi, Science. 294, 2518 (2001) 10.1126/science.1065068.
J. D. Fletcher, A. Carrington, P. Diener, P. Rodiere, J. P. Brison, R. Prozorov, T. Olheiser, and R. W. Giannetta, Phys. Rev. Lett. 98, 057003 (2007) 10.1103/PhysRevLett.98.057003.
Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. KieA, S. R. Kreitzman, P. Mulhern, T. M. Riseman, D. L. Williams, B. X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan, A. W. Sleight, M. A. Subramanian, C. L. Chien, M. Z. Cieplak, G. Xiao, V. Y. Lee, and B. W. Statt, Phys. Rev. Lett. 62, 2317 (1989) 10.1103/PhysRevLett.62.2317.
A. J. Drew, F. L. Pratt, T. Lancaster, S. J. Blundell, P. J. Baker, R. H. Liu, G. Wu, X. H. Chen, I. Watanabe, and C. Bernhard, Phys. Rev. Lett. 101, 097010 (2008) 10.1103/PhysRevLett.101.097010.
A. Adamski, C. Krellner, and M. Abdel-Hafiez, Phys. Rev. B 96, 100503 (2017) 10.1103/PhysRevB.96.100503.
M. Abdel-Hafiez, M. Mito, K. Shibayama, S. Takagi, M. Ishizuka, A. N. Vasiliev, C. Krellner, and H. K. Mao, Phys. Rev. B 98, 094504 (2018)) 10.1103/PhysRevB.98.094504.
C. Ren, Z. Wang, H. Luo, H. Yang, L. Shan, and H. Wen, Phys. Rev. Lett. 101, 257006 (2008) 10.1103/PhysRevLett.101.257006.
H. Luetkens, H. Klauss, R. Khasanov, A. Amato, R. Klingeler, I. Hellmann, N. Leps, A. Kondrat, C. Hess, A. Kohler, G. Behr, J. Werner, and B. Buchner, Phys. Rev. Lett. 101, 097009 (2008) 10.1103/PhysRevLett.101.097009.
F. Manzano, A. Carrington, N. E. Hussey, S. Lee, A. Yamamoto, and S. Tajima, Phys. Rev. Lett. 88, 047002 (2002) 10.1103/PhysRevLett.88.047002.