Quasi-point versus point nodes in Sr2RuO4, the case of a flat tight binding γ sheet

Authors

DOI:

https://doi.org/10.31349/RevMexFis.68.060501

Keywords:

Unconventional superconductivity, Flat bands, Triplet Reversal time broken state, Sr2RuO4, Wigner distributions, Point nodes, Comput mat design, Non-magnetic disorder, scattering cross-section

Abstract

We perform a numerical study of the unitary regime as a function of disorder concentration in the imaginary part of the elastic scattering cross-section for the compound Sr2RuO4 in the flat band non-disperse limit. By using a self-consistent tight binding (TB) method, we find a couple of families of Wigner probabilistic functions that help to explain macroscopically the distribution between Fermion dressed quasiparticles and Cooper pairs, and also the position of nodes in the order parameter for Sr2RuO4. Therefore, we are able to show that a TB model for the FS γ-sheet, numerically shows 4 point nodes in a flat γ sheet limit, or 4 quasi-point nodes for strong dispersion γ sheet limit in the reduced phase scattering space (RPS).

Author Biography

Pedro L. Contreras E., Universidad de Los Andes

Physics and Math lecturer (Professor)  with more than 15 years of lecturing and research experience in colleges and universities and with an eye on a science teacher position, willing to incorporate my learning multicultural experience.  

In previous roles, co-developed research and mentorship resulting in peer-review publications and tech. reports.

Winner of the "Van Kranendonk Teaching Assistant Award" at the University of Toronto recognizing outstanding contributions to the teaching of physics at the undergraduate level in 2003.

References

Y. Maeno et al., Superconductivity in a layered perovskite without copper, Nature 372 (1994) 53, https://doi.org/10. 1038/372532a0

C. Bergemann, A. P. Mackenzie, S. R. Julian, D. Forsythe, E. Ohmichi, Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4, Advances in Physics 52 (2003) 639, https://doi.org/10.1080/00018730310001621737

M. Suzuki, M. A. Tanatar, N. Kikugawa, Z. Q. Mao, Y. Maeno, and T. Ishiguro, Universal Heat Transport in Sr2RuO4, Phys. Rev. Lett. 88 (2002) 227004, https://doi.org/10.1103/PhysRevLett.88.227004

T. M. Rice and M. Sigrist, Sr2RuO4: an electronic analogue of He3 ?, Journal of Physics: Condensed Matter 7 (1995) L643, http://dx.doi.org/10.1088/0953-8984/7/47/002

K. Ishida, H. Mukuda, Y. Kitaoka et al., Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift, Nature 396 (1998) 658, https://doi.org/10.1038/25315

G. Luke, Y. Fudamoto, K. Kojima et al., Time-reversal symmetry-breaking superconductivity in Sr2RuO4, Nature 394 (1998) 558, https://doi.org/10.1038/29038

J. A. Duffy, S. M. Hayden, Y. Maeno, Z. Mao, J. Kulda, and G. J. Mclntyre, Polarized-Neutron Scattering Study of the Cooper-Pair Moment in Sr2RuO4, Phys. Rev. Lett. 85 (2000) 5412, https://doi.org/10.1103/PhysRevLett.85.5412

D. Osheroff, W. Gully, R. Richardson, and D. Lee, New Magnetic Phenomena in Liquid 3He below 3 mK. 1972. Phys. Rev. Lett. 29 (1972) 920, https://link.aps.org/doi/10.1103/PhysRevLett.29.920

V. Ambegaokar and N.D. Mermin, Thermal Anomalies of 3He: Pairing in a Magnetic Field. Phys. Rev. Lett. 30 (1973) 81-84, https://link.aps.org/doi/10.1103/PhysRevLett.30.81

W. A. Harrison, Electronic Structure and Properties of Solids (Dover, New York, 1980).

A. P. Mackenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing, Rev. Mod. Phys. 75 (2003) 657, https://doi.org/10.1103/RevModPhys.75.657

C. W. Hicks, D. O. Brodsky, E. A. Yelland et al., Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain, Science 344 (2014) 283, https://www.science.org/doi/10.1126/science.1248292

S. Benhabib, C. Lupien, I. Paul et al., Ultrasound evidence for a two-component superconducting order parameter in Sr2RuO4, Nat. Phys. 17 (2021) 194, https://doi.org/10.1038/s41567-020-1033-3

S. Ghosh, A. Shekhter, F. Jerzembeck et al., Thermodynamic evidence for a two-component superconducting order parameter in Sr2RuO4, Nat. Phys. 17 (2021) 199, https://doi.org/10.1038/s41567-020-1032-4

V. Grinenko, D. Das, R. Gupta et al., Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder. Nat Commun 12 (2021) 3920, https://doi.org/10.1038/s41467-021-24176-8

K. Miyake and O. Narikiyo, Model for Unconventional Superconductivity of Sr2RuO4: Effect of Impurity Scattering on Time-Reversal Breaking Triplet Pairing with a Tiny Gap, Phys. Rev. Lett. 83 (1999) 1423, https://doi.org/10.1103/PhysRevLett.83.1423

M. B. Walker and P. Contreras, Theory of elastic properties of Sr2RuO4 at the superconducting transition temperature, Phys. Rev. B 66 (2002) 214508, https://doi.org/10.1103/PhysRevB.66.214508

P. Carruthers and F. Zachariasen, Quantum collision theory with phase-space distributions, Rev. Mod. Phys. 55 (1983) 245, https://doi.org/10.1103/RevModPhys.55.245

P. Contreras, D. Osorio and S. Ramazanov, Non-magnetic tight binding effects on the γ sheet of Sr2RuO2. Rev. Mex. Fis. 68 (2022) 1, https://doi.org/10.31349/RevMexFis.68.020502

P. Contreras, Dianela Osorio, and E Beliayev, Dressed behavior of the quasiparticles lifetime in the unitary limit of two unconventional superconductors, Low Temp. Phys. 48 (2022) 187, https://doi.org/10.1063/10.0009535

Hase, I., Yanagisawa, T., and Kawashima, K. Computational Design of Flat-Band Material. Nanoscale research letters, 13 (2018) 63, https://doi.org/10.1186/s11671-018-2464-y

E. Schachinger and J. P. Carbotte, Residual absorption at zero temperature in d-wave superconductors, Phys. Rev. B 67 (2003) 134509, https://doi.org/10.1103/PhysRevB.67.134509 23. I. M. Lifshitz, S. A. Gredeskul and L. A. Pastur, Introduction to the theory of disordered systems (John Wiley and Sons, 1988).

J. M. Ziman, Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems, (Cambridge University Press, Cambridge, 1979).

V. Mineev and K. Samokhin, Introduction to Unconventional Superconductivity, (Amsterdam, Gordon and Breach Science Publish, 1999).

P. Contreras, M. Walker, and K. Samokhin, Determining the superconducting gap structure in from sound attenuation studies below Tc, Phys. Rev. B 70 (2004) 184528, https://doi.org/10.1103/PhysRevB.70.184528

P. Contreras, Electronic heat transport for a multiband superconducting gap in Sr2RuO4, Rev. Mex. Fis. 57 (2011) 395.

P. Contreras, et al., A numerical calculation of the electronic specific heat for the compound Sr2RuO4 below its superconducting transition temperature. Rev. Mex. Fis. 60 (2014) 184.

P. Contreras, and D. Osorio, Scattering Due to Non-magnetic Disorder in 2D Anisotropic d-wave High Tc Superconductors, Engineering Physics 5 (2021) 1, https://doi.org/10.11648/j.ep.20210501.11

P. J. Hirschfeld, P. Wolfle, and D. Einzel, Consequences of resonant impurity scattering in anisotropic superconductors: Thermal and spin relaxation properties, Phys. Rev. B 37 (1988) 83, https://doi.org/10.1103/PhysRevB.37.83

K. Maki and H. Won, Why d-wave superconductivity?, Journal de Physique I 6 (1996) 2317, https://doi.org/10.1051/jp1:1996220

C. J. Pethick and D. Pines, Transport processes in heavyfermion superconductors, Phys. Rev. Lett. 57 (1986) 118, https://doi.org/10.1103/PhysRevLett.57.118

S. Schmitt-Rink, K. Miyake, and C. M. Varma, Transport and Thermal Properties of Heavy-Fermion Superconductors: A Unified Picture, Phys. Rev. Lett. 57 (1986) 2575, https://doi.org/10.1103/PhysRevLett.57.2575

A. V. Balatsky, M. I. Salkola, and A. Rosengren, Impurityinduced virtual bound states in d-wave superconductors, Phys. Rev. B 51 (1995) 15547, https://doi.org/10.1103/PhysRevB.51.15547

L. P. Pitaevskii, Superfluid Fermi liquid in a unitary regime, Phys.-Usp. 51 (2008) 603, https://doi.org/10.1070/PU2008v051n06ABEH006548

Stefan Kasen, Response functions of strongly correlated electron systems: From perturbative to many-body techniques. Ph.D. Graduate Theses and Dissertations, 2020.

V. G. Yarzhemsky, Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials. Symmetry, 13 (2021) 1435, https://doi.org/10.3390/sym13081435

A. Leggett, and Y. Liu, Symmetry Properties of Superconducting Order Parameter in Sr2RuO4. J Supercond Nov Magn 34 (2021) 1647, https://doi.org/10.1007/s10948-020-05717-6

P. Contreras, J. Florez and R. Almeida, Symmetry Field Breaking Effects in Sr2RuO4 , Rev. Mex. Fis. 62 (2016) 442.

V. Shaginyan and M. Amusia, Strongly Correlated Fermi Systems: A New State of Matter (Springer, 2020).

L. Landau and E. Lifshitz, Quantum Mechanics, Nonrelativistic theory (Pergamon, 1965).

D. Rainer and J. A. Sauls. Strong Coupling Theory of Superconductivity in Superconductivity: From Basic Physics to the Latest Developments, World Scientific: 45, (1995). https://doi.org/10.1142/9789814503891.0002

Stefan Kasen. Response functions of strongly correlated electron systems: From perturbative to many-body techniques. Ph.D. Graduate Theses and Dissertations, 2020.

M. Hillery, R.F. O’Connell, M.O. Scully, and E.P. Wigner, Distribution functions in physics: Fundamentals, Physics Reports, 106 (1984) 121, https://doi.org/10.1016/0370-1573(84)90160-1

Downloads

Published

2022-11-01

How to Cite

[1]
P. L. Contreras E., D. Osorio, and S. Tsuchiya, “Quasi-point versus point nodes in Sr2RuO4, the case of a flat tight binding γ sheet”, Rev. Mex. Fís., vol. 68, no. 6 Nov-Dec, pp. 060501 1–, Nov. 2022.