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Influence of Finite Size Effects on the Fulde-Ferrell-Larkin-Ovchinnikov State

Published online by Cambridge University Press:  07 February 2017

Andrzej Ptok  and
Dawid Crivelli
Andrzej Ptok*
Affiliation:
Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków, Poland Institute of Physics, Maria Curie-Skłodowska University, Plac M. Skłodowskiej-Curie 1, 20-031 Lublin, Poland
Dawid Crivelli*
Affiliation:
Institute of Physics, University of Silesia, 40-007 Katowice, Poland Experimentalphysik I, Universität Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
*
*Corresponding author. Email addresses:aptok@mmj.pl (A. Ptok), dcrivelli@us.edu.pl (D. Crivelli)
*Corresponding author. Email addresses:aptok@mmj.pl (A. Ptok), dcrivelli@us.edu.pl (D. Crivelli)
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Abstract

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is the superconducting phase for which the Cooper pairs have a non-zero total momentum, depending on the splitting of the Fermi surface sheets for electrons with opposite spin. In infinite systems the momentum is a continuous function of the temperature. In this paper, we have shown how the finite size of the system, through the discretized geometry of the Fermi surface, affects the physical properties of the FFLO state by introducing discontinuities in the Cooper pair momentum. Our calculation in an isotropic system show that the superconducting state with two opposite Cooper pair momenta is more stable than state with one momentum also in nano-size systems, where finite size effects play a crucial role.

Keywords

SuperconductivityFFLOfinite sizenumerical instability
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 748 - 762
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Bardeen, J., Cooper, L. N., Schrieffer, J., Microscopic Theory of Superconductivity, Phys. Rev., 106 (1957), 162.Google Scholar
[2] Bardeen, J., Cooper, L. N., Schrieffer, J., Theory of Superconductivity, Phys. Rev., 108 (1957), 1175.Google Scholar
[3] Fulde, P., Ferrell, R. A., Superconductivity in a Strong Spin-Exchange Field, Phys. Rev., 135 (1964), A550.Google Scholar
[4] Larkin, A. I., Ovchinnikov, Yu. N., Inhomogeneous State of Superconductors, Zh. Eksp. Teor. Fiz., 47 (1964), 1136; [translation: Sov. Phys. JETP, 20 (1965), 762].Google Scholar
[5] Mierzejewski, M., Maśka, M. M., Critical field in a superconductivity model with local pairs, Phys. Rev. B, 69 (2004), 054502.CrossRefGoogle Scholar
[6] Clogston, A.M., Upper limit for the critical field in hard superconductors, Phys. Rev. Lett., 9 (1962), 266.Google Scholar
[7] Chandrasekhar, B. S., A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett., 1 (1962), 7.Google Scholar
[8] Kapcia, K., Robaszkiewicz, S., The magnetic field induced phase separation in a model of a superconductor with local electron pairing, J. Phys.: Condens. Matter, 25 (2013), 065603.Google Scholar
[9] Kapcia, K.J., Metastability and magnetic field Induced phase separation in the atomic limit of the Penson-Kolb-Hubbard model, Acta Phys. Pol. A, 126 (2014), A-53.CrossRefGoogle Scholar
[10] Beyer, R., Wosnitza, J., Emerging evidence for FFLO states in layered organic superconductors (Review Article), Low Temp. Phys., 39 (2013), 225 and references cited therein.Google Scholar
[11] Radovan, H. A., Fortune, N. A., Murphy, T. P., Hannahs, S. T., Palm, E. C., Tozer, S. W., Tozer, S. W., Hall, D., Magnetic enhancement of superconductivity from electron spin domains, Nature, 425 (2003), 51.Google Scholar
[12] Bianchi, A., Movshovich, R., Capan, C., Pagliuso, P. G., Sarrao, J. L., Possible Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in CeCoIn 5 , Phys. Rev. Lett., 91 (2003), 187004.Google Scholar
[13] Matsuda, Y., Shimahara, H., Fulde-Ferrell-Larkin-Ovchinnikov state in heavy fermion superconductors, J. Phys. Soc. Jpn., 76 (2007), 051005 and references cited therein.Google Scholar
[14] Ptok, A., Crivelli, D., The Fulde-Ferrell-Larkin-Ovchinnikov state in pnictides, J. Low Temp. Phys., 172 (2013), 226.Google Scholar
[15] Ptok, A., Influence of s± symmetry on unconventional superconductivity in pnictides above the Pauli limit - two-band model study, Eur. Phys. J. B, 87 (2014), 1.Google Scholar
[16] Crivelli, D., Ptok, A., Unconventional superconductivity in iron-based superconductors in a three-band model, Acta Phys. Pol. A, 126 (2014), A-16.Google Scholar
[17] Januszewski, M., Ptok, A., Crivelli, D., Gardas, B., GPU-based acceleration of free energy calculations in solid state physics, Comput. Phys. Commun., 192 (2015), 220.Google Scholar
[18] Ptok, A., Multiple phase transitions in Pauli limited iron-based superconductors, J. Phys.: Condens. Matter, 27 (2015), 482001.Google Scholar
[19] Ptok, A., Crivelli, D., Kapcia, K.J., Change of the sign of superconducting intraband order parameters induced by interband pair hopping interaction in iron-based high-temperature superconductors, Supercond. Sci. Technol., 28 (2015), 045010.Google Scholar
[20] Radzihovsky, L., Vishwanath, A., Quantum Liquid Crystals in an Imbalanced Fermi Gas: Fluctuations and Fractional Vortices in Larkin-Ovchinnikov States, Phys. Rev. Lett., 103 (2009), 010404.Google Scholar
[21] Guan, X.-W., Batchelor, M. T., Lee, Ch., Fermi gases in one dimension: From Bethe ansatz to experiments, Rev. Mod. Phys., 85 (2013), 1633 and references cited therein.Google Scholar
[22] Baarsma, J. E., Törmä, P., Larkin-Ovchinnikov phases in two-dimensional square lattices, J. Mod. Opt. 63 (2016), 1795.Google Scholar
[23] Casalbuoni, R., Nardulli, G., Inhomogeneous superconductivity in condensed matter and QCD Rev. Mod. Phys., 76 (2004), 263 and references cited therein.Google Scholar
[24] Alford, M. G., Schmitt, A., Rajagopal, K., Schäfer, T., Color superconductivity in dense quark matter Rev. Mod. Phys., 80 (2008), 1455 and references cited therein.Google Scholar
[25] Zegrodnik, M., Spałek, J., Spontaneous appearance of nonzero-momentum Cooper pairing: Possible application to the iron-pnictides, Phys. Rev. B, 90 (2014), 174507.Google Scholar
[26] Wójcik, P., Zegrodnik, M., Quantum size effect on the paramagnetic critical field in free-standing superconducting nanofilms, J. Phys.: Condens. Matter, 26 (2014), 455302.Google Scholar
[27] Wójcik, P., Zegrodnik, M., Spałek, J., Fulde-Ferrell state induced purely by the orbital effect in a superconducting nanowire, Phys. Rev. B, 91 (2015), 224511.Google Scholar
[28] Wójcik, P., Zegrodnik, M., Interplay between quantum confinement and Fulde-Ferrell-Larkin-Ovchinnikov phase in superconducting nanofilms, Phys. E 83 (2016), 442.Google Scholar
[29] Little, W. A., Parks, R. D., Observation of quantum periodicity in the transition temperature of a superconducting cylinder, Phys. Rev. Lett., 9 (1962), 9.Google Scholar
[30] Aoyama, K., Beaird, R., Sheehy, D. E., Vekhter, I., Inhomogeneous superconducting states of mesoscopic thin-walled cylinders in external magnetic fields, Phys. Rev. Lett., 110 (2013), 177004.CrossRefGoogle ScholarPubMed
[31] Maśka, M. M., Śledź, Ż., Czajka, K., Mierzejewski, M., Inhomogeneity-induced enhancement of the pairing interaction in cuprate superconductors, Phys. Rev. Lett., 99 (2007), 147006.Google Scholar
[32] Gao, B.-L., Xiong, S.-J., Combined effect of Rashba spin-orbit coupling and disorder on the symmetry of superconducting pairing, Phys. Rev. B, 75 (2007), 104507.Google Scholar
[33] Krzyszczak, J., Domański, T., Wysokiński, J. I., Micnas, R., Robaszkiewicz, S., Real space inhomogeneities in high temperature superconductors: the perspective of the two-component model, J. Phys.: Condens. Matter, 22 (2010), 255702.Google Scholar
[34] Ptok, A., Kapcia, K. J., Probe-type of superconductivity by impurity in materials with short coherence length - the s-wave and eta-wave phases study, Supercond. Sci. Technol., 28 (2015), 045022.Google Scholar
[35] Ptok, A., The Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in disordered systems, Acta Phys. Pol. A, 118 (2010), 420.Google Scholar
[36] Shimahara, H., Structure of the Fulde-Ferrell-Larkin-Ovchinnikov State in Two-Dimensional Superconductors, J. Phys. Soc. Jpn., 67 (1998), 736.CrossRefGoogle Scholar
[37] Mora, C., Combescot, R., Transition to Fulde-Ferrell-Larkin-Ovchinnikov phases in three dimensions: A quasiclassical investigation at low temperature with Fourier expansion, Phys. Rev. B, 71 (2005), 214504.Google Scholar
[38] Bogoliubov, N. N., Tolmachev, V. V., Shirkov, D. V., A new method in the theory of superconductivity, Sov. Phys. JETP, 7 (1958), 41.Google Scholar
[39] Romero-Bermúdez, A., García-García, A. M., Shape resonances and shell effects in thin-film multiband superconductors, Phys. Rev. B, 89 (2014), 024510.Google Scholar
[40] Romero-Bermúdez, A., García-García, A. M., Size effects in superconducting thin films coupled to a substrate, Phys. Rev. B, 89 (2014), 064508.Google Scholar
[41] Murawski, S., Kapcia, K. J., Pawowski, G., Robaszkiewicz, S., Some properties of two-dimensional extended repulsive Hubbard model with intersite magnetic interactions - a Monte Carlo study, Acta Phys. Pol. A, 126 (2014), A-110.CrossRefGoogle Scholar
[42] Tsindlekht, M. I., Genkin, V. M., Felner, I, Zeides, F., Katz, N., Gazi, Š., Chromik, Š, dc and ac magnetic properties of thin-walled superconducting niobium cylinders, Phys. Rev. B, 90 (2014), 014514.Google Scholar
[43] Zyuzin, A. A., Zyuzin, A. Yu., Anomalous transition temperature oscillations in the Larkin-Ovchinnikov-Fulde-Ferrell state, Phys. Rev. B, 79 (2009), 174514.CrossRefGoogle Scholar
[44] Mierzejewski, M., Maśka, M.M., Upper critical field for electrons in a two-dimensional lattice, Phys. Rev. B, 60 (1999), 6300.Google Scholar
[45] Kapcia, K. J., Murawski, S., Kłobus, W., and Robaszkiewicz, S., Magnetic orderings and phase separations in a simple model of insulating systems, Phys. A, 437 (2015), 218.Google Scholar
[46] Januszewski, M., Kostur, M., Accelerating numerical solution of stochastic differential equations with CUDA, Comput. Phys. Commun., 181 (2010), 183.Google Scholar
[47] Januszewski, M., Kostur, M., Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method, Comput. Phys. Commun., 185 (2014), 2350.Google Scholar
[48] Spiechowicz, J., Kostur, M., Machura, Ł., GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA, Comput. Phys. Commun., 191 (2015), 140.Google Scholar
[49] Biborski, A., Ka¸dzielawa, A. P., Spałek, J., Combined shared and distributed memory ab-initio computations of molecular-hydrogen systems in the correlated state: process pool solution and two-level parallelism, Comput. Phys. Commun., 197 (2015), 7.Google Scholar