Abstract
Study of fluctuation phenomena in superconductors (SCs) is the subject of great fundamental and practical importance. Understanding of their physics allowed to clear up the fundamental properties of SC state. Being predicted in 1968, one of the fluctuation effects, namely paraconductivity, was experimentally observed almost simultaneously. Since this time, fluctuations became a noticeable part of research in the field of superconductivity, and a variety of fluctuation effects have been discovered. The new wave of interest to fluctuations (FL) in superconductors was generated by the discovery of cuprate oxide superconductors (high-temperature superconductors, HTS), where, due to extremely short coherence length and low effective dimensionality of the electron system, superconductive fluctuations manifest themselves in a wide range of temperatures. Moreover, anomalous properties of the normal state of HTS were attributed by many theorists to strong FL in these systems. Being studied in the framework of the phenomenological Ginzburg–Landau theory and, more extensively, in diagrammatic microscopic approach, SC FLs side by side with other quantum corrections (weak localization, etc.) became a new tool for investigation and characterization of such new systems as HTS, disordered electron systems, granular metals, Josephson structures, artificial super-lattices, etc. The characteristic feature of SC FL is their strong dependence on temperature and magnetic fields in the vicinity of phase transition. This allows one to definitely separate the fluctuation effects from other contributions and to use them as the source of information about the microscopic parameters of a material. By their origin, SC FLs are very sensitive to relaxation processes, which break phase coherence. This allows using them for versatile characterization of SC. Today, one can speak about the “ fluctuoscopy” of superconductive systems. In review, we present the qualitative picture both of thermodynamic fluctuations close to critical temperature T c0and quantum fluctuations at zero temperature and in vicinity of the second critical field H c2(0). Then in the frameworks of the Ginzburg–Landau theory, we discuss the characteristic crossovers in fluctuation properties of superconductive nanoparticles and layered superconductors. We present the general expression for fluctuation magneto-conductivity valid through all phase diagram of superconductor and apply it to study of the quantum phase transition close to H c2(0). Fluctuation analysis of this transition allows us to present the scenario of fluctuation defragmentation of the Abrikosov lattice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A.I. Larkin, A.A. Varlamov, Theory of Fluctuations in Superconductors, 2nd edn (Oxford University Press, USA, 2009)
L.G. Aslamazov, A.I. Larkin, Soviet Solid State Phys. 10, 875 (1968)
K. Maki, Prog. Theor. Phys. 39, 897
K. Maki, Prog. Theor. Phys. 40, 193 (1968)
R.S. Thompson, Phys. Rev. B 1, 327 (1970)
L.B. Ioffe, A.I. Larkin, A.A. Varlamov, Yu. Lu, Phys. Rev. B 47, 8936 (1993)
V.V. Dorin, R.A. Klemm, A.A. Varlamov, A.I. Buzdin, D.V. Livanov, Phys. Rev. B 48, 12591 (1993)
L.G. Aslamazov, A.A. Varlamov, J. Low Temp. Phys. 38, 223 (1980)
A.I. Larkin, JETP Lett. 31, 219 (1980)
B.L. Altshuler, M.Yu. Reyzer, A.A. Varlamov, Soviet JETP 57, 1329 (1983)
J.M.B. Lopes dos Santos, E. Abrahams, Phys. Rev. B 31, 172 (1985)
I.S. Beloborodov, K.B. Efetov, Phys. Rev. Lett. 82, 3332 (1999)
I.S. Beloborodov, K.B. Efetov, A.I. Larkin, Phys. Rev. B 61, 9145 (2000)
V.M. Galitski, A.I. Larkin, Phys. Rev. Lett. 87, 087001 (2001)
M.A. Skvortsov, M. Serbin, A.A. Varlamov, V. Galitski, Phys. Rev. Lett. 102, 067001, (2009)
A. Glatz, A.A. Varlamov, V.M. Vinokur, Europhys. Lett. 94, 47005 (2011)
J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957)
J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)
Strictly speaking τ in the majority of future results should be understood as the electron transport scattering time τtr. Nevertheless, as is well known, in the case of isotropic scattering these values coincide; so for the sake of simplicity we will use hereafter the symbol τ
This particle density is defined in the (D)-dimensional space. This means that it determines the normal volume density of pairs in the 3Dcase, the density per square unit in the 2Dcase and the number of pairs per unit length in 1D. The real 3Dconcentration Ncan be defined too: N = N s (2) ∕ d, where dis the thickness of the film and \(N = {N}_{s}^{(1)}/S\), where Sis the wire cross-section
This formula is valid for the dimensionalities D = 2, 3, when the fluctuation Cooper pair has the ability to “ rotate” in the applied magnetic field and the average square of the rotation radius is < R 2 > ∼ ξ2(T). “Size” effects, important for low-dimensional samples, will be discussed later on
Z.A. Xu, et al., Nature 406, 486 (2000)
P.W. Anderson, arXiv:cond-mat/0603726.
D. Podolsky, S. Raghu, A. Vishwanath, Phys. Rev. Lett. 99, 117004 (2007)
A. Pouret, et al., Phys. Rev. Lett. 96, 176402 (2006)
I. Ussishkin, S.L. Sondhi, D.A. Huse, Phys. Rev. Lett. 89, 287001 (2002)
A. Levchenko, M. Norman, A.A. Varlamov, Phys. Rev. B 83, 020506 (R) (2011)
A.A. Varlamov, A. Kavokin, Europhys. Lett. 87, 47007 (2009)
A.A. Abrikosov, Fundamentals of the Theory of Metals(North Holland, 1988)
Hereafter \(\hslash= {k}_{\mathrm{B}} = c = 1\)
For simplicity in this subsection the magnetic field is assumed to be zero
V.V. Schmidt, in Proceedings of the 10th International Conference on Low Temperature Physics, C2, p. 205, VINITI, Moscow (1967)
T. Tsuboi, T. Suzuki, J. Phys. Soc. Jpn 42, 654 (1977)
The precise value of the effective charge e ∗ = 2ecould not be determined in the framework of the GL phenomenology. It was found in the Gor’kov’s microscopic rederivation of their equations
For a spherical particle \({H}_{\mathrm{c2(0})}^{\mathrm{sph}}(\epsilon ) = \frac{{\Phi }_{0}} {\pi d\xi }\sqrt{10\epsilon }\)
E. Bernardi, et al., Phys. Rev. B 74, 134509 (2006)
W.E. Lawrence, S. Doniach, in Proceedings of the 12th International Conference on Low Temperature Physics, ed. by E. Kanda, p.361 (Academic Press, Japan, Kyoto, 1971)
K. Yamaji, Phys. Lett. A 38, 43 (1972)
L.G. Aslamazov and A.I. Larkin, Zhurnal Eksperimentalnoi i Teoreticheskoi Fisiki 67, 647 (1973) [Soviet Phys. JETP 40, 321 (1974)]
A. Schmid, Phys. Rev. 180, 527 (1969)
H. Schmidt, Zeitschrift für Physik B 216, 336 (1968)
R.E. Prange, Phys. Rev. B 1, 2349 (1970)
B.R. Patton, V. Ambegaokar, J.W. Wilkins, Solid State Commun. 7, 1287 (1969)
J. Kurkijarvi, V. Ambegaokar, G. Eilenberger, Phys. Rev., B 5, 868 (1972)
J.P. Gollub, M.R. Beasley, R.S. Newbower, M. Tinkham, Phys. Rev. Lett. 22, 1288 (1969)
J.P. Gollub, M.R. Beasley, M. Tinkham, Phys. Rev. Lett. 25, 1646 (1970)
J.P. Gollub, M.R. Beasley, R. Callarotti, M. Tinkham, Phys. Rev. B 7, 3039 (1973)
P.A. Lee, S.R. Shenoy, Phys. Rev. Lett. 28, 1025 (1972)
S.P. Farrant, C.E. Gough, Phys. Rev. Lett. 34, 943 (1975)
W.J. Skocpol, M. Tinkham, Rep. Progress Phys. 38, 1094 (1975)
R.S. Thompson, V.Z. Kresin, Modern Phys. Lett. B 2, 1159 (1988)
K.F. Quader, E. Abrahams, Phys. Rev. B 38, 11977 (1988)
W.C. Lee, R.A. Klemm, D.C. Johnson, Phys. Rev. Lett. 63, 1012 (1989)
P. Carretta, A. Lascialfari, A. Rigamonti, A. Rosso, A.A. Varlamov, Phys. Rev. B 61, 12420 (2000)
T.M. Mishonov, E.S. Penev, Int. J. Modern Phys. 14, 3831 (2000)
A.I. Buzdin, V.V. Dorin, in Fluctuation phenomena in high temperature superconductors, ed. by M. Ausloos, A.A. Varlamov, NATO-ASI Series (Kluwer, Dordrecht, 1997)
S. Hikami, A. Fujita, A.I. Larkin, Phys. Rev. B 44, 10400 (1991)
C. Baraduc, A.I. Buzdin, J-Y. Henry, J.P. Brison, L. Puech, Phys. C 248, 138 (1995)
A. Junod, J-Y. Genoud, G. Triscone, Phys. C 294, 115 (1998)
A. Lascialfari, A. Rigamonti, P. Tedesco, A.A. Varlamov, Phys. Rev. B 65, 144523 (2002)
This term may have different origins. First of all, evidently, paraconductivity is analogous to paramagnetism and means excess conductivity. Another possible origin is an incorrect onomatopoeic translation from the Russian “paroprovodimost’ ” that means pair conductivity
A. Schmid, Physik Kondensierter Materie 5, 302 (1966)
C. Caroli, K. Maki, Phys. Rev. 159, 306 (1967)
C. Caroli, K. Maki, Phys. Rev. 159, 316 (1967)
E. Abrahams, T. Tsuneto, Phys. Rev. 152, 416 (1966)
J.W.F. Woo, E. Abrahams, Phys. Rev. 169, 407 (1968)
C. Di Castro, W. Young, Il Nuovo Cimento B 62, 273 (1969)
S. Ullah, A.T. Dorsey, Phys. Rev. B 44, 262 (1991)
S. Ullah, A.T. Dorsey, Phys. Rev. Lett. 65, 2066 (1990)
L.P. Gor’kov, G.M. Eliashberg, Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 54, 612 (1968) [Soviet Phys. JETP 27, 328 (1968)]
An equation of this type was considered by Landau and Khalatnikov in connection with the study of superfluid helium dynamics in early 1950s
Account for electron- hole asymmetry leads to the appearance of the imaginary part of γGLproportional to the derivative \(\partial \ln (\rho {v}^{2}\tau )/\partial E{\vert }_{{E}_{F}} \sim \mathcal{O}(1/{E}_{F})\). This is important for such phenomena as fluctuation Hall effect or fluctuation thermopower and, having in mind the writing of the most general formula, we will suppose \({\gamma }_{\mathrm{GL}} = \pi \alpha /8 + i\mathrm{Im} {\gamma }_{\mathrm{GL}}\), where necessary
L.D. Landau, E.M. Lifshitz, Quantum Mechanics. Course of Theoretical Physics,vol. 3 (Pergamon Press, Oxford, 1978)
L. Reggiani, R. Vaglio, A.A. Varlamov, Phys. Rev. B 44, 9541 (1991)
M. Ausloos, Ch. Laurent, Phys. Rev. B 37, 611 (1988)
P.P. Frietas, C.C. Tsuei, T.S. Plaskett, Phys. Rev. B 36, 833 (1987)
M. Hikita, M. Suzuki, Phys. Rev. B 41, 834 (1990)
M. Akinaga, D. Abukay, L. Rinderer, Modern Phys. Lett. 2, 891 (1988)
A. Poddar, P. Mandal, A.N. Das, B. Ghosh, P. Choudhury, Phys. C 159, 231 (1989)
D.H. Kim, A.M. Goldman, J.H. Kang, K.E. Gray, R.T. Kampwirth, Phys. Rev. B 39, 12275 (1989)
G. Balestrino, A. Nigro, R. Vaglio, Phys. Rev. B 39, 12264 (1989)
G. Kumm, K. Winzer, Phys. B 165-166, 1361 (1990)
M.R. Cimberle, C. Ferdeghini, D. Marrè, M. Putti, S. Siri, F. Federici, A.A. Varlamov, Phys. Rev. B 55, R14745 (1997)
G. Balestrino, E. Milani, A.A. Varlamov, Phys. C 210, 386 (1993)
I.V. Lerner, A.A. Varlamov, V.M. Vinokur, Phys. Rev. Lett. 100, 117003, (2008)
B. Leridon, J. Vanacken, T. Wambecq, V. Moshchalkov, Phys. Rev. B 76, 012503 (2007)
V.F. Gantmakher, S.N. Ermolov, G.E. Tsydynzhapov, A.A. Zhukov, T.I. Baturina, JETP Lett. 77, 498 (2003)
Acknowledgements
The author acknowledges valuable discussions and collaborations with G. Balestrino, A. Glatz, B. Leridon, A. Rigamonti, V. Vinokur and also support of the MIUR under the project PRIN 2008.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Varlamov, A.A. (2011). “Fluctuoscopy” of Superconductors. In: Sidorenko, A. (eds) Fundamentals of Superconducting Nanoelectronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20158-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-20158-5_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20157-8
Online ISBN: 978-3-642-20158-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)