Superconductivity - Overview Last week (20-21.11.2017) This week (27-28.11.2017) Classification of Superconductors - Theory Summary - Josephson Effect - Paraconductivity Reading tasks Kittel: Chapter: Superconductivity Reading tasks Kittel: Chapter: Superconductivity Next - Next week (4-5.11.2017) 13.11 Guest Lecture: Marta Gibert Oxide electronics 14.11 Guest Lecture: Christof Aegerter Multiple scattering of light
Superconductivity Course strategy This course -- Experimental phenomenology -- London Theory -- Ginzburg-Landau Theory Condensed Matter Theory Course Spring 2018 Prof. Titus Neupert Bardeen-Cooper-Schrieffer (BCS) theory
Summary From Kittel London Theory Penetration depth λ m λ = μ 1 n 3 e 5 Type I1 superconductor n s = super electrons Ginzburg-Landau Theory 0 Penetration depth λ Coherence length ξ Length scale for magnetic field Length scale for variation of superconducting order parameter ψ
Summary From Kittel Type I1 superconductor Ginzburg-Landau Theory Penetration depth λ Length scale for magnetic field 0 Coherence length ξ Length scale for variation of superconducting order parameter ψ
Superconductivity Classification Low-T c Superc. T c < 30 K High-T c Superc. T c > 30 K Type 1 Type 2 λ < ξ λ > ξ Clean Superconductor Electron mean free path l ξ Conventional BCS theory Dirty Superconductor Electron mean free path l ξ Unconventional Beyond BCS theory
Type II Superconductors Vortex lattice vs Vortex Liquid Vortex Solid Resistance milliohms 200 180 160 140 120 100 80 60 40 20 https://journals.aps.org/prb/p Magnetic Field Tesla df/10.1103/physrevb.86.1745 30 01 Vortex Melting Field Tesla 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 25 20 15 10 5 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Temperature Kelvin https://journals.aps.org/prb/pdf/10.1103/physrevb.86.174501
Superconducting Magnets Ideal: Large upper critical field Hc2 Large upper critical current Strong vortex pinning (avoidance of vortex liquid)
Isotope effect The smoking gun experiment T C T E M GH α 0.5 T D Debye temperature M = atomic mass A. Bussmann-Holder and H. Keller Journal of Physics: Condensed Matter, Volume 24, Number 23 http://ee.sharif.edu/~varahram/hts-course/coop.htm
BCS-Theory of Superconductivity Bardeen Cooper Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) ψ = Δ e GOP = Pairing Amplitude φ = phase
SC Gap & Transition Temperature 0 exp (T C ) 0 k a T C 0 1/T C 0 ln (T C )
Summary: Theory Superconductivity London Theory Ginzburg-Landau Theory Penetration depth λ m λ = μ 1 n 3 e 5 n s = number of super electrons Penetration depth λ Coherence length ξ H C5 = Φ 1 2πξ 5 Length scale for magnetic field Length scale for variation of superconducting order parameter ψ BCS Theory: Key Results Macroscopic Wavefunction: ψ = Δ e GOP 2 0 = 3.5k a T C ξ = ħv j πδ super electrons are Cooper Pairs
BCS Theory Predictive Power BCS Theory: Key Results Macroscopic Wavefunction: ψ = Δ e GOP 2 0 = 3.5k a T C ξ = ħv j πδ super electrons are Cooper Pairs T C = 1.13 ħω E exp(-1/ζ) ζ = Electron Phonon coupling constant 2 x [DOS E F ] ω E = Debye Frequency
Two-band superconductors Example of multi-sheet Fermi surface doi:10.1209/0295-5075/82/47011
Josephson Effect https://mappingignorance.org/2015/04/30/ho w-to-measure-tiny-temperature-differencesusing-a-josephson-junction/
Superconducting Quantum Interference Device (SQUID) https://www.asme.org/engineering-topics/articles/ bioengineering/a-mini-sensor-for-brain-scanning http://hyperphysics.phyastr.gsu.edu/hbase/solids/squid.html
Published in: Junyi Ge; Shixun Cao; Shujuan Yuan; Baojuan Kang; Jincang Zhang; Journal of Applied Physics 2010, 108, DOI: 10.1063/1.3481096 Paraconductivity
Paraconductivity SUPERCONDUCTING FLUCTUATIONS IN A THIN NbN... FIG. 2. (a) Hall resistivity PHYSICAL ρ xy isotherms REVIEW for T B T 95,224501(2017) c,15.3and 20.0 K. The inset displays the high-field linear field dependence of ρ xy.(b)thenonlinearhallresistance ρ xy obtained by subtracting (a) the linear high-field dependence for each of the respective isotherms. Solid lines are guides to the eye. 2 Institut für Mikro- und Nanoelektronische Systeme (IMS), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany We present a comprehensive study of how superconducting fluctuations in the normal state contribute to the conductivity tensor in a thin (119 Å) film of NbN. It is shown how these fluctuations drive a sign change in the Hall coefficient R H for low magnetic fields near the superconducting transition. The scaling behaviors as a function of distance to the transition ϵ = ln(t/t c ) of the longitudinal (σ xx )andtransverse(σ xy )conductivity are found to be consistent with Gaussian fluctuation theory. Moreover, excellent quantitative agreement between theory and experiment is obtained without any adjustable parameters. Our experimental results thus provide a FIG. 1. In-plane resistivity of a 119 Å thin NbN film as a function of temperature for magnetic fields in steps of 1 T. The magnetic field is applied perpendicular to the film plane. Solid lines are guides to thedaniel eye. The upper Destraz critical et fieldal., B c2 (T ) (shown in the inset) is defined by PRB the point with the steepest slope on the respective transitions. The case study 2017 of the conductivity tensor originating from short-lived Cooper pairs. red line in the inset is a linear fit used to evaluate B c2 (0) see the maindoi: text 10.1103/PhysRevB.95.224501 for further explanation. I. INTRODUCTION served as a model system for studies of out-of-equilibrium 224501-2 transition temperature where the coherence length ξ and the penetration depth [33] diverge,thesuperconductinglength scales are generally larger than the film thickness. Our system thus displays two-dimensional superconductivity whereas the electrons sense a three-dimensional environment due to their short mean free path. PHYSICAL REVIEW B 95,224501(2017) Hall effect isotherms taken near the superconducting transition T c display a sign change from negative to positive Superconducting fluctuations in a thin NbN film probed by the values Hall effect at low magnetic fields [Fig. 2(a)]. This sign change is observed in a narrow temperature window of 0.3 K above Daniel Destraz, 1,* Konstantin Ilin, 2 Michael Siegel, 2 Andreas Schilling, 1 and Johan Chang (a) T c.deviationsfromlinearlow-fielddependenceare,however, 1 1 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland observed up to 1 Kabovethesuperconductingtransition. (Received 14 December 2016; published 2 June 2017) We thus analyze the isotherms in terms of a negative normal state contribution ρ xy B and a positive response with a nonlinear field dependence. To investigate the positive response, the negative linear normal state component is subtracted, i.e., ρ xy = ρ xy ρxy n.asshowninfig.2(b), thepositive Hall effect response ρ xy decreases rapidly with increasing temperature. In fact, it vanishes below the detection limit about 1KaboveT c.
LITERATURE CLUB - II (1) 2015 Discoveries of superconductivity Nature 525, 73 76 (2015) 203 K Superconductivity in HS 2 Nature Materials 14, 285 289 (2015) 103 K Superc. in FeSe (2) Anti-ferromagnetic excitations Phys. Rev. Lett. 108, 177003 (2012) in Sr 2 IrO 4 (RIXS) Phys. Rev. Lett. 105, 247001 (2010) in La 2 CuO 4 (Neutron scattering) (3) Unconventional superconductivity Science 336, 1554-1557 (2012) Penetration depth @ QCP Nature Physics 11, 17 20 (2015) SC fluctuations in URu 2 Si 2 (4) Ferromagnetism & Skymions Science 323, 915-919 (2009) Skymions in reciprocal space (MnSi) Nature 465, 901 904 (17 June 2010) Skymions in real space (Fe 0.5 Co 0.5 Si)