Title: LARGE Vortices in YBCO and Other TypeII Superconductors
1LARGE Vortices in YBCO and Other Type-II
Superconductors
?
2Collaborators
Simon Fraser Fergal Callaghan Mikko
Laulajainen David Broun
Sherbrooke Louis Taillefer Etienne Boaknin (Yale)
UBC Jess Brewer Rob Kiefl Doug Bonn Walter
Hardy Roger Miller (U. Penn)
McMaster Jules Carbotte
Okayama Kazushige Machida
3Structure of Magnetic Vortices
Each vortex carries one quantum of flux ?0 hc/2e
?
Normal
Supercurrents
Superconducting
B(r)B0e-r/??
Hc2 ?0/2??2
4Why are the vortices so large at low fields in
YBCO?
J.E. Sonier et al. PRL 83 4156 (1999)
5Muon Spin Rotation
? ??Blocal
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8The muon spin precession signal (in the time
domain) is fit assuming the vortex lattice is
adequately described by the following analytical
Ginzburg-Landau field profile
B(r)B0(1-b4) ? e-iGruK1(u)/?ab2G2
u22?ab2G2(1b4)1-2b(1-b)2
where,
G
bB0/Bc2
Thus, ?ab and ?ab are simultaneously determined.
9YBa2Cu3O6.60 ?ab 1699 ? 5 Å YBa2Cu3O6.95 ?ab
1125 ? 3 Å
J.E. Sonier et al. PRL 72, 744 (1994) PRL 79,
2875 (1997) PRL 83 4156 (1999)
Absolute value of ?ab determined by ?SR studies
of single-crystal YBCO recently verified by
zero-field ESR. T. Pereg-Barnea et al.
cond-mat/0311555
10The supercurrent density J(r) at a vortex site
rises to its maximum value over a distance which
is consistent with the sharp rise of the pair
potential ?(r) in the same region
vortex core size r0
Distance from vortex core center
11Vortex Squeezing superposition of
supercurrent density profiles from individual
vortices
12Field dependence of the vortex core size in NbSe2
?
J.E. Sonier et al. PRL 79, 1742 (1997)
13Vortex Electronic Structure
Beyond GL theory
GL theory assumes that the order parameter varies
slowly in space. At low temperatures where the
gap parameter ? varies rapidly on the scale of
?(T 0), GL theory is no longer accurate. A
quantum mechanical treatment of the vortex
lattice requires solutions of the Bogoliubov-de
Gennes equations.
Caroli, de Gennes Matricon Physics Letters 9,
307 (1964)
14First observation of bound core states
STM on 2H-NbSe2
H.F. Hess et al. PRL 65, 1820 (1990)
core center
outside core
15Effect of Bound Core States on Vortex Structure
Thermal population of higher energy core
states leads to an expansion of the core
radius with increasing temperature, because
the higher energy bound states extend outwards to
larger radii.
L. Kramer W. Pesch, Z. Phys. 269, 59 (1974)
?0
?1 ? ?0 T/Tc
?1 is slope of ?(r) at vortex core center
?1
16Temperature dependence of the vortex core size in
an s-wave superconductor
Hayashi et al., PRL 80, 2921 (1998)
17Kramer-Pesch effect in s-wave superconductor
2H-NbSe2
J.E. Sonier et al., PRL 79, 1742 (1997) R.I.
Miller et al., PRL 85, 1540 (2000)
18Conduction by Electrons in Solids
Intervortex Quasiparticle Transfer in a
Superconductor
19Comparsion to thermal conductivity measurements
of E. Boaknin et al. PRL 90, 117003 (2003)
20Field Dependence of the Vortex Core SizeThe
delocalization of quasiparticle core states in an
interacting lattice of vortices is predicted to
modify the slope of ?(r) and the position of the
peak of J(r) along the direction of neighbouring
vortices.
Ichioka, Hasegawa Machida, PRB 59, 184 (1999)
PRB 59, 8902 (1999).
21Field dependence of the vortex core size in a
conventional s-wave superconductor
Hc2 3.5 kOe
J.E. Sonier et al. PRL 79, 1742 (1997)
22V3Si STM images
Sosolik et al. PRB 68, 140503 (2003)
23J.E. Sonier et al. to appear in PRL
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26Square VL
Hexagonal VL
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28NbSe2 Multiband Superconductivity
NbSe2 is a multiband superconductor characterized
by two superconducting gaps (similar to MgB2), a
small energy gap ?S and a large energy gap ?L ? 3
?S on distinct parts of the Fermi surface. T.
Yokoya et al. Science 294, 2518 (2001)
29Nakai, Ichioka Machida, J. Phys. Soc. Jpn. 71,
23 (2002)
30Field dependence of the vortex core size in a
conventional s-wave superconductor
Hc2 3.5 kOe
J.E. Sonier et al. PRL 79, 1742 (1997)
31Tunneling Conductance Subgap Structure in YBCO
I. Maggio-Aprile et al. PRL 75, 2754 (1995)
J.M. Valles et al. PRB 44, 11986 (1991)
?CuO ? 5.5 meV ?CuO2 ? 20 meV
32W.A. Atkinson J.P. Carbotte PRB 52, 10601
(1995) Proximity Effect ? small gap in the CuO
chains induced by proximity
to the superconducting CuO2 planes
through coherent
single-electron tunneling T. Xiang J.M.
Wheatley PRL 76, 134 (1996) coupling of chains
and planes through Josephson-like pair tunneling
Energy gap with nodes on the chain Fermi
surface (i.e. gap with 2D character)
33N.D. Whelan J.P. Carbotte PRB 62, 15221 (2000)
Chain Fermi Surface
34Vortex Lattice Transformation in YBCO
- Perfect hexagonal VL
- ? ? ? 60?
- (not observed)
- Perfect square VL
- ? 90? ? ? 45?
- (observed at high field)
S.P. Brown et al. PRL 92, 067004 (2004)
35Possible Sources of Square Vortex Lattice
Formation
Energy gap anisotropy (d-wave) increasing
importance of anisotropic vortex cores at
high fields Fermi surface/velocity
anisotropy couples to vortex lattice
Dynamical stripes or charge density waves
36?S/?L 4.6 0.8 ?CuO2/?CuO ? 20 meV / 5.5 meV
3.7
37For a magnetic field applied along the c-axis
direction, chain-plane coupling likely leads to
vortex cores that are elongated in the
b-direction
Cross-section of vortex core at low fields
Cross-section of vortex core at high fields (?
4.5 T)
Note ?SR measures ?ab, not ?a and ?b
38Summary
Large vortex cores in YBCO apparently due to
chain superconductivity A theoretical
description of vortices that includes
superconductivity on both the chain and plane
layers is needed
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40Thermal Conductivity M. Chiao et al. PRL 82,
2943 (1999)
R. Hill et al. PRL 92, 027001 (2004)