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Measurements on Corbino Discs of type-II superconductors
PHYSICS
Volume 26A. number 2
LETTERS
is known to have as only solutions [7,9] (5)
%o = bgho ,
if the inverse of map Mis unique up to uniform scale transformations of gxo. Substitution of eq. (5) in eq. (3) shows that the scalar b must be a constant. Hence, if the map M is one to one up to uniform scale transformations of g,x, then the free Yang-Mills equations is equivalent to the set of free Einstein equations with all cosmological constants. The condition that the map M-l gives rise to a Riemannian event space demands that the holonomy group of the FK(xA) operating on Dirac spin space or on the Lie algebra space of the local Lorentz transformations be the Lorentz group or a subgroup thereof. The condition of uniqueness of the inverse of map M up to constant scale transformations is known to be satisfied except for a set of cases of zero measure [7.9],
18 &cember 1967
which includes V4 geometries with a large amount of symmetry, such as the Schwarzschild metric
[91. References R.Utiyama, Phys. Rev. 101 (1956) 1597. 2. T. W.B.Kibble, J. Math. Phys. 2 (1961) 212. 1.
3. S.I.FickIer, (1961); H.G.Loos,
Ph. D. Thesis,
Syracuse University
Nucl. Phys. 72 (1965) 677; Ann. Phys.
(N.Y.) 36 (1966) 486.
4. C. N. Yang and R. L.Mills,
Phys. Rev. 96 (1954) 191.
We call any gauge field with field eq. (1) a free Yang-Mills field, regardless of Lie-algebra properties. 5. Y. Ne’eman, Nucl. Phys. 26 (1961) 222. 6. E.Schr&iinger, Sitz Ber. preuss. Akad. Wiss. Physik-Math.KL XI (1932) 105.
7. H.G.Loos, Ann. Phys. (N.Y.) 25 (1963) 91. 6. R.P.Treat, Phys. Rev. Letters 12 (1964) 407. 9. R. P. Treat, Ph. D. Thesis, University of California, Riverside (1967).
*****
MEASUREMENTS
ON CORBINO
DISCS
OF
TYPE-II
SUPERCONDUCTORS
J.B.McKINNON and A.C.ROSE-INNES University
of Manchester
Institute of Science and Technology,
Received
13 November
England
1967
We report some measurements on specimens of type-II superconductors in the form of “Corbino Discs”. It is shown that this is a useful configuration to observe critical currents and flux flow voltages without the complication of surface superconductivity.
Measurements of the bulk current-carrying capacity of the usual strip or rod-shaped samples are complicated by the surface superconductivity which exists where the surface is parallel to the applied magnetic field. Consider, however, a disc specimen situated in a magnetic field perpendicular to its plane and suppose that current is fed from an electrode at the centre to another encircling the rim (“Corbino disc”, see inset fig. 1). Between the electrodes there is no surface of the specimen parallel to the applied field and hence nor surface contribution to the supercurrent. We have measured current transport proper ties of Corbino Disc specimens of pbS4-In16 and Tatjo-Nbgg approximately 2.5 cm in diameter and 0.03 cm thick. Four groups of four spring-loaded 92
potential probes arranged in a cross are pressed against the specimens, so that the groups lie along radii. Voltages between any pair can be measured. Fig. 1 shows the voltages measured between pairs of probes along one radius of a disc of Pb-In alloy as the current through the disc was varied. The disc had been driven into the mixed state by a magnetic field applied perpendicular to its plane. The current-voltage characteristics appear to be of the normal flux flow type. There can be no net radial component of fluxon motion because fluxons cannot be created at the centre, so the fluxons must move in closed paths, ideally circles, about the centre. The force on a fluxon should be F = j(r) %, where j(v) is the current density at radius Y.
Volume
26A, number 2
PHYSICS
LETTERS
18 December
Pb-In Disc 1. 4.2OK. +-Corbino Disc -+-After Cutting Slot
!3p~~inm Fig. 1. Flux flow voltages
Current measured
on a Corbino
0 L h-s_*
(a) I loo0 Magnetic
Disc.
If the thickness of the disc is d, j(r) = i/2nrd, where i is the current passed through the disc. We find that for a given strength of applied field, a voltage is first detected between any pair of probes at a current i, which is proportional, within 5’j& to the radial distance of the inner of the two probes from the centre of the disc. This is consistent with a flux flow region spreading out from the centre to the outer electrode as the current is increased. Note that at a current such as ia, we can achieve the situation where flux flow is occuring in the centre of the specimen while the periphery is still resistanceless. Furthermore, the voltages we observe are consistent with the flux lattice being non rigid. Since j(r) is inversely proportional to r, this implies that the fluxons further from the centre are moving at a slower rate so that the fluxon lattice is continually shearing. On the scale of our experiment, where the voltage probes are 2.5 mm apart, we detect no rigidity of the fluxon lattice even for fields close to Hc2. Fig. 2 shows the critical current at which a voltage [criterion 4@V,,cm] appears between an inner pair of potential probes such as Nl,N2, as a function of applied magnetic field. The solid curve refers to the critical current measured for
Fig. 2. Effect
I moo FdcI
1967
b
I 3ooo
1 J
Oe.
of a slot on the current of a Corbino Disc.
carrying
capacity
a disc of Pbg4-InI5. The absence of any surface superconductivity can be observed, since at Hc2 the critical current falls precipitously, and above this field there is no measurable resistanceless current. The broken curve shows the critical current for the same disc after a thin radial slot had been cut from electrode to electrode, as shown on the figure. A small critical current is now observed above Hc2, presumably flowing along the edges of the slot. This current could be eliminated by copper-plating the slot. The critical current has also been increased below Hc2. Other specimens gave similar results. Our experiments show that the Corbino Disc geometry is a very useful configuration for studying flux flow and critical currents in superconductors since surface superconductivity and edge effects are entirely eliminated.
One of us (JBM) is grateful to the Mullard Company for a Fellowship.
93
Volume 26A. number 2
LETTERS
is known to have as only solutions [7,9] (5)
%o = bgho ,
if the inverse of map Mis unique up to uniform scale transformations of gxo. Substitution of eq. (5) in eq. (3) shows that the scalar b must be a constant. Hence, if the map M is one to one up to uniform scale transformations of g,x, then the free Yang-Mills equations is equivalent to the set of free Einstein equations with all cosmological constants. The condition that the map M-l gives rise to a Riemannian event space demands that the holonomy group of the FK(xA) operating on Dirac spin space or on the Lie algebra space of the local Lorentz transformations be the Lorentz group or a subgroup thereof. The condition of uniqueness of the inverse of map M up to constant scale transformations is known to be satisfied except for a set of cases of zero measure [7.9],
18 &cember 1967
which includes V4 geometries with a large amount of symmetry, such as the Schwarzschild metric
[91. References R.Utiyama, Phys. Rev. 101 (1956) 1597. 2. T. W.B.Kibble, J. Math. Phys. 2 (1961) 212. 1.
3. S.I.FickIer, (1961); H.G.Loos,
Ph. D. Thesis,
Syracuse University
Nucl. Phys. 72 (1965) 677; Ann. Phys.
(N.Y.) 36 (1966) 486.
4. C. N. Yang and R. L.Mills,
Phys. Rev. 96 (1954) 191.
We call any gauge field with field eq. (1) a free Yang-Mills field, regardless of Lie-algebra properties. 5. Y. Ne’eman, Nucl. Phys. 26 (1961) 222. 6. E.Schr&iinger, Sitz Ber. preuss. Akad. Wiss. Physik-Math.KL XI (1932) 105.
7. H.G.Loos, Ann. Phys. (N.Y.) 25 (1963) 91. 6. R.P.Treat, Phys. Rev. Letters 12 (1964) 407. 9. R. P. Treat, Ph. D. Thesis, University of California, Riverside (1967).
*****
MEASUREMENTS
ON CORBINO
DISCS
OF
TYPE-II
SUPERCONDUCTORS
J.B.McKINNON and A.C.ROSE-INNES University
of Manchester
Institute of Science and Technology,
Received
13 November
England
1967
We report some measurements on specimens of type-II superconductors in the form of “Corbino Discs”. It is shown that this is a useful configuration to observe critical currents and flux flow voltages without the complication of surface superconductivity.
Measurements of the bulk current-carrying capacity of the usual strip or rod-shaped samples are complicated by the surface superconductivity which exists where the surface is parallel to the applied magnetic field. Consider, however, a disc specimen situated in a magnetic field perpendicular to its plane and suppose that current is fed from an electrode at the centre to another encircling the rim (“Corbino disc”, see inset fig. 1). Between the electrodes there is no surface of the specimen parallel to the applied field and hence nor surface contribution to the supercurrent. We have measured current transport proper ties of Corbino Disc specimens of pbS4-In16 and Tatjo-Nbgg approximately 2.5 cm in diameter and 0.03 cm thick. Four groups of four spring-loaded 92
potential probes arranged in a cross are pressed against the specimens, so that the groups lie along radii. Voltages between any pair can be measured. Fig. 1 shows the voltages measured between pairs of probes along one radius of a disc of Pb-In alloy as the current through the disc was varied. The disc had been driven into the mixed state by a magnetic field applied perpendicular to its plane. The current-voltage characteristics appear to be of the normal flux flow type. There can be no net radial component of fluxon motion because fluxons cannot be created at the centre, so the fluxons must move in closed paths, ideally circles, about the centre. The force on a fluxon should be F = j(r) %, where j(v) is the current density at radius Y.
Volume
26A, number 2
PHYSICS
LETTERS
18 December
Pb-In Disc 1. 4.2OK. +-Corbino Disc -+-After Cutting Slot
!3p~~inm Fig. 1. Flux flow voltages
Current measured
on a Corbino
0 L h-s_*
(a) I loo0 Magnetic
Disc.
If the thickness of the disc is d, j(r) = i/2nrd, where i is the current passed through the disc. We find that for a given strength of applied field, a voltage is first detected between any pair of probes at a current i, which is proportional, within 5’j& to the radial distance of the inner of the two probes from the centre of the disc. This is consistent with a flux flow region spreading out from the centre to the outer electrode as the current is increased. Note that at a current such as ia, we can achieve the situation where flux flow is occuring in the centre of the specimen while the periphery is still resistanceless. Furthermore, the voltages we observe are consistent with the flux lattice being non rigid. Since j(r) is inversely proportional to r, this implies that the fluxons further from the centre are moving at a slower rate so that the fluxon lattice is continually shearing. On the scale of our experiment, where the voltage probes are 2.5 mm apart, we detect no rigidity of the fluxon lattice even for fields close to Hc2. Fig. 2 shows the critical current at which a voltage [criterion 4@V,,cm] appears between an inner pair of potential probes such as Nl,N2, as a function of applied magnetic field. The solid curve refers to the critical current measured for
Fig. 2. Effect
I moo FdcI
1967
b
I 3ooo
1 J
Oe.
of a slot on the current of a Corbino Disc.
carrying
capacity
a disc of Pbg4-InI5. The absence of any surface superconductivity can be observed, since at Hc2 the critical current falls precipitously, and above this field there is no measurable resistanceless current. The broken curve shows the critical current for the same disc after a thin radial slot had been cut from electrode to electrode, as shown on the figure. A small critical current is now observed above Hc2, presumably flowing along the edges of the slot. This current could be eliminated by copper-plating the slot. The critical current has also been increased below Hc2. Other specimens gave similar results. Our experiments show that the Corbino Disc geometry is a very useful configuration for studying flux flow and critical currents in superconductors since surface superconductivity and edge effects are entirely eliminated.
One of us (JBM) is grateful to the Mullard Company for a Fellowship.
93