Antivortex motion in the mixed state of 2-D superconductors

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Physica C 235-240 (1994) 1417-1418

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PHYSICA@

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Antivortex motion in the mixed state of 2-D superconductors M, Viret

Department of Pure and ApDlied Physics, Trinity College, Dublin 2, Ireland. The sign reversal of the Hall voltage in the mixed state of high temperature superconductors is explained by the motion of antivortices in bundles ot the vortex lattice. In the frame of the KosterlitzThouless mechanism of vortex-antivortex pair generation in 2-D superconductors, it is shown that the antivortex moves with a much larger Hall angle than other vortices.

1. INTRODUCTION The unusual properties observed in the mixed state of high-temperature superconductors have been attributed to their layered structures, high transition temperatures and short coherence lengths. In particular, the Hall effect of copper oxide superconductors presents an unusual sign reversal at sufficiently low magnetic fields just below Tc [1]. This behaviour is related to vortex motion under the action of the Lorentz force and is indicative of a general property of type II layered superconductors. In order to explain this sign reversal of the Hall voltage, the classical models of current driven vortex motion, i.e. BardeenStephen (BS) [2] and Nozi~res-Vinen (NV) [3] models, had to be modified. Several attempts to find a way of predicting a backflow component of individual vortices have been published [4]. They are all based on the introduction of a combined BS and NV friction force, which is not physically justified. We recently presented data supporting a model of moving vortex bundles in which shortlived defects (like antivortices) could induce a negative component in the Hall voltage of Bi2Sr2CaCu20 e superconductors [1]. In twodimensional systems, the Kosterlitz-Thouless mechanism of vortex-antivortex pair creation takes place which can lead to melting of the vortex lattice. We argued that pair breaking generates different motion types for the vortex and the antivortex. In fact, it was shown that the vortex compels the lattice to rearrange without creating a phase slip (i. e. in a non-dissipating manner) although the antivortex, by jumping toward a vortex lattice site, contributes to the establishement of the totai voltage accross the 092i-4534/94/5(17.00 © 1994 - Flscvier Science 1].V, All fights reserved. SSD! (7)21-4534(94)01272-5

sample [5]. It is argued here that the Hall angle generated by such a motion is much larger than that associated with simple vortex motion. We base our calculation on the classical BS and NV models both of which, in the case of antivortex motion, predict a negative contribution to the Hall effect (the normal state Hall voltage beeing positive in these compounds). However, a dissipation mechanism dominated by antivorte'<, movements would fail to predict correctly the positive sign measured for the Nernst effect. Also, dissociation of vortex-antivortex pairs is known to induce deDinning of the vortex lattice, the motion of which contributes positively to the Hall voltage. The total Hall effect is therefore the result of the two opposite contributions. We show here that theHall angle for antivortices is much larger than that for vortices, therefore enhancing their contribution toward a negative Hall effect while only marginally affecting the total resistivity. 2. RESULTS AND DISCUSSION During pair breaking the lattice rearranges itself to assimilate the pair and only those antivortices hav=ng enough energy to leave their pair partner and jump to another vortex site generate dissipation. Sy neglecting the effect of the local vortex la~ice deformation due to the antivortex, we estimated the energy barrier to be:

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Iv/, Viret/Physica C 235-240 (1994) 1417-1418

where d = coherence length of a vortex along the field, ~,ab = penetration depth in the a,b plane, P, = coherence length in the a,b plane, and B = applied field. Once the antivortex is completely separated from its pair companion, it finds itself in two current circulations, created by the vortex lattice and the applied electric field. The average antivortex Hall angle can be estimated in the frame of a very simple model in which the vortex lattice current circulation has circular symetry and is constant (figure 1). The effects of this crude simplification on the estimated Hall angle are briefly discussed below. In order not to distinguish between the BS and NV models, we consider for the calculation that the antivortex just moves at an angle 0TH to the Lorentz force (the two models disagreeing only in the field and temperature dependence of this angle). We can then write for the antivortex line velocity, v, : VL = K [ (VvLCOS(OAv - 0TH ) + VTCOS(0TH) )er (VvLSin(0AV - erR)- VTSin(eTH))¢9 ] where VVL is the current circulation due to the vortex lattice, VT the transport current and K a constant, er and ee are orthogonal unit vectors in polar coordinates. The angular dependence of the flux line velocity depends on the initial conditions, but we can neglect it for the cases of interest corresponding to a pair being given just the energy U necessary to break itself (a much smaller number have higher energies since the separation process is thermally activated). This approximation also allows us to be in the regime where the BS and NV models are valid i.e. constant velocity for the flux line. We then find for 0AV: sin(OAv- OTH) = VVL sin(OTH) vT VVL/VT corresponds to the ratio of the force exerted by the vortex lattice to that due to the transport current. The former force can be estimated by considering that its work on a distance ao/2 (ao is the vortex lattice spacing) corresponds to the energy U, and the latter is simply the Lorentz force due to the applied current density J. By taking typical experimental conditions of current density of the order of 100A/cm 2 and a magnetic field of 1 T, one obtains a ratio of the order of 100.

I YU,. . . . . . I

I Figure 1: Schematic of the current circulations applied to the antivortex for the calculation of its Hall angle. VVL,the vortex lattice circulation, has circular symetn/and VT for the applied current is along the x axis. We therefore demonstrated, in an order of magnitude calculation, that the Hall angle for antivortex motion is much larger than that for vortex motion. Although the calculation is very simple, the main approximation, namely the circular character of the vortex lattice current circulation, can be justified, hi a more realistic model where this potential would have an hexagonal symetry, a form of "guided motion" would have to be considered. In fact, its effect would be to multiply the ratio found here by a coefficient of the order of 0.25 (if we consider the average guided motion angle to be 30").

REFERENCES 1. M Viret and J M D Coey, Physical Review B49 (1994), 5, 3457. 2. J Bardeen and M J Stephen, Phys. Rev. A140, 1197 (1965). 3. P Nozieres and W F Vinen, Philos. Mag. 14, 667 (1966). 4. S J Hagen, C J Lobb, R L Green, M G Forrester, J Talvacchio, Phys. Rev. B42, 6777. 5. H J Jensen, P Minnhagen, E Sonin and H Weber, 1992, Europhys. Lett., 20, 463.