Sign change of the flux flow Hall effect in HTSC

Physica C 235-240 (1994)3127-3128 North-Holland

PHYS~CA

Sign Change of the F l u x Flow Hall Effect in H T S C M. V. Feigel'man a, V. B. Geshkenbein ",~,c, A. I. Larkin a'*'c, and V. M. Vinokur d aLandau Institute for Theoretical Physics, 117940 Moscow, Russia, ~Weizmann Insitute of Science, 76100 Rehovot, Israel, ~Theoretische Physik, ETH-HSnggerberg, 8093 Zfirich, Switzerland, dArgonne National Laboratory, Argonne, Illinois 60439, USA. A novel mechanism for the sign change of the Hall effect in flux flow region is proposed. The di~erence 6 . between the electron density at the center of the vortex core and that far outside the vortex causes the additional contribution to the Hall conductivity 6u=~ = -6nec/B. This contribution can be bigger than the conventional one in the dirty case A(T)7" < 1. If the electron density inside the core exceeds the electron density outside the core the double sign change may occur as a function of temperature and magnetic field.

A sign change of the Hall effect in the mixed state of H T S C is the most puzzling and controversal phenomenon in physics of magnetic propertics of these materials [1]. Inspite of the numerous a t t e m p s to explain this anomaly the origin of the Hall resistivity sign reversal remains unclear. C o m p a r i n g experimental d a t a for different materials including the convential superconductors Hagen et al. [1] argued that the sign reversal is the intrinsic property of the vortex motion and occurs in the range of parameters where the transport m e a n free p a t h 1 becomes of the order of the vortex core size ~. In the present paper we propose an explanation of the Hall resistivity sign reveral. W e show that the sign change m a y follow from the difference 6n between the electron density at the center of the vortex core and the density far outside the core. To understand the basic physics we will consider an oversimplified model of the fully normal core with a sharp boundary at a radius rc with the superconductive material [2,3]. W e denote the vortex velocity in the laboratory frame and that of the normal carriers inside the core as vL and vc respectively. W h e n the vortex moves a force acting on the normal electrons inside the

core

fo

= e~o x (v~

-

vo)/2~

arises [3,4].

This force can be viewed as an electromagnetic force e E due to the electric field inside the core [2], but actualy it does not depends upon charge e@o/XC = h and exists also in neutral superfiuid. That is also w h y it depends on the relative ve-

locity of the vortex and the normal excitations v~ - vc. This force accelerates normal electrons. Due to the impurity scattering the m o m e n t u m gained by the normal excitations from the condensate is transfered to the lattice and the velocity vc in the steady state is determined from the relation vc = fcr/rn,(1" and m are the transport time and the effective mass respectively. This gives [3] ~OoVZ × (v L - re) = re,

(I)

here we introduced ~oo = h/2r~m ~_ A2/hE/, and z is the unit vector along the vortex. Solving this equation one gets Wor (taoV) 2 •. x vL + 1 + (Wor) 2 VL v, -- 1 + (COor)~

(2)

If the carrier density (no) inside the core is equal to that (noo) outside the core, than noevc is equal to the transport current Jz [2,3] and the above equation coinsides with the result of the microscopic calculations [5]. If, however, no ~ noo than noevc can not be equal to the jr. D u e to the current conservation in the frame moving with the vortex one has noe(Vc - eL) = jT -- nooevL. Plugging this in the Eq.(2) one obtains

jT =

enowo~-. × ~ X + (~or) ~

no(~°r)2 + e(1 + (~o~) ~

6.)vL, (3)

where din = no - noo, which gives the flux flow

0921-4534/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0921-4534(94)02129-5

3128

M. ~ Feigel'man et al./Physica C 235 240 (1994) 312L 312~'

Hall conductivity -

, 0ec ( B 1+

0r) 2

6,

c B

(4)

The additional contribution to the Hall conductivity 6a,~ = - 6 n e c / B is our main result. It is possible to show from the topological arguments [6,7] as well as from the time dependent Ginzburg Landau theory [7] that in general case 6n is the difference between the electron density on the axis of the vortex core and that far outside the core. In neutral system this change in density is of the order of 6 n / n ,.~ ( A / E F ) 2. In the "jellium" model with the positive background charge the density fluctuations are suppressed and 6 n / n ,~ ( A / E F ) 4. However the compressibility of the crystal is of the same order as that of the electron gas and 6 n / n ,.~ ( A / E F ) ~ with coefficient inversely proportional to the compressibility. The crucial point for the discussion is the sign of 6n. Taking as an estimate 6 n / n = s i g n ( 6 n ) ( A / E F ) 2 and wo = A 2 / E F << r -1 one arrives at noec A s a~ _ T E ~ ((Ar)~ - sign(6n)).

(5)

The new term we have found is important in a dirty case A r < 1 and can lead to the sign change if 6n > 0 (the density of the carriers in the core is bigger than outside). Let us consider this case in more details in application to HTSC. In this materials A r > 1 at low temperature and A v --* 0 at T~. Note that what enters in Eq.(5) is A ( T ) rather than A(0). Thus at low temperature we can neglect this 6n contribution and the sign of cr~ is positive (as in the normal state). As the temperature approaches To, Av ~ 1 and a~y changes the sign to the negative value. Near Hc2(T) the normal state contribution is to be taken into account (conductivity is the sum of the normal and the superconductive parts [8]). Since the superconductive contribution (5) goes to zero as H~2- H the Hall effect changes sign back to the normal value in this region [8]. This are just two sign changes observed in Bi and Tl baaed materials (we believe that in Y B C O the low temperature sign change back to the normal sign is not seen since p=u is suppressed by pinning). The temperature dependence of the Hall conductivity (5) is

in very good agreement with data by Samoilov eg al. [9] who found for T B C C O that B -1- term in the Hall conductivity changes sign around 83 K and at higher temperature is oc Tc - T. In the simple BCS model Tc depends upon the density of states and increases with increased density leading to the density in the superconductive state higher than in the normal state and thus 6n < 0. However one can consider a simple tight binding model with large effective mass exponentialy dependent upon the lattice constant. Then under compression carriers become lighter and T~ decreases leading to 6n > 0. Experimentaly 6n is difficult to measure. The preasure dependence of Tc is rather ambiguous, and has different signs for the pressure along a and b axes. On the other hand Tc in the overdoped materials decreases with increasing hole density which should lead to the positive 6n and to the sign change. MVF, VBG and AIL acknowledge support from the Swiss National Foundation and the Landau Weizmann program for Theoretical Physics. VMV acknowledges the support through US Department of Energy BES-Materials Sciences, under contract No. W-31-109-ENG-38. REFERENCES 1.

S. :I. Hagen e~ al. Phys. Rev. B 47, 1064

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