- Email: [email protected]
Possibility of Tc enhancement with halogen doping in fulleride superconductors
Solid'State Communications, Voi. 80, No. 9, pp. 725-726, 1991. Printed in Great Britain.
0038-1098/91 $3.00 + .00 Pergamon Press plc
POSSIBILITY O F Tc E N H A N C E M E N T W I T H H A L O G E N D O P I N G IN FULLERIDE SUPERCONDUCTORS R. Lal
Theory Group, National Physical Laboratory, Dr. K.S. Krishnan Road, New Delhi 110 012, India and S.K. Joshi Council of Scientific and Industrial Research, Raft Marg, New Delhi 110 001, India
(Received 1 August 1991 by C.N.R. Rao) The excitonic mechanism is found to be more favourable in alkali fulleride superconductors than the phononic mechanism. On this basis it is discussed that halogen doped alkali fullerides A 3MxCr0 (A = alkali atom, M = halogen atom, x ,~ 1) may have higher Tc than A3C60. T H E R E C E N T discovery of bulk superconductivity [1, 2] in alkali fullerides K3C60and RbsCr0 has stimulated on intense interest in the physical and chemical properties of these systems. The observed [1] T~ of K3C60 is 18 K, while that [2] of RbsC60 is 28 K. These values of Tc are much less than the highest T,. of 125 K observed in Tl-based copper oxide superconductors [3]. There is, therefore, a need for searching avenues which may enhance the T~ of alkali fullerides. In this communication we present an idea which may turn out to be a possible approach for the enhancement of Tc in alkali fulleride superconductors. Our idea is based on the assumption that superconductivity in alkali fullerides is due to excitonic mechanism. That is to say, in alkali fullerides the conduction electrons experience an exciton-mediated interaction which, below TC, binds them to form Cooper pairs. It is too early to say anything with certainty about excitonic mechanism being the mechanism operative in alkali fulleride superconductors. Phononic and other mechanisms are also possible [4] in alkali fullerides. However, phononic and excitonic mechanism are considered to be main mechanisms of superconductivity in fullerides [2, 5]. In order to see which one of these two will dominate in fulleride superconductors we consider the excitonic mechanism vis-h-vis the phononic mechanism in the following manner. In the BCS framework when the indirect electronelectron interaction is mediated by a boson (phonon, exciton etc.) the transition temperature is given by
Tc =
1.14we exp ( - 1/VNF).
(1)
Here wc is the characteristic energy corresponding to the indirect electron-electron interaction - it is
Debye temperature for phonons, while exciton binding energy for excitons. V is the negative of the indirect electron-electron interaction, and NF is the density of states of the Fermi energy. The density of states N F will be the same in both the phononic and the excitonic mechanisms. Only the values of wc and V will be different for phonons and excitons. Thus in order to see which one of these two types of excitations will be favourably involved in the mechanism of superconductivity in alkali fullerides we shall see how wc and V vary in the two cases when we go from K3C60 to Rb3C60. Since Rb3Cr0 has higher To, according to equation (1), those excitations will be involved in the superconductivity of alkali fullerides for which w, and V have relatively more values when we go from K3C60 to Rb3C60. Let us first consider phonons. According to [2], in the case of phonons, V is less in Rb3C60. The Debye temperature is also expected to be less in Rb3C60 because Rb is heavier than K. If the force constants do not change much, then some phonon frequencies will be lowered by replacement of K by Rb. The net result of the contribution of phonons is that while going from K3C60 to Rb3C60 w, and V will become less. On the other hand we expect that both wc and V will be similar in K3C60 and Rb3C60 because both of these quantities are electronic in nature and will be determined mainly by the C60 molecules. This type of contribution of excitons to wc and V, when compared with the above type of contribution of phonons to wc and V leads us to the conclusion that superconductivity in alkali fullerides is governed by the excitonic mechansim. When it is so, we propose that apart from doping the fullerides with alkali atoms, one dopes them with some halogen atoms also. The halogen
725
726
POSSIBILITY OF Tc E N H A N C E M E N T WITH H A L O G E N D O P I N G
atoms are 4 to 40 times lighter than a C60 molecule; they (the halogen atoms) are point like charges, and are less electronegative than C60 molecules. In view of these crucial differences, it will be unlikely that a halogen atom substitutes a C60 molecule in the A3MxC60 solid. In fact under such circumstances we expect the halogen atoms to occupy the interstitial [6] spaces between C60 molecules of the face-centeredcubic structure [6]. We now see in what way we will have higher Tc in A3MxC60 than in A3C60.Let r~, denote the position of an electron which lies on the nth atom of the i th C60 molecule. Also let r~ denote the position of an electron on the/~th halogen atom. Then the interelectron Coulomb interaction seen by an electron due to all the C60 molecules and due to a single halogen atom will be given by
u
=
u,+
uh,
(2)
where 82
Uc = e,,' )-" E01r,, - rj, l '
(3)
and
u~
e2
E0lr, - re, I
(4)
Here e is electronic charge and E0 is dielectric screening constant [7]. We emphasize that the interelectron Coulomb interaction due to a halogen atom, Uh (equation 4), will show its significance through the electronegativity of the halogen atom. In fact due to high electronegativity of a halogen atom it will be quite probable that an electron occupying conduction band states stays, for some time, on halogen atoms also. In this sense the halogen atoms will locally affect the motion of a conduction electron in an important manner. The main effect will be that near the halogen atom the off-diagonal matrix elements of Uc + Uh between the three-fold degenerate t~u lowest-unoccupiedmolecular-orbital-derived bands will be more. Much away from a halogen atom the contribution of offdiagonal matrix elements of Uh will be negligible. Only the contribution of U~ will remain in effect. What we
Vol. 80,'No. 9
want to say means that Uh will enhance the interband transitions of conduction electrons when there are already interband transitions due to U~. The enhancement of interband transitions will depend on the type of the halogen atom (F, C1, Br, I or At) and on the dopant concentration x. The net result of enhancement of interband transitions will be that the indirect interaction between electrons due to exciton formation (electronic polarization) will be increased. The increment, for x ,~ 1, will be
~2U, UhpI~Ix. Here p is the probability of a conduction electron to be on a halogen atom, and p is electronic polarization. Uc and Oh are off-diagonal matrix elements of U~ and Uh, respectively, in terms of the partially filled bands of the system. When it is so, then Vwill be more and so according to equation (1) the T,. of the system will be increased over its value for x = 0. In this way we expect that halogen doping will enhance T, of alkali fulleride superconductors. In conclusion, the above study will advance our understanding regarding alkali fulleride superconductors. This is because, if experiments with halogen doped alkali fullerides show enhancement of T~, a support will be provided to the excitonic mechanism in these superconductors. On the other hand, if experiments on halogen doped systems do not show enhancement in TC, possibility of excitonic mechanism in alkali fulleride superconductors will be disfavoured.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
A.F. Hebard et al., Nature 350, 600 (1991). M.J. Rosseinsky et al., Phys. Rev. Lett. 66, 2830 (1991). P.B. Allen, in High-Temperature Superconductivity, (Edited by J.W. Lynn), p. 304, Springer, New York (1990). W.E. Pickett, Nature 351, 602 (1991). P.J. Benning et al., Science 252, 1417 (1991). P.W. Steppens et al., Nature 351, 631 (1991). S. Saito & A. Oshiyama, Phys. Rev. Lett. 66, 2637 (1991).
0038-1098/91 $3.00 + .00 Pergamon Press plc
POSSIBILITY O F Tc E N H A N C E M E N T W I T H H A L O G E N D O P I N G IN FULLERIDE SUPERCONDUCTORS R. Lal
Theory Group, National Physical Laboratory, Dr. K.S. Krishnan Road, New Delhi 110 012, India and S.K. Joshi Council of Scientific and Industrial Research, Raft Marg, New Delhi 110 001, India
(Received 1 August 1991 by C.N.R. Rao) The excitonic mechanism is found to be more favourable in alkali fulleride superconductors than the phononic mechanism. On this basis it is discussed that halogen doped alkali fullerides A 3MxCr0 (A = alkali atom, M = halogen atom, x ,~ 1) may have higher Tc than A3C60. T H E R E C E N T discovery of bulk superconductivity [1, 2] in alkali fullerides K3C60and RbsCr0 has stimulated on intense interest in the physical and chemical properties of these systems. The observed [1] T~ of K3C60 is 18 K, while that [2] of RbsC60 is 28 K. These values of Tc are much less than the highest T,. of 125 K observed in Tl-based copper oxide superconductors [3]. There is, therefore, a need for searching avenues which may enhance the T~ of alkali fullerides. In this communication we present an idea which may turn out to be a possible approach for the enhancement of Tc in alkali fulleride superconductors. Our idea is based on the assumption that superconductivity in alkali fullerides is due to excitonic mechanism. That is to say, in alkali fullerides the conduction electrons experience an exciton-mediated interaction which, below TC, binds them to form Cooper pairs. It is too early to say anything with certainty about excitonic mechanism being the mechanism operative in alkali fulleride superconductors. Phononic and other mechanisms are also possible [4] in alkali fullerides. However, phononic and excitonic mechanism are considered to be main mechanisms of superconductivity in fullerides [2, 5]. In order to see which one of these two will dominate in fulleride superconductors we consider the excitonic mechanism vis-h-vis the phononic mechanism in the following manner. In the BCS framework when the indirect electronelectron interaction is mediated by a boson (phonon, exciton etc.) the transition temperature is given by
Tc =
1.14we exp ( - 1/VNF).
(1)
Here wc is the characteristic energy corresponding to the indirect electron-electron interaction - it is
Debye temperature for phonons, while exciton binding energy for excitons. V is the negative of the indirect electron-electron interaction, and NF is the density of states of the Fermi energy. The density of states N F will be the same in both the phononic and the excitonic mechanisms. Only the values of wc and V will be different for phonons and excitons. Thus in order to see which one of these two types of excitations will be favourably involved in the mechanism of superconductivity in alkali fullerides we shall see how wc and V vary in the two cases when we go from K3C60 to Rb3C60. Since Rb3Cr0 has higher To, according to equation (1), those excitations will be involved in the superconductivity of alkali fullerides for which w, and V have relatively more values when we go from K3C60 to Rb3C60. Let us first consider phonons. According to [2], in the case of phonons, V is less in Rb3C60. The Debye temperature is also expected to be less in Rb3C60 because Rb is heavier than K. If the force constants do not change much, then some phonon frequencies will be lowered by replacement of K by Rb. The net result of the contribution of phonons is that while going from K3C60 to Rb3C60 w, and V will become less. On the other hand we expect that both wc and V will be similar in K3C60 and Rb3C60 because both of these quantities are electronic in nature and will be determined mainly by the C60 molecules. This type of contribution of excitons to wc and V, when compared with the above type of contribution of phonons to wc and V leads us to the conclusion that superconductivity in alkali fullerides is governed by the excitonic mechansim. When it is so, we propose that apart from doping the fullerides with alkali atoms, one dopes them with some halogen atoms also. The halogen
725
726
POSSIBILITY OF Tc E N H A N C E M E N T WITH H A L O G E N D O P I N G
atoms are 4 to 40 times lighter than a C60 molecule; they (the halogen atoms) are point like charges, and are less electronegative than C60 molecules. In view of these crucial differences, it will be unlikely that a halogen atom substitutes a C60 molecule in the A3MxC60 solid. In fact under such circumstances we expect the halogen atoms to occupy the interstitial [6] spaces between C60 molecules of the face-centeredcubic structure [6]. We now see in what way we will have higher Tc in A3MxC60 than in A3C60.Let r~, denote the position of an electron which lies on the nth atom of the i th C60 molecule. Also let r~ denote the position of an electron on the/~th halogen atom. Then the interelectron Coulomb interaction seen by an electron due to all the C60 molecules and due to a single halogen atom will be given by
u
=
u,+
uh,
(2)
where 82
Uc = e,,' )-" E01r,, - rj, l '
(3)
and
u~
e2
E0lr, - re, I
(4)
Here e is electronic charge and E0 is dielectric screening constant [7]. We emphasize that the interelectron Coulomb interaction due to a halogen atom, Uh (equation 4), will show its significance through the electronegativity of the halogen atom. In fact due to high electronegativity of a halogen atom it will be quite probable that an electron occupying conduction band states stays, for some time, on halogen atoms also. In this sense the halogen atoms will locally affect the motion of a conduction electron in an important manner. The main effect will be that near the halogen atom the off-diagonal matrix elements of Uc + Uh between the three-fold degenerate t~u lowest-unoccupiedmolecular-orbital-derived bands will be more. Much away from a halogen atom the contribution of offdiagonal matrix elements of Uh will be negligible. Only the contribution of U~ will remain in effect. What we
Vol. 80,'No. 9
want to say means that Uh will enhance the interband transitions of conduction electrons when there are already interband transitions due to U~. The enhancement of interband transitions will depend on the type of the halogen atom (F, C1, Br, I or At) and on the dopant concentration x. The net result of enhancement of interband transitions will be that the indirect interaction between electrons due to exciton formation (electronic polarization) will be increased. The increment, for x ,~ 1, will be
~2U, UhpI~Ix. Here p is the probability of a conduction electron to be on a halogen atom, and p is electronic polarization. Uc and Oh are off-diagonal matrix elements of U~ and Uh, respectively, in terms of the partially filled bands of the system. When it is so, then Vwill be more and so according to equation (1) the T,. of the system will be increased over its value for x = 0. In this way we expect that halogen doping will enhance T, of alkali fulleride superconductors. In conclusion, the above study will advance our understanding regarding alkali fulleride superconductors. This is because, if experiments with halogen doped alkali fullerides show enhancement of T~, a support will be provided to the excitonic mechanism in these superconductors. On the other hand, if experiments on halogen doped systems do not show enhancement in TC, possibility of excitonic mechanism in alkali fulleride superconductors will be disfavoured.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
A.F. Hebard et al., Nature 350, 600 (1991). M.J. Rosseinsky et al., Phys. Rev. Lett. 66, 2830 (1991). P.B. Allen, in High-Temperature Superconductivity, (Edited by J.W. Lynn), p. 304, Springer, New York (1990). W.E. Pickett, Nature 351, 602 (1991). P.J. Benning et al., Science 252, 1417 (1991). P.W. Steppens et al., Nature 351, 631 (1991). S. Saito & A. Oshiyama, Phys. Rev. Lett. 66, 2637 (1991).