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Tunneling asymmetry: A test of superconductivity mechanisms
Physica C 159 (1989) 157-160 North-Holland, Amsterdam
TUNNELING ASYMMETRY: A TEST OF SUPERCONDUCTIVITY MECHANISMS F. MARSIGLIO and J.E. HIRSCH Department of Physics, B-019, University of California, San Diego, La Jolla, CA 92093, USA Received 20 March 1989
Within the conventional electron-phonon mechanism of superconductivity, normal-insulator-superconductor (N-I-S) tunneling characteristics are expected to be symmetric with respect to the sign of the bias voltage. A recently proposed mechanism of superconductivity based on pairing of hole carriers predicts an asymmetry of universal sign: the tunneling current should be larger for a negatively biased sample. We suggest a search for this asymmetry in conventional superconductors, as well as in "hole" and "electron" oxide superconductors: its systematic observation would provide direct evidence in favor of the hole pairing mechanism of superconductivity.
Tunneling experiments [ I ] are a powerful tool for the study of superconductivity, as they provide a direct probe of the superconducting energy gap. It was the detailed analysis of the structure in the tunneling characteristics of strong coupling superconductors [2] that has provided the most convincing evidence for the validity of the electron-phonon mechanism. It is only natural that if that mechanism is incorrect or requires modification, tunneling experiments should play an important role in establishing this. Recently, a new mechanism for superconductivity has been proposed for the high Tc oxides, as well as for conventional materials, based on the pairing of hole carriers [ 3-5 ]. The characteristic feature of this mechanism is that it leads to an energy gap that has a linear dependence on the kinetic energy of the holes in the band:
a(~h=am(- ~ck +c)
(1)
where e~ is the kinetic energy for holes in a full band, defined such that:
~k=0,
(2)
k
D is the bandwidth and zfm and c are constants (,fro is positive). The energy dependence because the attractive part of the interaction originates in a modulation of the hopping amplitude of holes when other
holes are present on the sites, of the form:
H~ttr=-At (~ij> (c~cj~+h.c.)(n~,_~+nj,_~)
(3a)
t7
where c$ is a hole creation operator and the sum runs over nearest neighbor sites. The repulsive part of the interaction is modeled by an on-site and nearestneighbor Coulomb repulsion:
Hrep=U~i ni, n i ~ + V "
~, ninj
(3b)
(i,j)
and we treat the model within the approximation. The quasi-particle energy is given by: E(e~) =X/(ek--/t)2 +Zl(ek) 2
BCS
(4)
with/z the chemical potential, and the quasi-particle gap obtained from minimization of eq. (4) is:
J(u) ,to= ~/1 + ( ~ l m / ( D / 2 ) ) 2"
(5)
The energy dependence of the gap eq. ( 1 ) will lead to an asymmetry in a normal-insulator-superconductor ( N - I - S ) tunneling junction that always has the same sign. Because the slope ofxl(Ek) in eq. (1) is negative, it is slightly easier to inject holes rather than electrons into the superconducting sample. This translates into a slightly higher peak in the d u d V tunneling characteristic when the sample is nega-
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
158
F. Marsiglio, J.E. Hirsch /Tunneling asymmetry
tively biased, as will be shown below. In contrast, in the conventional approach with the electron-phonon interaction or another boson exchange mechanism the energy dependence of the gap A (o9) is symmetric with respect to the sign of 09, leading to symmetric tunneling characteristics. Thus, observation of an asymmetry of the sign discussed above would provide strong evidence in favor of the hole pairing mechanism of superconductivity. Below we give quantitative estimates for the expected effect. The ratio of superconducting to normal density of states is given by [ 6 ].
N,(w) N(0)
D/2 t~
-
}
dE [U2(E)8(to--#--E)
--D/2
+v2(E)~(~-lt+E)]
(6)
where we have assumed a constant density of states around the Fermi energy. Here,
U2(~)= I ( l'[- E---~)'E--~
v2(~)= 5
(7a)
E--/t
with E ( e ) given by eq. (4). With the form of the gap eq. (1) the integral in eq. (6) can be easily performed, and for ( w - # ) < < ( D / 2 ) + / t we obtain: N,(w)
1
d--~ (V) = a
do9 Ns(og)
(9)
Oo9
where a is an undetermined constant that disappears upon normalization o f d / / d Vto be normal state value. Since the Fermi function derivative merely weighs the density of states symmetrically about V, d//dVwill be larger on the positive side, i.e. for hole injection. In the oxide superconductors, the asymmetry obtained from eqs. (8) and (9) is substantial, as the energy gap is comparable to the Fermi energy. Figure 1 shows a typical example of the expected effect. We have given other quantitative elsewhere [ 3 ]. In fact, observation of asymmetry in the tunneling characteristics of oxides has been reported in several instances, and in all cases where the sign of the bias voltage was explicitly stated [ 7 ] (except one [ 8 ] ) the sign of the asymmetry was as expected from our theory. Unfortunately, tunneling data in oxide superconductors are somewhat uncertain because of the large variations in the gap observed (which our model provides an explanation for [ 3 ] ). Nevertheless, we propose that a systematic search for asymmetries in the tunneling characteristics in oxide superconductors will reveal that the sign is as predicted by our theory. In conventional materials the effect should be small but still observable as high quality tunneling mea-
N(O) - x/1 + (A,,,/ ( D / 2 ) ) 2
co--#+v
x
0 5 ~
I
'
' ~
'
'
' ~
'
I •
~
~
~
•
•
o(~o-~-~Jo) ~ / ( o ~ _ ~ ) 2 _ a ~
0.4 #-og- v
1
+0[- (~o-~)-~to1 x/(~o_~)2_Agj
T / T c • 0.4
(8a)
03L
with
z~O Am V~--"N/1 .ap(Am/(D/2) )2 D I 2 "
(8b)
Equation (8) clearly shows the asymmetry in the density of states that originated in the energy dependence of the gap, given by u. The size of the effect is proportional to An,/(D/2), and thus very small for conventional materials: Am is typically a few times the quasiparticle gap Ao. From eq. (8) we compute the I-V characteristics as:
00.
I
-4,0
~
-~.0
0.0 V
I
2.0
,
4.0
+#
Fig. 1. Typicald//d Vcurve expectedfor oxidesuperconductors. Here, ,Jm/(D)/2)=0.25, c= -0.4, n=0.2 and T/Tc=0.4. The sign convention is such that the largerpeak correspondsto a negativelybiased sample.The same conventionis used in the following examples.
F. Marsiglio,J.E. Hirsch/Tunneling asymmetry surements can be performed. As an example, we choose p a r a m e t e r s in the theory to yield a " t y p i c a l " T~ versus concentration d e p e n d e n c e as observed, for example, in the transition metal series [ 9 ], as shown in fig. 2. The gap ratio for this case is given to high accuracy by 2~Jo/kT¢= 3.53, as in the usual BCS theory, for all hole densities. The b a n d w i d t h was chosen as D = 1 eV, a n d the values o f Zlr, range from 3 K to 21 K in the range o f density studied. Figure 3 illustrates I - V characteristics for a hole concentration o f n = 0 . 2 , as a function o f reduced
2 0 - 0 ~ '
'
[
'
'
~ '
I
. . . .
I
. . . .
I
. . . .
temperature, T/Tc. The relative a s y m m e t r y is not strongly t e m p e r a t u r e dependent. F o r T/Tc=0.3, we have t a b u l a t e d the percent o f a s y m m e t r y for various hole concentrations in table I, as well as plotted t h e m in fig. 2. As the t e m p e r a t u r e goes to zero, the maxi m u m a s y m m e t r y for this case increases to 0.72%. A s y m m e t r i e s o f this degree can be discerned experimentally; to our knowledge, no one has systematically looked for t h e m up to now. A n a s y m m e t r y can also arise from a non-constant n o r m a l state density o f states. F o r example, with N ( e ) = ( N ) ( 0 ) (1 + me/(D/2) ), one obtains, instead o f eq. ( 8 ) :
--
N+(o))=
lO.O
1.o
•
"
%
0.5 ,%
•
,
{
x/l+(zlrn/(D/2)) 2 ( I o ~ - l z l ± v )
lt+u~ m X l + m D / 2 ] +--D/2 x
1 u)2_jU
(lO)
30
Here, t h e + ( - ) sign refers to the positive (negative) side o f the chemical potential. The last term in the curly brackets in eq. (10) causes an a d d i t i o n a l a s y m m e t r y in the peaks o f the I - V characteristic. However, the contribution will be small, since it is p r o p o r t i o n a l to both the slope in the density o f states a n d Io~-~l -Ao. In fig. 4 we plot the T/Tc=0.3 IV characteristic o f fig. 3 for m = - 0 . 5 , 0, a n d 0.5. The effects are fairly small on this e x p a n d e d scale. Most o f the a s y m m e t r y r e m a i n s due to the gap function energy dependence. In summary, we have investigated the conse-
E.O
Table I Percentage asymmetry in the tunneling characteristic as function of hole concentration for the case discussed in the text.
0.0
0.0
0.2
0.4
'''
0.0 %
n
Fig. 2. Plot of Tc (left scale ) vs. hole concentration with parameters [Eq. (3)] U=I0 eV, V=2 eV, At=0.80 eV, number of nearest neighbors z=8, and D = I eV. Also shown are points showing the percentage asymmetry (right scale) in the dI/dV curves at T/T¢ = 0.3, as a function of hole concentration (see table I).
> -o
159
1.0
-3.E4
-3.22
-3.20 V+/a
-3.18
-3.16
Fig. 3. Plot of d//d V vs. V for a hole concentration n = 0.2, for T / To= 0.05 (solid), 0.1 (short-dashed), and 0.3 (long-dashed). The asymmetry is indicated by the horizontal lines.
n
% asymmetry
0.04 0.07 0.10 0.15 0.20 0.25 0.30 0.35 0.38
0.10 0.22 0.35 0.51 0.58 0.53 0.38 0.19 0.09
F. Marsiglio, J.E. Hirsch /Tunneling asymmetry
160 1.57
....
~
1
....
I'''
] 4 >
J
1.56
conductors [ 12]. This would indicate that in these systems hole carriers on the oxygen are induced by electron doping on Cu sites [ 13 ] and that the mechanism of superconductivity is the same as in all other materials.
Acknowledgements 1.56
, , , LtL
-3.23
J L , I ~ ~ , , I , , ~ ~ I , ~ , ,
-3.20 V+/.z
, , J
LIT
Fig. 4. Expanded plot ofd//dVvs. Vfor n=0.2, T/T¢=0.3, and density of states slope m = -0.5, 0, 0.5 (see text). The asymmetry due to the varying normal state density of states is very small compared to the asymmetry due to the gap energy dependence. The positively sloped density of states as function of hole energy gives the largest peak on the right and the smallest on the left, i.e. it enhances the asymmetry.
quences for tunneling characteristics of the energy dependence of the gap function across the Fermi level that emerges naturally in a theory of superconductivity based on pairing of hole carriers [3-5]. We find that both in high Tc as well as in conventional low Tc materials the energy dependence leads to an asymmetry in the superconducting density of states which ought to be experimentally accessible in tunneling experiments. In fact, some published data on an A 15 compound suggest an asymmetry of the type expected here [ l0 ], and observation of an asymmetry in Pb, of sign unknown to us, has been reported [ 11 ]. We propose that a systematic search in conventional materials, particularly transition metals and A15 compound, as well as in oxide superconductors, will consistently show an asymmetry where the peak is higher when holes are injected into the sample. An interesting intermediate case should be the "old" oxide superconductor BaPbl_xBixO3, with maximum Tc of 13 K. We expect here the superconductivity to be driven by hole carriers in a narrow oxygen band thus giving rise to a sizeable asymmetry despite the low T~. Finally, we predict that this effect, with the same sign, will be observed in the recently discovered "electron-carrier" oxide super-
This work was supported by NSF Grant # DMR84-51899 and NSERC of Canada. We are grateful to A. Goldman, I.K. Schuller and A. Zettl for discussions.
References [ 1 ] I. Giaver and K. Megerle, Phys. Rev. 122 ( 1961 ) 1101. [2] Superconductivity, ed. R.D. Parks (Dekker, New York, 1969), particularly Chpts. 10 an 11. [3] J.E. Hirsch and F. Marsiglio, UCSD preprint, December 1988; Phys. Rev. B, to be published. [4] J.E. Hirsch, Phys. Lett. A 134 (1989) 451; Physica C 158 (1989) 326. [5] J.E. Hirsch and S. Tang, Sol. St. Comm. 69 (1989) 987; UCSD preprint, December 1988. [6 ] G. Rickayzen, ref. [2], Chpt. 2. [7] N. Hohn et al., Physica C 153-155 (1988) 1381; M.D. Kirk, Phys. Rev. B 35 (1987) 8850; A. Goldman, private communication. [ 8 ] M.F. Crommie et al., Phys. Rev. B 35 ( 1987 ) 8853; however, the actual sign of the bias here could have been opposite to that reported in the paper (A. Zettl, private communication ). [9]S. Vonsovsky, Y. Izyumov and E. Kurmaev, Superconductivity of Transition Metals (Springer, Berlin, 1982). [lO] J. Geerk et al., Superconductivity in d- and f-band Metals, eds. W. Buckel and W. Weber (Kerknforschungszentrum Karlsruhe, Karlsruhe, 1982 ) p. 23. [11] S. yon Molnar, W.A. Thompson and A.S. Edelstein, Appl. Phys. Lett. II (1967) 163. [121 Y. Tokura, H. Takagi and S. Uchida, nature 337 ( 189 ) 345. [13] The very same fact that allows for electron doping of Cu in these structures, absence of apical oxygens, makes it energetically favorable for the added electrons to induce hole carriers on neighboring oxygens.
TUNNELING ASYMMETRY: A TEST OF SUPERCONDUCTIVITY MECHANISMS F. MARSIGLIO and J.E. HIRSCH Department of Physics, B-019, University of California, San Diego, La Jolla, CA 92093, USA Received 20 March 1989
Within the conventional electron-phonon mechanism of superconductivity, normal-insulator-superconductor (N-I-S) tunneling characteristics are expected to be symmetric with respect to the sign of the bias voltage. A recently proposed mechanism of superconductivity based on pairing of hole carriers predicts an asymmetry of universal sign: the tunneling current should be larger for a negatively biased sample. We suggest a search for this asymmetry in conventional superconductors, as well as in "hole" and "electron" oxide superconductors: its systematic observation would provide direct evidence in favor of the hole pairing mechanism of superconductivity.
Tunneling experiments [ I ] are a powerful tool for the study of superconductivity, as they provide a direct probe of the superconducting energy gap. It was the detailed analysis of the structure in the tunneling characteristics of strong coupling superconductors [2] that has provided the most convincing evidence for the validity of the electron-phonon mechanism. It is only natural that if that mechanism is incorrect or requires modification, tunneling experiments should play an important role in establishing this. Recently, a new mechanism for superconductivity has been proposed for the high Tc oxides, as well as for conventional materials, based on the pairing of hole carriers [ 3-5 ]. The characteristic feature of this mechanism is that it leads to an energy gap that has a linear dependence on the kinetic energy of the holes in the band:
a(~h=am(- ~ck +c)
(1)
where e~ is the kinetic energy for holes in a full band, defined such that:
~k=0,
(2)
k
D is the bandwidth and zfm and c are constants (,fro is positive). The energy dependence because the attractive part of the interaction originates in a modulation of the hopping amplitude of holes when other
holes are present on the sites, of the form:
H~ttr=-At (~ij> (c~cj~+h.c.)(n~,_~+nj,_~)
(3a)
t7
where c$ is a hole creation operator and the sum runs over nearest neighbor sites. The repulsive part of the interaction is modeled by an on-site and nearestneighbor Coulomb repulsion:
Hrep=U~i ni, n i ~ + V "
~, ninj
(3b)
(i,j)
and we treat the model within the approximation. The quasi-particle energy is given by: E(e~) =X/(ek--/t)2 +Zl(ek) 2
BCS
(4)
with/z the chemical potential, and the quasi-particle gap obtained from minimization of eq. (4) is:
J(u) ,to= ~/1 + ( ~ l m / ( D / 2 ) ) 2"
(5)
The energy dependence of the gap eq. ( 1 ) will lead to an asymmetry in a normal-insulator-superconductor ( N - I - S ) tunneling junction that always has the same sign. Because the slope ofxl(Ek) in eq. (1) is negative, it is slightly easier to inject holes rather than electrons into the superconducting sample. This translates into a slightly higher peak in the d u d V tunneling characteristic when the sample is nega-
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
158
F. Marsiglio, J.E. Hirsch /Tunneling asymmetry
tively biased, as will be shown below. In contrast, in the conventional approach with the electron-phonon interaction or another boson exchange mechanism the energy dependence of the gap A (o9) is symmetric with respect to the sign of 09, leading to symmetric tunneling characteristics. Thus, observation of an asymmetry of the sign discussed above would provide strong evidence in favor of the hole pairing mechanism of superconductivity. Below we give quantitative estimates for the expected effect. The ratio of superconducting to normal density of states is given by [ 6 ].
N,(w) N(0)
D/2 t~
-
}
dE [U2(E)8(to--#--E)
--D/2
+v2(E)~(~-lt+E)]
(6)
where we have assumed a constant density of states around the Fermi energy. Here,
U2(~)= I ( l'[- E---~)'E--~
v2(~)= 5
(7a)
E--/t
with E ( e ) given by eq. (4). With the form of the gap eq. (1) the integral in eq. (6) can be easily performed, and for ( w - # ) < < ( D / 2 ) + / t we obtain: N,(w)
1
d--~ (V) = a
do9 Ns(og)
(9)
Oo9
where a is an undetermined constant that disappears upon normalization o f d / / d Vto be normal state value. Since the Fermi function derivative merely weighs the density of states symmetrically about V, d//dVwill be larger on the positive side, i.e. for hole injection. In the oxide superconductors, the asymmetry obtained from eqs. (8) and (9) is substantial, as the energy gap is comparable to the Fermi energy. Figure 1 shows a typical example of the expected effect. We have given other quantitative elsewhere [ 3 ]. In fact, observation of asymmetry in the tunneling characteristics of oxides has been reported in several instances, and in all cases where the sign of the bias voltage was explicitly stated [ 7 ] (except one [ 8 ] ) the sign of the asymmetry was as expected from our theory. Unfortunately, tunneling data in oxide superconductors are somewhat uncertain because of the large variations in the gap observed (which our model provides an explanation for [ 3 ] ). Nevertheless, we propose that a systematic search for asymmetries in the tunneling characteristics in oxide superconductors will reveal that the sign is as predicted by our theory. In conventional materials the effect should be small but still observable as high quality tunneling mea-
N(O) - x/1 + (A,,,/ ( D / 2 ) ) 2
co--#+v
x
0 5 ~
I
'
' ~
'
'
' ~
'
I •
~
~
~
•
•
o(~o-~-~Jo) ~ / ( o ~ _ ~ ) 2 _ a ~
0.4 #-og- v
1
+0[- (~o-~)-~to1 x/(~o_~)2_Agj
T / T c • 0.4
(8a)
03L
with
z~O Am V~--"N/1 .ap(Am/(D/2) )2 D I 2 "
(8b)
Equation (8) clearly shows the asymmetry in the density of states that originated in the energy dependence of the gap, given by u. The size of the effect is proportional to An,/(D/2), and thus very small for conventional materials: Am is typically a few times the quasiparticle gap Ao. From eq. (8) we compute the I-V characteristics as:
00.
I
-4,0
~
-~.0
0.0 V
I
2.0
,
4.0
+#
Fig. 1. Typicald//d Vcurve expectedfor oxidesuperconductors. Here, ,Jm/(D)/2)=0.25, c= -0.4, n=0.2 and T/Tc=0.4. The sign convention is such that the largerpeak correspondsto a negativelybiased sample.The same conventionis used in the following examples.
F. Marsiglio,J.E. Hirsch/Tunneling asymmetry surements can be performed. As an example, we choose p a r a m e t e r s in the theory to yield a " t y p i c a l " T~ versus concentration d e p e n d e n c e as observed, for example, in the transition metal series [ 9 ], as shown in fig. 2. The gap ratio for this case is given to high accuracy by 2~Jo/kT¢= 3.53, as in the usual BCS theory, for all hole densities. The b a n d w i d t h was chosen as D = 1 eV, a n d the values o f Zlr, range from 3 K to 21 K in the range o f density studied. Figure 3 illustrates I - V characteristics for a hole concentration o f n = 0 . 2 , as a function o f reduced
2 0 - 0 ~ '
'
[
'
'
~ '
I
. . . .
I
. . . .
I
. . . .
temperature, T/Tc. The relative a s y m m e t r y is not strongly t e m p e r a t u r e dependent. F o r T/Tc=0.3, we have t a b u l a t e d the percent o f a s y m m e t r y for various hole concentrations in table I, as well as plotted t h e m in fig. 2. As the t e m p e r a t u r e goes to zero, the maxi m u m a s y m m e t r y for this case increases to 0.72%. A s y m m e t r i e s o f this degree can be discerned experimentally; to our knowledge, no one has systematically looked for t h e m up to now. A n a s y m m e t r y can also arise from a non-constant n o r m a l state density o f states. F o r example, with N ( e ) = ( N ) ( 0 ) (1 + me/(D/2) ), one obtains, instead o f eq. ( 8 ) :
--
N+(o))=
lO.O
1.o
•
"
%
0.5 ,%
•
,
{
x/l+(zlrn/(D/2)) 2 ( I o ~ - l z l ± v )
lt+u~ m X l + m D / 2 ] +--D/2 x
1 u)2_jU
(lO)
30
Here, t h e + ( - ) sign refers to the positive (negative) side o f the chemical potential. The last term in the curly brackets in eq. (10) causes an a d d i t i o n a l a s y m m e t r y in the peaks o f the I - V characteristic. However, the contribution will be small, since it is p r o p o r t i o n a l to both the slope in the density o f states a n d Io~-~l -Ao. In fig. 4 we plot the T/Tc=0.3 IV characteristic o f fig. 3 for m = - 0 . 5 , 0, a n d 0.5. The effects are fairly small on this e x p a n d e d scale. Most o f the a s y m m e t r y r e m a i n s due to the gap function energy dependence. In summary, we have investigated the conse-
E.O
Table I Percentage asymmetry in the tunneling characteristic as function of hole concentration for the case discussed in the text.
0.0
0.0
0.2
0.4
'''
0.0 %
n
Fig. 2. Plot of Tc (left scale ) vs. hole concentration with parameters [Eq. (3)] U=I0 eV, V=2 eV, At=0.80 eV, number of nearest neighbors z=8, and D = I eV. Also shown are points showing the percentage asymmetry (right scale) in the dI/dV curves at T/T¢ = 0.3, as a function of hole concentration (see table I).
> -o
159
1.0
-3.E4
-3.22
-3.20 V+/a
-3.18
-3.16
Fig. 3. Plot of d//d V vs. V for a hole concentration n = 0.2, for T / To= 0.05 (solid), 0.1 (short-dashed), and 0.3 (long-dashed). The asymmetry is indicated by the horizontal lines.
n
% asymmetry
0.04 0.07 0.10 0.15 0.20 0.25 0.30 0.35 0.38
0.10 0.22 0.35 0.51 0.58 0.53 0.38 0.19 0.09
F. Marsiglio, J.E. Hirsch /Tunneling asymmetry
160 1.57
....
~
1
....
I'''
] 4 >
J
1.56
conductors [ 12]. This would indicate that in these systems hole carriers on the oxygen are induced by electron doping on Cu sites [ 13 ] and that the mechanism of superconductivity is the same as in all other materials.
Acknowledgements 1.56
, , , LtL
-3.23
J L , I ~ ~ , , I , , ~ ~ I , ~ , ,
-3.20 V+/.z
, , J
LIT
Fig. 4. Expanded plot ofd//dVvs. Vfor n=0.2, T/T¢=0.3, and density of states slope m = -0.5, 0, 0.5 (see text). The asymmetry due to the varying normal state density of states is very small compared to the asymmetry due to the gap energy dependence. The positively sloped density of states as function of hole energy gives the largest peak on the right and the smallest on the left, i.e. it enhances the asymmetry.
quences for tunneling characteristics of the energy dependence of the gap function across the Fermi level that emerges naturally in a theory of superconductivity based on pairing of hole carriers [3-5]. We find that both in high Tc as well as in conventional low Tc materials the energy dependence leads to an asymmetry in the superconducting density of states which ought to be experimentally accessible in tunneling experiments. In fact, some published data on an A 15 compound suggest an asymmetry of the type expected here [ l0 ], and observation of an asymmetry in Pb, of sign unknown to us, has been reported [ 11 ]. We propose that a systematic search in conventional materials, particularly transition metals and A15 compound, as well as in oxide superconductors, will consistently show an asymmetry where the peak is higher when holes are injected into the sample. An interesting intermediate case should be the "old" oxide superconductor BaPbl_xBixO3, with maximum Tc of 13 K. We expect here the superconductivity to be driven by hole carriers in a narrow oxygen band thus giving rise to a sizeable asymmetry despite the low T~. Finally, we predict that this effect, with the same sign, will be observed in the recently discovered "electron-carrier" oxide super-
This work was supported by NSF Grant # DMR84-51899 and NSERC of Canada. We are grateful to A. Goldman, I.K. Schuller and A. Zettl for discussions.
References [ 1 ] I. Giaver and K. Megerle, Phys. Rev. 122 ( 1961 ) 1101. [2] Superconductivity, ed. R.D. Parks (Dekker, New York, 1969), particularly Chpts. 10 an 11. [3] J.E. Hirsch and F. Marsiglio, UCSD preprint, December 1988; Phys. Rev. B, to be published. [4] J.E. Hirsch, Phys. Lett. A 134 (1989) 451; Physica C 158 (1989) 326. [5] J.E. Hirsch and S. Tang, Sol. St. Comm. 69 (1989) 987; UCSD preprint, December 1988. [6 ] G. Rickayzen, ref. [2], Chpt. 2. [7] N. Hohn et al., Physica C 153-155 (1988) 1381; M.D. Kirk, Phys. Rev. B 35 (1987) 8850; A. Goldman, private communication. [ 8 ] M.F. Crommie et al., Phys. Rev. B 35 ( 1987 ) 8853; however, the actual sign of the bias here could have been opposite to that reported in the paper (A. Zettl, private communication ). [9]S. Vonsovsky, Y. Izyumov and E. Kurmaev, Superconductivity of Transition Metals (Springer, Berlin, 1982). [lO] J. Geerk et al., Superconductivity in d- and f-band Metals, eds. W. Buckel and W. Weber (Kerknforschungszentrum Karlsruhe, Karlsruhe, 1982 ) p. 23. [11] S. yon Molnar, W.A. Thompson and A.S. Edelstein, Appl. Phys. Lett. II (1967) 163. [121 Y. Tokura, H. Takagi and S. Uchida, nature 337 ( 189 ) 345. [13] The very same fact that allows for electron doping of Cu in these structures, absence of apical oxygens, makes it energetically favorable for the added electrons to induce hole carriers on neighboring oxygens.