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Electronic states near the metal-insulator transition in oxide superconductors
Physiea C 162-164 (1989) 221-222 North-Holland
kn~2CTRONIC STATES NEAR THE METAL-INSULATOR TRANSITION IN OXIDE SUPERCONDUCTORS H. Matstmloto, M. Sasaki and M. Tachiki Institute for Materials Reseach, Tohoku University, Sendai 980, JAPAN The metal-insulator transition region of high T c superconducting oxides is studied in the p-d mixing model. A new narrow band arises spontaneously inside the charge transfer gap due to a many-body effect via spin fluctuations and it broadens with hole doping. Various observed features of the optical conductivity are interpreted in terms of intram and inter-band transitions involving the new narrow band. The carriers in this band may be responsible for superconductivity.
In high Tc oxlde superconductors, the superconductivity(SC) appears only in a small intermediate region near the metal-insulator transitionI. The mechanism of the high-Tc SC may be closely related to a special electronic structure realized in this region. The photo~nission experiments and the optical experiments have shown that the d-electrons at Cu-sites have a strong Coulomb repulsion U about 7eV and the energy gap in the insulator phase is about 1.5~2eV. The infrared absorption exPeriment using single crystal films of La2_xSrxCUO 4 shows a new absorption peak inside the energy gap 2. The recent EELS and XPS experiments by use of YBa2Cu3073, Bi 2Sr2CaCu208 and TiBa2Can_iCUn02n+3 also revealed the enhanced density of states(DOS) at a narrow region of the Fermi level(FL), and FL does not shift much its position. Furthermore, the enhancement in Bi- and TIcctnpounds is observed only in the superconductive samples, and not in the semi-conductive samples with Ca-ions being replaced by Y-ions. This fact indicates that a new level is formed at FL inside the charge transfer gap without shifting FL to the lower p-band and that it is not an impurity band but intrinsic in oxide superconductors. In order to have the above mentioned situation, one needs to have certain mechanism to induce energy splitting in hole states due to a macroscopic amount of hole doping. Since the p-d transfer energy is comparable with the charge transfer gap energy, we start from the p-d mixing model. In this paper, we show that spin fluctuations (SF) induced in the p-d hopping and the fermi edge
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
effect work to modify hole-states and that a new narrow band is formed at FL inside t h e charge transfer energy gap. We start from the Anderson lattice Hamiltonian H = Z t +Z ~ d t d EpiJPi~PJo i~ d i a ia ija +ZUn n +Zt (dt p +p.t d ), (i) i iT iI ijij la 3a 3a ia where Pi~ and d i~ are p- and d-electron operators with the spin a(=T, I) at the i-th site, respectively, and ni ~d~ dia. By keeping ~ (=~d+U) constant and considering the limit ~d---~, only the transition between ni=l (ni~ni T+ni i) and ni=2 states are considered. The relevant operator is nia(= diani_ ~) , which satisfies the equation ( i a - E )n (x) = t n a _ _I Z (a#) n (x)t(a)p (x) , (2) 2 as ~ s ;z,s where at--a/at, a =(-l,a) with ~ = 0,1,2,3, n =]~ ,sd:(~t~)asds with a =(I,-~). Eq.(2) shows that SF and charge fluctuation(CF) are simultaneously emitted in the electron hopping. The n-propagator and p-propagator are obtained as
S
t(~,~)
= n/2[~--~ -,Z(~,~) - t (k)n/2(~-~p(k))],
s
t(~,~) PP
(3)
= 1/.[~,-~ (~') 2-. P - t (k)n/2(~-~ -~(~,k))],
The self-energy Z(~,~) is evaluated in one loop approximation of p-electron and CF. By use of a local decomposition of operator n as <~n (x) n(z) ~t(y)>--<6n (x) 6n
(4) the SF& the (z)
222
H. M a t s u m o t o et al. / Electronic states near the metal-insulator transition
>Jv and an approximation of replacing the momentum integration by its average, we calculate the spectrals ~ ( ~ ) = (2~)-2;d2k(-i/~)ImS nt(~,~) and ~_(~)=(~)-2 P ;d2k(-i/=)ImS__t(o,k), The contribution of SF to Z(~,k)-~[~ evaluated as 2 2(~,k) = t Id~d~'ep(~)30s(~')(l-fF(~)) x(l-f (~'))/(~-~-~'+iE) F
,
~), we perform the self-consistent calculation to obtain a (~) and ~_(~). The result is shown in Fig.l. We see t~at a new narrow band appears inside the charge transfer gap, and grows up to a wider metallic band with increasing ~p. The state near the FL in the metallic region is mainly of the p-electron character. Fig.2 shows the spectral intensity of p-electron,~ppt(W,~). _ The dispersion crosslng FL is very narrow and it shows a rapid increase of width above FL. In the optical absorption in La-Sr-Cu-O 2 , the new peak at 1.5eV is interpreted as the transition from the new narrow band to the upper band. The additional inter-band transition of ~ 0 . 5 e V frem the lower p-band to the new band may be indentified as a broad peak observed around this region, which is same as the energy region identified as the plasma
In the o p t i c a l
>
U3
O
l
=
1
1
T
= [
(b)
05
0.0
.
-2
060
.
.
(e~)
.
.
4
FIGURE 1 Electron density of states, G_(o) and ~ (~). paralneters are E -~ =3.4eV, t~2.0eV, s=~.8eV, = 0 . 0 2 e V , T=0.0~e~, and E_=-0.54eV(a), 0~52eV(b), -0.30eV(c). P
O"pp" ,,
i
-1-0.5 0 0.5@ (ev)
c o n d u c t i v i t y 5"6, we
may identify the behavior near ~ ~ 0 as the intra-band transition of the new narrow band which is strongly dependent on temperature and concentration of the hole, and the peak in the mid-infrared range as the inter-band transition from the lower p-band to the new band. The carriers in this narrow band may be responsible for SC. Also one expects a modification of SF and a strong CF due to the slow electron motion in the narrow conduction band, which may be important for the mechanism of high T c SC.
=
]F-~
1.0
(5)
where ~s(~)(= (i/2)~s(~)(l+ 2fB(o))/(2-n)) is a normalized spectral of SF. Approximating ~p(~) to produce a flat density as +s (2=)-2[d2k'=(i/2s)[ P d~, and ~ (~)=7 /~( 2+ S S J J ~p-S
edge 2 ' 4 .
7
FIGURE2 Spectral intensity annt(o,~). Parameters are for the case (c) in F~g.l. 61 (1988) 1127. 2. M.Suzuki, Phys. Rev. B39 (1989) 2312. 3. J. Fink, et.al., in "Proc. Int. Sym. on Electronic Structu-re of High-T c Superconductor", (Roma, Oct.5-7, 1988). 4
S. Tajima, et.al., Physica C136 (1988) 90.
5. G. A. Thomas, et.al., Phys. Rev. Lett. 61 (1988) 1313.
R~ENCES i. J. B. Torrance, et.al, Phys.
Rev.
Lett.
6. R. T. Collins, et. al., Phys. Rev. B39 (1989) 6571.
kn~2CTRONIC STATES NEAR THE METAL-INSULATOR TRANSITION IN OXIDE SUPERCONDUCTORS H. Matstmloto, M. Sasaki and M. Tachiki Institute for Materials Reseach, Tohoku University, Sendai 980, JAPAN The metal-insulator transition region of high T c superconducting oxides is studied in the p-d mixing model. A new narrow band arises spontaneously inside the charge transfer gap due to a many-body effect via spin fluctuations and it broadens with hole doping. Various observed features of the optical conductivity are interpreted in terms of intram and inter-band transitions involving the new narrow band. The carriers in this band may be responsible for superconductivity.
In high Tc oxlde superconductors, the superconductivity(SC) appears only in a small intermediate region near the metal-insulator transitionI. The mechanism of the high-Tc SC may be closely related to a special electronic structure realized in this region. The photo~nission experiments and the optical experiments have shown that the d-electrons at Cu-sites have a strong Coulomb repulsion U about 7eV and the energy gap in the insulator phase is about 1.5~2eV. The infrared absorption exPeriment using single crystal films of La2_xSrxCUO 4 shows a new absorption peak inside the energy gap 2. The recent EELS and XPS experiments by use of YBa2Cu3073, Bi 2Sr2CaCu208 and TiBa2Can_iCUn02n+3 also revealed the enhanced density of states(DOS) at a narrow region of the Fermi level(FL), and FL does not shift much its position. Furthermore, the enhancement in Bi- and TIcctnpounds is observed only in the superconductive samples, and not in the semi-conductive samples with Ca-ions being replaced by Y-ions. This fact indicates that a new level is formed at FL inside the charge transfer gap without shifting FL to the lower p-band and that it is not an impurity band but intrinsic in oxide superconductors. In order to have the above mentioned situation, one needs to have certain mechanism to induce energy splitting in hole states due to a macroscopic amount of hole doping. Since the p-d transfer energy is comparable with the charge transfer gap energy, we start from the p-d mixing model. In this paper, we show that spin fluctuations (SF) induced in the p-d hopping and the fermi edge
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
effect work to modify hole-states and that a new narrow band is formed at FL inside t h e charge transfer energy gap. We start from the Anderson lattice Hamiltonian H = Z t +Z ~ d t d EpiJPi~PJo i~ d i a ia ija +ZUn n +Zt (dt p +p.t d ), (i) i iT iI ijij la 3a 3a ia where Pi~ and d i~ are p- and d-electron operators with the spin a(=T, I) at the i-th site, respectively, and ni ~d~ dia. By keeping ~ (=~d+U) constant and considering the limit ~d---~, only the transition between ni=l (ni~ni T+ni i) and ni=2 states are considered. The relevant operator is nia(= diani_ ~) , which satisfies the equation ( i a - E )n (x) = t n a _ _I Z (a#) n (x)t(a)p (x) , (2) 2 as ~ s ;z,s where at--a/at, a =(-l,a) with ~ = 0,1,2,3, n =]~ ,sd:(~t~)asds with a =(I,-~). Eq.(2) shows that SF and charge fluctuation(CF) are simultaneously emitted in the electron hopping. The n-propagator and p-propagator are obtained as
S
t(~,~)
= n/2[~--~ -,Z(~,~) - t (k)n/2(~-~p(k))],
s
t(~,~) PP
(3)
= 1/.[~,-~ (~') 2-. P - t (k)n/2(~-~ -~(~,k))],
The self-energy Z(~,~) is evaluated in one loop approximation of p-electron and CF. By use of a local decomposition of operator n as <~n (x) n(z) ~t(y)>--<6n (x) 6n
(4) the SF& the (z)
222
H. M a t s u m o t o et al. / Electronic states near the metal-insulator transition
>Jv
,
~), we perform the self-consistent calculation to obtain a (~) and ~_(~). The result is shown in Fig.l. We see t~at a new narrow band appears inside the charge transfer gap, and grows up to a wider metallic band with increasing ~p. The state near the FL in the metallic region is mainly of the p-electron character. Fig.2 shows the spectral intensity of p-electron,~ppt(W,~). _ The dispersion crosslng FL is very narrow and it shows a rapid increase of width above FL. In the optical absorption in La-Sr-Cu-O 2 , the new peak at 1.5eV is interpreted as the transition from the new narrow band to the upper band. The additional inter-band transition of ~ 0 . 5 e V frem the lower p-band to the new band may be indentified as a broad peak observed around this region, which is same as the energy region identified as the plasma
In the o p t i c a l
>
U3
O
l
=
1
1
T
= [
(b)
05
0.0
.
-2
060
.
.
(e~)
.
.
4
FIGURE 1 Electron density of states, G_(o) and ~ (~). paralneters are E -~ =3.4eV, t~2.0eV, s=~.8eV, = 0 . 0 2 e V , T=0.0~e~, and E_=-0.54eV(a), 0~52eV(b), -0.30eV(c). P
O"pp" ,,
i
-1-0.5 0 0.5@ (ev)
c o n d u c t i v i t y 5"6, we
may identify the behavior near ~ ~ 0 as the intra-band transition of the new narrow band which is strongly dependent on temperature and concentration of the hole, and the peak in the mid-infrared range as the inter-band transition from the lower p-band to the new band. The carriers in this narrow band may be responsible for SC. Also one expects a modification of SF and a strong CF due to the slow electron motion in the narrow conduction band, which may be important for the mechanism of high T c SC.
=
]F-~
1.0
(5)
where ~s(~)(= (i/2)~s(~)(l+ 2fB(o))/(2-n)) is a normalized spectral of SF. Approximating ~p(~) to produce a flat density as +s (2=)-2[d2k'=(i/2s)[ P d~, and ~ (~)=7 /~( 2+ S S J J ~p-S
edge 2 ' 4 .
7
FIGURE2 Spectral intensity annt(o,~). Parameters are for the case (c) in F~g.l. 61 (1988) 1127. 2. M.Suzuki, Phys. Rev. B39 (1989) 2312. 3. J. Fink, et.al., in "Proc. Int. Sym. on Electronic Structu-re of High-T c Superconductor", (Roma, Oct.5-7, 1988). 4
S. Tajima, et.al., Physica C136 (1988) 90.
5. G. A. Thomas, et.al., Phys. Rev. Lett. 61 (1988) 1313.
R~ENCES i. J. B. Torrance, et.al, Phys.
Rev.
Lett.
6. R. T. Collins, et. al., Phys. Rev. B39 (1989) 6571.