Chapter 4
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High-Temperature Superconductivity from Charged Boson Pairing M. J. Rice and Y. R. Wang Xerox Webster Research Center, Webster, NY 14580 The mean field theory of the paired holon superconductor and its predictions are reviewed for the case in which charged holons on different magnetic sublattices in a doped CuO layer interact via a weak attractive pairing potential V. The physical properties of this superconductor often reflect the essential gaplessness of its excitation spectrum. 2
In the resonating-valence-bond (RVB) model (J.) of the cupric oxide superconductors holes doped into a half-filled Mott-Hubbard insulator on a square lattice are thought to delocalize as spinless charged bosons (2), or holons. It has recently been suggested by us (1) and by the Princeton group (4) that in this model high temperature superconductivity might arise from pair condensation of the holon gas, rather than from some kind of single particle (BoseEinstein) condensation. The possibility of holon pairing stems from our observation (2) that the strictly two-dimensional (2D) bose gas becomes unstable toward pair condensation as arbitrarily weak attractive interactions (V) between its particles are switched on. This property, which does not arise for an isotropic 3D bose gas at zero temperature (T=0), is reminiscent of the Cooper-pair instability in a Fermi gas. In our work, the origin of V is left as an open question and we concentrate on the calculation of the mean-field properties of the resulting paired holon superconductor. In the Princeton work V is identified as an effective in plane attractive interaction between holons driven by interlayer tunneling of holon pairs. In this paper we review the predicted mean field properties of the paired holon superconductor (3.5.6). Specifically, we shall discuss the temperature dependences of the pair potential Δ(Τ), the specific heat Cu(T), the critical field Hc(T) and the London penetration depth \(T). We also discuss the Tiicrowave absorption (6) which is found to be quite different from 0097-6156/88/0377-0044$06.00/0 ° 1988 American Chemical Society Nelson and George; Chemistry of High-Temperature Superconductors II ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
4.
RICE & WANG
45
Charged Boson Pairing
B a r d e e n - C o o p e r - S c h r i e f f e r (£) (BCS) M a t t i s - B a r d e e n b e h a v i o r (8) and which, t h e r e f o r e , p r o v i d e s t h e p o s s i b i l i t y o f an e x p e r i m e n t a l means of i d e n t i f y i n g the p a i r e d holon superconductor. The model we i n t r o d u c e t o d e s c r i b e t h e i n t e r a c t i n g h o l o n system i n a doped Cu02 l a y e r i s a p p r o p r i a t e f o r the n e a r e s t - n e i g h b o u r RVB s t a t e i n which charged h o l o n s d e l o c a l i z e d on d i f f e r e n t magnetic s u b l a t t i c e s ( a and b) i n t e r a c t v i a a weak a t t r a c t i v e pairing p o t e n t i a l V. I n t e r a c t i o n s between h o l o n s on t h e same s u b l a t t i c e a r e d e s c r i b e d by a c o n s t a n t r e p u l s i v e H a r t r e e - F o c k p o t e n t i a l U. The H a m i l t o n i a n d e s c r i b i n g t h i s model i s
Downloaded by UNIV OF TEXAS AT AUSTIN on August 27, 2017 | http://pubs.acs.org Publication Date: September 26, 1988 | doi: 10.1021/bk-1988-0377.ch004
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+
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Η = Σ {a | a c(eK^a+PaU)+b bK(€ c^ +p U)}-(V/A)ra b .Kb.icaif C
l
K
l
b
b
(1)
K
κ
κ
In (1) a K , b K , a K and bic a r e boson c r e a t i o n and a n n i h i l a t i o n o p e r a t o r s f o r the a and b H a r t r e e - F o c k particle states with momentum hie and k i n e t i c energy €ic=A k /2m. p and pb denote the d e n s i t i e s o f the component h o l o n gases w h i l e p and denote t h e i r r e s p e c t i v e chemical p o t e n t i a l s . In e q u i l i b r i u m , μa=μb μ» where u i s determined by the c o n d i t i o n t h a t t h e s t a t i s t i c a l average o f A Σκ ( a K a K + b K i c ) be e q u a l t o p=pa+Pb=N/A, t h e t o t a l number o f h o l o n s per u n i t a r e a (N ·•· , A · ). V i s taken t o s a t i s f y V < < U , so that the c o m p r e s s i b i l i t y o f the holon g a s , X=2p U, i s not d r a s t i c a l l y a f f e c t e d by t h e presence o f t h e second term i n ( 1 ) which d e s c r i b e s the p a i r i n g i n t e r a c t i o n . Finally, V i s restricted to o p e r a t e between h o l o n s w i t h €K ξ(Τ). F o r Τ = 0, we have ξ(0) « ( N o V p ) ~ , i . e . , o f o r d e r o n l y a few t i m e s the mean i n t e r - h o l o n d i s t a n c e p " f o r v a l u e s o f NoV ~ 0.1. By c o n t r a s t , t h e observed v a l u e s o f λ(0) a r e o f o r d e r o f 1000Â. The dependence o f λ(Τ)/λ(0) on T/T as c a l c u l a t e d from Eqs. (12) and (13) i s shown as t h e f u l l curve i n F i g s . 4 and 5. F o r weak c o u p l i n g t h i s dependence i s p r a c t i c a l l y independent o f NoV. F o r example, t h e v a l u e s o f λ(Τ)/λ(0) f o r NoV as l a r g e as 0.6 d i f f e r from t h o s e f o r NoV = 0.1 o n l y i n t h e t h i r d d e c i m a l p l a c e f o r most v a l u e s o f T/T . Thus λ(Τ)/λ(0) i s e s s e n t i a l l y a u n i v e r s a l f u n c t i o n o f T/T . In F i g . 4 t h i s dependence i s compared with the e x p e r i m e n t a l dependence measured by Cooper e t a l . ( 1 4 ) f o r YBa2Cu307_ô w h i l e F i g . 5 shows t h e comparison w i t h the d a t a o f A e p p l i e t a l . (15) o b t a i n e d f o r L a i . 8 5 $ 0 . 1 5 C U O 4 . The agreement w i t h t h e e x t e n s i v e d a t a o f Cooper e t a l . i s p a r t i c u l a r l y e x c e l l e n t . In F i g . 6 we have p l o t t e d t h e c a l c u l a t e d v a l u e s o f λ(Τ)/λ(0) v e r s u s (T/T ) i n o r d e r t o check the e x p e r i m e n t a l l y r e p o r t e d low temperature T dependence o f λ(Τ)-λ(0). I t i s seen that the t h e o r e t i c a l dependence i s indeed c o n s i s t e n t w i t h a T dependence, p r o v i d e d t h a t Τ i s n o t t o o low. We note t h a t i n t h e a c t u a l T / T * 0 l i m i t , Eqs. (12) and (13) p r e d i c t 1/2
1 / 2
c
c
c
Γ
2
c
2
2
c
λ(Τ)/λ(0) = 1 + 3
c(3)k T /2T A (0) 2
3
B
2
0
(14)
However, t h i s temperature regime, which r e f l e c t s t h e u l t r a low temperature limit o f the e x c i t a t i o n spectrum o f the holon s u p e r c o n d u c t o r , s e t s i n o n l y f o r k B T < < A ( 0 ) . S i n c e Δ(0) ~ NfjVkBTo, this temperature c r i t e r i o n i s T/T <
