Compatibility of BCS pairing and the peierls distortion in two-band systems

Volume 67A, number 4

PHYSICS LETTERS

21 August 1978

COMPATIBILITY OF BCS PAIRING AND THE PEIERLS DISTORTION IN TWO-BAND SYSTEMS M.E. PALISTRANT Institute of AppliedPhysics, Moldavian Academy of Sciences, USSR Received 11 May 1978

The effect of the Peierls transition on superconductivity in a two-band system, where one of the bands is flat, is examined theoretically. We find that superconductivity appears at the background of the insulating phase (Tp> Ta). At Tc> Tp only the superconducting transition is possible.

The purpose of the present paper is to investigate the relationship between the BCS superconducting and the Peierls insulating phase transition in two-band systems, where one of bandsboth is supposed to be flat. In this case we have to the consider the deviation from a half-filled zone (p ~ 0, p is the chemical potential) and the umklapp-process. The hamiltonian of the investigated system differs from that of the usual twoband problem [1] by two additional terms (He, the electron—phonon hamiltonian which precipitates the Peierls transition, E0, the lattice elastic energy which opposes crystal distortion) and by the one-dimensionality of one of the zones. H~operates on the electrons of the flat band only. Generalising the method of calculation of ref. [2] for the analysed system, where Q Q0 +qandpt&O(Qisthecharge densitywavevector, possibility Q0 = ir/d, dofissuperconductivity the chain period),appearing we may study the at the background of the insulating phase, where T T,~.We assume Tc ~ ‘y (y is the insulating gap). The value of Tc considerably depends on the correlation between ~ and p÷= p ±Wsin ~-qd,where W is the flat band

where L

=

r w —

1 [in

VP

—

],

_______

N

arctg

—

~

~‘D

2

—~

~J72

p

2

are the effective electron—electron interaction constants, N 1 and N2 are the electron state densities of the one- and three-dimensional zones, respectively, Vp is the Peierls electron—phonon interaction constant. It is easy to see that in the simple case, when Vnn’ = V, the deviation from a half-filled band (p ~ 0) leads to an increase of 7~by the factor N1 ~ exp ~ /2 2 arctg / 2 2 V7 withP the case, V7 as compared p = 0.PWhen p_ we obtain _________

—

=

—

exp

1

—

<7

<~.ç,

[—(N 2u22+n2P+n1v11)

half width. For i-~_
2111 122 (3) ±~/(N2v22+n2p+fl1v11)2÷4fl1fl2(J._v11p) ~2

2

n1 —N1(q)p÷/~p÷ —‘y N1(q)=N1/cos4qd,

, (4)

303

Volume 67A, number 4

P=

—

—

PHYSICS LETTERS

and p_ <7 < p~,superconductivity appears in the presence of a high electron state density of a flat zone, in which the insulating gap appears not exactly at the

N1 In P_

r

Fermi level. Moreover the presence of a three-dimensional zone together with a flat zone leads both to an arctg

+ N1 (q) ~ [~~—

(5) 2)

+

_______

V1P~

—

2(p~—y

in

72

________

From the two solutions (3) we take the one with the greater value of T~.For v,~’= v we have

I

expi—

I n1

+

(6)

at the background of superconductivity (Tc > T~) shows that only the solution with 7 = 0 is possible. Hence, superconductivity prevents the insulating transition. References

N2

When N2 = 0, this expression reduces to formula (46) of ref. [3]. Thus, we find the compatibility of BCS pairing and Peierls distortion in the analysed two-band model in the mean-field approximation. When r~ ~

304

increase of the total electron state density and to the increase of the factor before the exponential function in expression of ref. [3]. (6) as compared with that of the result The analysis of appearance of the insulating phase

~.0 1(p~ + V’!.L~— 72)

____

21 August 1978

[1) V.A. Moskalenko, F’iz. Metal. Metalloved. 8(1959)503. [2] K. Levin, D.L. Mills and S.L. Cunningham, Phys. Rev.

BlO (1974) 3832. [3] R.Kh. Timerov, Zh. Eksp. Teor. Fiz. 72 (1977) 2309.