8/3/2019 Marcello B. Silva Neto- Charge stripe order from antiphase spin spirals in the spin-Fermion model

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a

rXiv:cond-mat/060

9539v1

[cond-mat.str-el]21Sep200

6

2x x 4

J

px py 3dx2y2

++

t

JK

J

2x x 4 x > 5.5%

2x x 4

H = Ht + HK + HJ

Ht = t

i,j,

(pi,pj, + h.c.) i

pi,pi,

HK =JK

2

i,,

Si pi, pi,

HJ = Ji,j

Si Sj ,

pi, i t

JK

++

J

JK/t

tJ

http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1http://arxiv.org/abs/cond-mat/0609539v1

8/3/2019 Marcello B. Silva Neto- Charge stripe order from antiphase spin spirals in the spin-Fermion model

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Si = (0, 0, S)

HK = (JK/2)S

i(pi,pi, pi,pi,)

t > J 2x x 4 t/J 3

(2)

U(xi) = eii/2 = cos

i

2

+ i

sin

i

2

.

(2)

pi,pi,

= U(xi)

ci,ci,

,

i = q xi,

q = (, ) EAF = 4N JS2 N

0

0

q = (qx, ).

Ht = t

i,j,

cos

q (xi xj)

2

(ci,cj, + h.c.)

ti,j

sin

q (xi xj)

2

(ieici,cj, ie

icj,ci,),

HK =JKS

2

i

(ci,ci, ci,ci,),

HJ = 2NJS2 [1 cos qx] .

Antiphase or spirals

... n1 n n + 1 ...

m

m+1

Inphase or 0spirals

clockwise

clockwise

clockwise

clockwise

counter

(1, 0)

m

(1, 0)

m

m + 1

Ht

HJ 4N JS2

H =k

( ck, ck, )

0

(k) +

JKS

2 2

(k)2(k) 0(k) JKS

2

ck,ck,

,

0(k) = 2t cos kx cos qx2

,

2(k) = 2t

sin kx sinqx2

+ sin ky

.

0 (k) = 0(k)

22(k) + JKS

22

,

k0 = (/2, /2)

0

0

E0kin =k

0 (k)( 0 (k)),

8/3/2019 Marcello B. Silva Neto- Charge stripe order from antiphase spin spirals in the spin-Fermion model

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n

ty

2t

2t

1 32 4 5 6 87

t2

2 t_

= 1/8

(JKS)/2 JK/t 1 kF =

2

0

qm = (()mqx, ),

m

++

m n

Ht = t m,n,

cos qx2

(c(m,n+1)c(m,n) + h.c.)

tm,n,

sin(nqx)(c(m+1,n)c(m,n) + h.c.)

+ tm,n

cos(nqx)(ieic

(m+1,n)c(m,n) + h.c.)

+ tm,n

cos(nqx)(ieic(m+1,n)c(m,n) + h.c.)

HK =JKS

2

m,n

(c(m,n)c(m,n) c(m,n)c(m,n))

HJ = 2N JS2 cos qx.

0

n = 2, 6

n = 0, 4, 8

0

H =k

( ck, c

k+q, c

k, c

k+q, )

0(k) +JKS2

(k) ei2(k) ei(k)(k) 0(k + q) + JKS2 ei(k) ei2(k + q)

ei2(k) ei(k) 0(k) JKS2 (k)ei(k) ei2(k + q) (k) 0(k + q) JKS2

ck,ck+q,

ck,ck+q,

.

(,) (k) =

FI(k) 2

FII(k),

8/3/2019 Marcello B. Silva Neto- Charge stripe order from antiphase spin spirals in the spin-Fermion model

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0 0.01 0.02 0.03 0.04 0.05 0.06 0 .0 7 0 .08

Hole concentration

0

0.05

0.1

0.15

0.2

ESpiral

/E

Neel

E

- -spiral

E0

- 0-spiral

0

E > E0

FI(k) = 22(k) +

20(k) + 2

2(k) +

JKS

2

2,

FII(k) = (2(k)2(k)0(k))2+

JKS

2

2(20(k)+

2(k)).

(k) = t sin ky

(k + q) = (k)

= 0 = 0 (+) (k) () (k)

0 (k)

Ekin =1

2

k

(+) (k)( (+) (k))

+

k() (k)( () (k))

,

5% 0

J = 1 t = 3 JK = 5

JK > t > J

0

S

2x x 4

0 t J

2x x 4