Electron Tunneling in Charge-Density and Spin-Density Waves
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ELECTRON TUNNELING IN CHARGE-DENSITY AND SPIN-DENSITY WAVES X. Z. HUANG and K. MAKI University of Southern California, Department of Physics, Los Angeles, California 90089-0484 ABSTRACT First we calculate the tunneling density of states of quasi-two dimensional charge density waves (CDW) or spin density waves (SDW) in the presence of impurity scattering. Second, we consider the tunneling current between two CDWs or two SDWs. We point out the existence of new contribution, which gives rise to the a.c. current when one CDW is sliding relative to the other one. INTRODUCTION There are accumulating evidences that most of the CDW observed in the quasione dimensional compounds like NbSe 3and TaS 3are two or three dimensional. For example both the impurity concentration dependence of the threshold field [1] and the resistivity anomaly of orthorhomic TaS 3near the transition temperature [2] indicate that the CDW in o-TaS3is three dimensional. A similar analysis of the CDWs in NbSe 3indicates that they are two dimensional [3]. We have shown earlier [4] that both the tunneling density of states and the large ratio of 2G/kBT, = 11.4 14.4 (where G is the apparent energy gap) observed by the electron tunneling experiment [5,6] can be accounted for by quasitwo-dimensional model with imperfect nesting. For definiteness we take the quasi-particle
spectrum [71 E(p)
=
-2t, cos(apl) - 2tb cos(bp 2) -i
-
v(p1 - PF) -
2
tb cos(bp2) -
E0cos(2bP)
(1)
where we neglect the third transfer integral tc for simplicity. Further we simplifies Eq.(1) following Yamaji [8] and Hasegawa and Fukuyama [9] £O
=
-jtb cos(apF)(tsin2 apF)-'
For the simple nesting vector Q = (2pF,7r/b,7r/c) the last term in rise to the imperfect nesting. If we assume that E0 increases linearly with pressure, the present model describes very well both the pressure dependence transition temperature observed in NbSe3[10] and that of the SDW transition in (TMTSF)2 PF 6 [11].
(2) Eq.(1) gives the external of the CDW temperature
DENSITY OF STATES Within mean field theory the single particle Green's function in the CDW is given
by G-l(W,,P) = iw, -qv -
P3 - Ap1
(3)
where w,, is the Matsubara frequency
S=
v(p1- PF) - 2tb cos(bp 2)
S= CCos(24 2) Mat. Res. Soc. Symp. Proc. Vol. 173. @1990 Materials Research Society
(4)
264
and pi 's are the Pauli matrices operating on the spinor space consisting of the right going and the left going electrons. We also have quite similar Green's function for a SDW [12]. In the presence of impurity scattering both o,,, and A in Eq.(3) have to be replaced by 5,, and A respectively where (5)
+(r 1+
+
=
+i
=
(6)
where r1 and r 2 are the forward and the backward scattering rate due to the impurity scattering and (.-.) means the average over P2 [13]. Unlike in a superconductor the impurity suppresses both the CDW and the SDW. Therefore we assume in the following ri/AD < 0.1, where A0 is the order parameter at T = OK. Solving the gap equation we obtain S
A00
2
(r, + r 2 )
+~F r
O
dz((z -bT)X) ((z-
dooaZ (X) ((Z
-
i77
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