Microwave absorption of longitudinal Josephson plasma in cuprate high Tc superconductors

PHYSICA E EL.SEVtER

Physica C 282-287

(1997) 242 1-2422

Microwave Absorption of Longitudinal High Tc Superconductors M. Tachiki,a

S. Takahashi,b Institute

Josephson

Plasma in Cuprate

and K. KadowakiC

*National

Research

for Metals,

bInstitute

for Materials

Research,

CInstitute

for Materials

Science,

Tohoku

Sengen

1-2-1, Tsukuba

University,

The University

Sendai

of Tsukuba,

305, Japan

980-77, Japan Tsukuba,

Ibaraki

305, Japan

Longitudinal Josephson plasma in high-T, cuprates is formulated by using a intrinsic Josephson coupling model in which the charging effect due to the Cooper pair transfer between the layers is taken into account. The power absorption of microwave due to the longitudinal plasma excitation is calculated. It is verified that the sharp absorption peak observed in the microwave experiments in Bi2Sr&aCu208+6 originates from the excitation of the longitudinal plasma.

1. INTRODUCTION

2. LONGITUDINAL

PLASMA

Superconducting properties of cuprate superconductors is well described by a model in which the superconducting CuOs layers are coupled by the Josephson current through the block layers. The Josephson current coupled with the electromagnetic field generates the Josephson plasma oscillations along the c axis [1,2]. The transverse plasma (TP) wave propagating in the ab plane is a composite wave of Josephson current and electromagnetic field and has been observed by infrared reflectivity experiments in Laz_,Sr,Cu04[3]. The longitudinal plasma (LP) wave propagating along the c axis is a composite wave of the Cooper-pair charge and the longitudinal electric field. The LP is the Nambu-Goldstone mode arising from the broken phase symmetry in the superconducting phase and has a gap due to the Anderson-H&s mechanism. In this paper we formulate the longitudinal plasma in the cuprates and calculate the power absorption of microwave due to the excitation of the LP. It is clarified that the sharp resonance of microwave absorption observed in Bi&sCaCusOs+a[4-61 is caused by the LP excitation.

Let us consider a single crystal film whose surfaces are parallel to the ab plane. The microwave electric field E,” = Eoemiwt is applied parallel to c axis. Prom the current conservation the induced current across the CuOs layers is equal to the displacement current in vacuum:

where pe+i,l is the gauge invariant phase difference between the CuO2 layers labeled by e and e + 1, jo the critical current, 0 the c axis conductivity of quasi-particles, and e the high-frequency dielectric constant. The charge density p is induced in response to the scalar potential A0 as p = -(e/47rp2)Ao, where p is a charge screening length of the order of the interlayer distance s. Combining these relations with the Maxwell equations, we obtain

>

E, = at”E,o, ELJ;

(2)

with (Y = 4no/(tipe) and wp = c/X,&. If we take (Y = 0 and EO = 0, Eq. (2) has a solution corresponding to the LP with wn~ = wpdm. Assuming that electrons are specularly reflected 0921-4534/97/$17.00 0 Elsevier Science B.V. All rights reserved. PI1 SO921-4534(97)01272-O

M. Tuchiki CI al. /Physica

2422

at the surfaces

C 282-287 (1997) 2421-2422

of the film, we obtain

&!?5~’

(-l)n

n=O k, w2 + iaw,w

cos(&Z)eWiwt - $(l

+ pz1c;) ’

(3) where k, = (2n + l)r/d, d being the film thickness. The joule heat by microwave absorption, P = 1232 i3:: is calculated as dgE0” p = 2E

(4%)4 [(w/f_+)2 - 112+ aq.LJ/wp)2’

0

-5

(4)

In the microwave experiment the power absorption P is measured by varying the external magnetic field B at the fixed microwave frequency we. The magnetic field introduces vortices which reduces the effective Josephson coupling between the layers jlff = je(cospe+r,e) and works to decreases the plasma frequency w,(B) = w,(cos cpe+i,e)1/2 [2]. The microwave experiments [5] and theories [7,8] reveal that wp(B) depends on B as the plasma frequency wp(B) 0: B-1’2, which enables us to transform P from we/w,(B) to B/Be dependence via the scaling B/B0 = wg/wi(B), where Bo is the resonance field. Using Eq. (4), we calculate the power absorption P as a function of the normalized external field B/Be. Figure 1 shows the power absorption P vs B/Be. The parameter values are taken as e=25 and cr = 0.4/w. As seen in Fig. 1, the resonance peak is sharp and slightly asymmetric with respect to the resonance field Be, in agreement with the experimental result shown in Fig. 2. Such a sharp peak of the longitudinal plasma originates from the extremely small dispersion of the longitudinal plasma. If the transverse plasma is excited, the shape of the resonance peak would be very broad and highly asymmetric, since the transverse plasma has a much stronger dispersion than the longitudinal plasma. Therefore, we conclude that the sharp peak observed in BizSrzCaCuzOs+6 arises from the resonance of the microwave with the longitudinal Josephson plasma.

and

S. Takahashi,

-2

-1

0

1

2

Figure 1. Normalized power absorption tion of normalized magnetic field.

3

4

5

as a func-

1

1 Experiment

h

2 $0.5 &I

01.“‘.‘.““.,,...,, -0.4

-0.2

0.2

0.4

B ‘Cr)

Figure 2. Microwave GHz versus magnetic

2. 3. 4. 5.

REFERENCES T. Koyama,

-3

B/Be

6.

1. M. Tachiki,

-4

7. 8.

absorption spectrum at 45 field in Bi:!SrqCaCu208+~.

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