~
Solid State Communications, Printed in Great Britain.
Vol.49,No.4, pp.335-338,
POLARIZED
REFLECTANCE
H.P.Geserich Institut
f~r a n g e w a n d t e
Physik, Federal
]984.
SPECTRA
0038-1098/84 %3.00 + .00 Pergamon Press Ltd.
OF NbSe~
and G . S c h e i b e r
U n i v e r s i t ~ t Karlsruhe, Republic of Germany
D-7500
Karlsruhe,
F.L4vy Institut
de Physique
Appliqu&e,
EPF Lausanne,
CH-IO]5
Lausanne,
Switzerland
and P. Monceau Centre
de Recherchessur Les Tr~s Basses Temperatures, F-38042 Grenoble Cedex, France (Received
Sept.
]5,
CNRS,
]983 by M.Cardona)
The optical r e f l e c t a n c e of NbSe3 single crystals was i n v e s t i g a t e d in the energy range b e t w e e n 0.]5 and 5 eV under i r r a d i a t i o n with p o l a r i z e d light. For light polarized p e r p e n d i c u l a r to the m e t a l l i c axis the crystals exhibit the optical b e h a v i o u r of a semiconductor, whereas for light p o l a r i z e d parallel to the m e t a l l i c axis a strongly damped plasma edge below ] eV is observed. The e x p e r i m e n t a l data are analyzed in terms of a L o r e n t z - D r u d e model in order to determine the electrical conductivity, the effective mass and the collision time of the free carriers, the width of the c o n d u c t i o n band, and the c o n t r i b u t i o n of interband absorption.
forming slabs of IO ~ thickness which are held toghether in the a direction by van der Waals bonds. The crystals have w e l l - r e f l e c t i n g surfaces with a m e t a l l i c luster. The r e f l e c t a n c e spectra were taken by a s i n g l e - b e a m s p e c t r o m e t e r e s p e c i a l l y adapted to tiny crystals. Fig.] shows the r e f l e c t a n c e spectra of
The transition metal t r i c h a l c o g e n i d e NbSe3 is a highly a n i s o t r o p i e m e t a l l i c conductor, c o n s i s t i n g of n i o b i u m chains w h i c h are located in the center of tritonal s e l e n i u m prisms 1. Due to this quasi-one-dimensional (]d) structure NbSe3 u n d e r g o e s two i n d e p e n d e n t charge density wave transitions at 145 K and 59 K with incommensurate spanning vectors 2. This leads to many unusual electrical properties a s s o c i a t e d with the motion of charge density waves 3-10. It is the aim of the present paper to contribute to the e x p l a n a t i o n of these f a s c i n a t i n g e l e c t r i c a l effects by d e t e r m i n i n g from optical data at room t em p e r a t u r e some e l e c t r o n i c transport parameters such as the conductivity, the c o l l i s i o n time and the e f f e c t i v e mass of the charge carriers, and the width of the c o n d u c t i o n band. The crystals i n v e s t i g a t e d were grown from the vapor phase as d e s c r i b e d in ref.]]. Single crystals with the shape of fibrous ribbons with a length of several mm, a w i d t h up to 250 ~m and a thickness of a few Um were obtained. The t w o - d i m e n s l o n a l shape of the monoclinic crystals reflects that the infinite s e l e n i u m prisms e x t e n d i n g along the b d i r e c t i o n are linked together in the c d i r e c t i o n by n i o b i u m - s e l e n i u m bonds b e t w e e n n e i g h b o u r l n g prisms,
100
80
6O
~~0 ~J ~U
cw 2O
.1
0.5
1
2
IcY) Fig.!
This work was s u p p o r t e d Volkswagenwerk.
0.2
by Stiftung
335
P o l a r i z e d r e f l e c t a n c e spectra of a NbSe3 single crystal Dashed line: L o r e n t z - D r u d e fit.
Vol. 49, No. 4
POLARIZED REFLECTANCE SPECTRA O F N b S e 3
336
one of t h e s e c r y s t a l s at r o o m t e m p e r a ture u n d e r i r r a d i a t i o n w i t h p o l a r i z e d light, w h e r e the d i r e c t i o n of the inc i d e n t light is p e r p e n d i c u l a r to the slabs. If the p o l a r i z a t i o n is p a r a l l e l to the axis of the n i o b i u m c h a i n s , the s p e c t r u m o b t a i n e d i n d i c a t e s o p t i c a l abs o r p t i o n b y free c a r r i e r s . The r e f l e c t a n c e r e a c h e s h i g h v a l u e s at l o w e r p h o ton e n e r g i e s , f o l l o w e d by a s m o o t h p l a s m a edge b e l o w I eV. At h i g h e r p h o t o n e n e r g i e s the r e f l e c t i v i t y is d o m i n a t e d by i n t e r b a n d t r a n s i t i o n s . If the direction of p o l a r i z a t i o n is p e r p e n d i c u l a r t o the c h a i n axis, the m e t a l l i c b e h a v i o u r v a n i s h e s and the c r y s t a l s show the optical b e h a v i o u r of a s e m i c o n d u c t o r w i t h r e l a t i v e l y high, b u t n e a r l y c o n s t a n t v a l u e s of the r e f l e e t i v i t y . It is i n t e r e s t i n g to n o t e that the m e t a l - l i k e l u s t e r of the c r y s t a l s is not due to the f r e e - c a r r i e r a b s o r p t i o n b u t is c a u s e d by the h i g h v a l u e s of the r e f r a c t i v e i n d e x for the p o l a r i z a t i o n d i r e c t i o n p e r p e n d i c u l a r to the m e t a l l i c c h a i n s . The r e f l e c t a n c e s p e c t r u m Rwl w a s e v a l u a t e d by a L o r e n t z - D r u d e m o d e l of the following form n
~2
~2
Ne 2 £o~m~
terms
results
= lO = 1 . 1 5 eV = IxlO -Is sec.
= ~ Tp ~
In F i g . 2 a and 2b the s p e c t r a l d e p e n d e n c e of the real p a r t £i, and of the i m a g i n ary p a r t E211of the d i e l e c t r i c f u n c t i o n are p l o t t e d v e r s u s a l o g a r i t h m i c e n e r g y scale. B o t h c u r v e s r e f l e c t the s t r o n g d a m p i n g of the free c a r r i e r s and the inf l u e n c e of the i n t e r b a n d t r a n s i t i o n s . It s h o u l d be e m p h a s i z e d that due to the s t r o n g c o n t r i b u t i o n of the L o r e n t z o s c i l l a t o r s to ~I! the p l a s m a f r e q u e n c y def i n e d by e q . ( 2 ) does n o t c o i n c i d e e x a c t l y
20 E
10
(l)
-10
The c o n t r i b u t i o n to the d i e l e c t r i c f u n c t i o n f r o m the v a c u u m p o l a r i z a t i o n and f r o m t r a n s i t i o n s b e y o n d the m e a s u r e ment l i m i t of 5 eV are l u m p e d t o g e t h e r in e~. The m p n d e n o t e the s t r e n g t h s , the ~ o n the e i g e n f r e q u e n c i e s and the r n the d a m p i n g c o n s t a n t s of the e l e c t r o n i c t r a n s i t i o n s , w h i c h are r e s p o n s i b l e for the s t r u c t u r e of the r e f l e c t i v i t y b e t w e e n 0.7 and 5 eV. In the d e f i n i t i o n of the p l a s m a f r e q u e n c y of the free carriers
P
the D r u d e
to o
e(o)) = ~ + ~ pn + P oo I ~02 - O~2-it0~ a2+ito/x on n
~2
For
O0.1
-2
I
,
,
0.2
I
,,,,I
0.5
I
1
2
100
(2)
30 the d i e l e c t r i c s c r e e n i n g due to e l e c t r o nic t r a n s i t i o n s a b o v e 5 eV is i n c l u d e d . N, m ~ and T d e n o t e the c o n c e n t r a t i o n , the e f f e c t i v e m a s s and the c o l l i s i o n time of the free c a r r i e r s . The d a s h e d line in Fig.l r e p r e s e n t s the b e s t fit of the L o r e n t z - D r u d e m o d e l to the e x p e r i m e n t a l data. The f o l l o w i n g v a l u e s for the L o r e n t z o s c i l l a t o r s are obtained: ha = 0.93 hF? I = 0.27 hapl = 0.95
eV eV eV
ha = 1.52 hF~ ~ = 0 . 3 2 hap2 = 0.65
eV eV eV
h~o~ hr3 h~p3
eV eV eV
h~o~ hF~ hap4
eV eV eV
= 2.00 = 0.31 = 0.67
h~ = 3 . 8 0 eV hF~ s 1.13 eV h m p s = 7.50 eV
= 2.34 = 0.31 = 0.65
10
% %
1 0.1
I
02
,
,
I ....
05
I
%1
I
2
5
t~w leVi Fig.2
S p e c t r a l d e p e n d e n c e of the real part (a) and the i m a g i n a r y p a r t (b) of the d i e l e c t r i c f u n c t i o n of N b S e 3 p a r a l l e l to the c h a i n axis. D a s h e d line: c o n t r i b u t i o n of Drude-type.
Vol. 49, No. 4
POLARIZED REFLECTANCE SPECTRA OF NbSe 3
w i t h the p o s i t i o n of the m a x i m u m e n e r g y loss f u n c t i o n -Im(I/ell). A c c o r d i n g to the r e l a t i o n
C(~)
=
E2(~)EO~
of
the
(3)
the i m a g i n a r y p a r t of the d i e l e c t r i c f u n c t i o n e21 was t r a n s f o r m e d into the real p a r t of the c o n d u c t l v l t y f u n c t z o n o|i. In F i g . 3 this f u n c t i o n is p l o t t e d v e r s u s a l i n e a r e n e r g y scale. The d a s h e d lines r e p r e s e n t the s e p a r a t e c o n t r i b u t i o n s of the free c a r r i e r s o D a n d of the i n t e r b a n d t r a n s i t i o n s o L. By e x t r a p o l a t i o n of the c o n t r i b u t i o n of the free c a r r i e r s tow a r d s zero e n e r g y one o b t a i n s f r o m the relation
Co
= ~2p
Eo ~
~
(4)
a v a l u e of ODii = 2.6 x]O3(~cm) -I as an o p t i c a l l y d e t e r m i n e d v a l u e for the dcc o n d u c t i v i t y at r o o m t e m p e r a t u r e . This value shows only very little variations b e t w e e n d i f f e r e n t s a m p l e s . In c o n t r a s t to that the c o r r e s p o n d i n g v a l u e s d e t e r m i n e d by e l e c t r i c a l m e a s u r e m e n t s v a r y a b o u t the w i d e r a n g e b e t w e e n 1.6xlO3(~cm) -I and m o r e t h a n ] O ~ ( ~ c m ) -I 4 , 7 , 1 0 , ] 2 , 1 3 . In o r d e r to c l a r i f y t h e s e d i f f e r e n c e s we p l a n to e x t e n d the o p t i c a l m e a s u r e m e n t s to l o w e r e n e r g i e s . As p o i n t e d out in r e f . l O , a d i s c u s s i o n of the c h e m i c a l b o n d s in N b S e 3 leads to a free c h a r g e of 2 = 0.5 e l e c t r o n s per n i o b i u m atom, c o r r e s p o n d i n g to a free c a r r i e r c o n c e n t r a t i o n of N n = 3.9 x ]O21cm-3. This i m p l i e s , that we p r e f e r to d e s c r i b e N b S e 3 at r o o m t e m p e r a t u r e as a n - t y p e c o n d u c t o r and not as a s e m i m e t a l w i t h s m a l l p o c k e t s of e l e c t r o n s and h o l e s as p r o p o s e d by Ongl4, 15. K n o w i n g the v a l u e of Nn, the e f f e c t i v e m a s s of the free c h a r g e c a r r i e r s m a y be c o m p u t e d to m * = 0 . 4 0 m o. This v a l u e is c o n s i d e r a b l y s m a l l e r than the free e l e c tron m a s s , w h i c h is a t y p i c a l v a l u e for the e f f e c t i v e mass of m a n y o r g a n i c ]dm e t a l s 16,17 but it is m o r e than t w i c e as l a r g e as the e f f e c t i v e mass of the ino r g a n i c I d - c o n d u c t o r K C P 18 On the b a s i s of a t i g h t b i n d i n g m o d e l the b a n d w i d t h 4t f o l l o w s f r o m =
(5) m ~ b s i n ( k F • b)
w h e r e b = 3.48 ~ d e n o t e s the d i s t a n c e b e t w e e n two n i o b i u m a t o m s a l o n g the c h a i n axis and k~ the F e r m i v e c t o r , which can be c a l c u l a t e ~ f r o m the free c h a r g e per n i o b i u m a t o m a c c o r d i n g to the relation kF
= (p/2)
b e c a u s e in N b S e 3 six niobium chains in nonequivalent positions exist,resulting in a s i x fold s p l i t t i n g of the c o n d u c t i o n band. N e v e r t h e l e s s the v a l u e for the cond u c t i o n b a n d w i d t h g i v e n here is v e r y c l o s e to the b a n d w i d t h r e s u l t i n g f r o m the b a n d s t r u c t u r e c a l c u l a t i o n s of Bullet 20. A f t e r d i s c u s s i n g the c o n t r i b u t i o n of D r u d e type to the o p t i c a l a b s o r p t i o n , we w i l l turn to the c o n t r i b u t i o n of L o r e n t z type o~ (Fig.3). T a k i n g into a c c o u n t the B u r s t e l n s h i f t due to the o c c u p i e d s t a t e s in the c o n d u c t i o n band, the t h r e s h o l d e n e r g y for d i r e c t t r a n s i t i o n s b e t w e e n v a l e n c e and c o n d u c t i o n b a n d s h o u l d be h i g h e r t h a n ] eV. If this is true, the lowest oscillator-like s t r u c t u r e at 0.9 eV c a n n o t , as d i s t i n g u i s h e d f r o m the a b s o r p t i o n at h i g h e r e n e r g y , be a t t r i b u t e d to i n t e r b a n d t r a n s i t i o n s . On the o t h e r h a n d , this a b s o r p t i o n s t r u c t u r e is c o r r e l a t e d w i t h p e a k s of the e n e r g y loss f u n c t i o n b e t w e e n 0.75 and ].05 eV. As f o u n d e a r l i e r in the ] d - c o n d u c t o r KCP, such an a b s o r p t i o n p e a k can be exp l a i n e d by i n e l a s t i c s c a t t e r i n g of the free c h a r g e c a r r i e r s w i t h s i m u l t a n e o u s e m i s s i o n of p l a s m o n s 18. For a q u a n t i t a tive i n v e s t i g a t i o n of this e f f e c t
3 • 103 I
2 • 10 ~
I
E
"T ~
0
(T/b).
(6)
With p = 0.5 a value of k F = 0.25 ~/b follows in good agreement with the experimental value of k F = 0.243 ~/b determined from the superlattice wave vector below 145 K 1 9 , l e a d i n g to a value of 4t = 3.5 eV for the c o n d u c t i o n b a n d width, I n d e e d this b a n d m o d e l is h i g h l y simplified,
103
~"
0
I
1
I
I
2
I
--
3
(eV) Fig.3
2h 2 k F 4t
337
S p e c t r a l d e p e n d e n c e of the e l e c t r i c a l c o n d u c t i v i t y of N b S e 3 p a r a l l e l to the c h a i n axis. D a s h e d lines: c o n t r i b u t i o n of D r u d e (OD) and of L o r e n t z - t y p e
(on). f u r t h e r m e a s u r e m e n t s in c o n j u n c t i o n w i t h a Kramers-Kronig a n a l y s i s w i l l be done. As m e n t i o n e d above, the i n c r e a s e of the o p t i c a l a b s o r p t i o n a b o v e 1.2 eV is c a u s e d by i n t e r b a n d t r a n s i t i o n s , w h e r e the s t r u c t u r e in Oil(~) , or e21~(~) resp e c t i v i l y , r e f l e c t s the s t r u c t u r e in the j o i n e d d e n s i t y of s t a t e s due to the com-. p l e x s t r u c t u r e of the v a l e n c e and cond u c t l o n b a n d s in N b S e 3 2 0 .
338
POLARIZED REFLECTANCE SPECTRA OF NbSe 3
In summary the optical reflectance spectra give clear evidence for a strong electrical anisotropy of NbSe~ within the slabs formed by the li~ked selenium prisms. Whereas in the direction along the niobium chains metallic behaviour is observed, the crystals show semicon-
Vol. 49, No. 4
ducting properties perpendicular to these chains. From the metallic reflectance some important electronic transport parameters are determined. This work will be continued by optical investigation of the charge density wave transitions.
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A.Meerschaut and J.Rouxel, J.LessCommon Metals 39, 197 (|975). 2) P.Haen, P.Monceau, B.Tissier, G.Waysand, A.Meerschaut, P.Molinie and J.Rouxel, Proceedings of the 14th International Conference on Low Temperature Physics, Otaniemi, Finland 1975, Vol.5, p.445. 3) P.Monceau, N.P.Ong, A.M.Portis, A.Meerschaut, and J.Rouxel, Phys.Rev. Letters 37, 602 (1976). 4) N.P.Ong and P.Monceau, Phys.Rev. Bl_~6, 3443 (1977). 5) R.Fleming and C.C.Grimes, Phys.Rev. Letters 42, 1423 (1979). 6) A.Briggs, P.Monceau, M.Nunez-Re~eiro. J.Peyrad, M.Ribeault and J.Richard, J.Phys.C 13, 2117 (1980). 7) P.Monceau, J.Richard, and M.Renard, Phys.Rev. Letters 45,43 (1980) 8) G.Grfiner, L.C.Tippie, J.Sanny, W.G. Clark, and N.P.Ong, Phys,Rev. Letters 45, 935 (1980). 9) R.Fleming, Phys.Rev. B 22, 5606(1990) I0) P.Monceau, J.Richard, and M.Renard, Phys. Rev. B 25, 93| (1982) and B25, 948 (1982)
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