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THE CHANGE OF THE CONNECTIV1TY OF Bi
ELECTRON FERMI SURFACE UNDER PRESSURE
N. Brandt, V. Moshalkov, S. Chudinov
To cite this version:
JOURNAL DE PHYSIQUE
Colioque C6, supplPment au no 8, Tome 39, aofit 1978, page
C6-1106
THE CHANGE
OF THE
CONNECTIVITYOF
B i ELECTRONFERMI
SURFACE UNDER PRESSUREN.B. Brandt, V.V. Moshalkov, S.M. Chudinov
Low Temperature Laboratory, Physics Department, Moscow State University, USSR
R6sum6.- On a 6 t a b l i que sous I ' i n f l u e n c e de l a p r e s s i o n h y d r o s t a t i q u e l a s u r f a c e de Fermi d e s d l e c t r o n s (FSE) du bismuth p a s s e d'une forme q u a s i e l l i p s o I d a l e P c e l l e d'une "poign6e". Le "col" d e s poign6es diminue sous l a p r e s s i o n e t on observe l a r u p t u r e de FSE en deux s u r f a c e s i s o l 6 e s i n d u i t e par un champ magn6tique 6levB. On a d6montr6 que l e r a p p o r t des paramstres d e l a l o i de d i s p e r s i o n de McClure Q : ~ / ~ ~ e s t i n f 6 r i e u r P 0.0005 u n i t d s atomiques.
A b s t r a c t . - The t r a n s i t i o n of t h e Bi e l e t r o n Fermi s u r f a c e (EFS) from e l l i p s o i d a l t o dumb-bell shaped and t h e n t o a doubly connected shape under h y d r o s t a t i c p r e s s u r e h a s been e s t a b l i s h e d . For t h e p r e s s u r e a t i n t e r v a l , i n which t h e "neck" c r o s s - s e c t i o n becomes q u i t e s m a l l , a change of t h e c o n n e c t i v i t y of t h e EFS induced by magnetic f i e l d i s observed. The r a t i o qZ2/av of McClure's d i s p e r s i o n law parameters h a s been found t o be l e s s t h a n a t l e a s t 0.0005 a t . u n i t s .
The appearance of a s a d d l e p o i n t i n t h e i n v e r s e ( E = €(L )
-
€(L ) < 0 ) L - e l e c t r o n spec-+ gL -
trum ~ ( k ) of Bi-type semimetals was p r e d i c t e d t h e o r e t i c a l l y by Abrikosov and F a l k o v s k i i / l / . When c e r t a i n c o n d i t i o n s a r e s a t i s f i e d , t h i s phe- nomenon must b e accompanied by a q u a l i t a t i v e chan- ge of t h e EFS shape. From t h i s p o i n t of view i t was of i n t e r e s t t o i n v e s t i g a t e t h e i n f l u e n c e of h y d r o s t a t i c p r e s s u r e on t h e shape of t h e EFS because of the' p o s s i b i l i t y of making t h e e l e c t r o n Fermi l e v e l pass through t h e Ls term / 2 / . Then i f a q u a l i t a t i v e change of t h e EFS t a k e s place,. t h e e x i s t e n c e of t h e s a d d l e p o i n t a t ( € = E (LS),
+-
k = 0 ) would b e proved.
I n o r d e r t o s t u d y t h e EFS of Bi a t d i f f e - r e n t p r e s s u r e s p522 kbar, measurements of Shubni- kov-de Haas o s c i l l a t i o n s i n B i and Bi-Te monocrys- t a l l i n e samples were c a r r i e d o u t i n magnetic f i e l d s up t o 60 kOe a t helium temperatures. The harmonic c o n t e n t of t h e ShdH o s c i l l a t i o n s was de-
termined w i t h t h e h e l p of a s t a n d a r d f a s t F o u r i e r t r a n s f o r m on a Computer.
Samples of Bi s l i g h t l y doped w i t h Te have some advantages over pure Bi, i n which t h e c a r r i e r c p n c e n t r a t i o n i s known t o b e d r a s t i c a l l y reduced by p r e s s u r e / 3 / . The u s e of Bi-Te samples t h u s g i v e s t h e p o s s i b i l i t y of o b s e r v i n g d i s t i n c t l y a l a r g e number of o s c i l l a t i o n s i n t h e whole p r e s s u r e i n t e r v a l .
For
8
p a r a l l e l t o t h e l o n g e s t a x i s o f t h e Bi EFS(8
11
o s c i l l a t i o n f r e q u e n c i e s correspon- d i n g t o one of t h e t h r e e EFS depend an p r e s s u r ei n t h e f o l l o w i n g way (Figure Ib) : f o r p55 kbar only t h e monochromatic o s c i l l a t i o n s from t h e cen- t r a l minimum c r o s s - s e c t i o n of t h e EFS i s observed.
I n p r e s s u r e i n t e r v a l 5 5 ~ 5 1 2 kbar b e a t i n g o f two o s c i l l a t i o n f r e q u e n c i e s i s t a k i n g p l a c e , t h e second frequency b e i n g from t h e extremal c r o s s s e c t i o n corresponding t o t h e "belly" of t h e dumb- b e l l EFS. The d i f f e r e n c e between t h e neck (S1) and b e l l y (S2) c r o s s - s e c t i o n s i n c r e a s e s w i t h p r e s s u r e and S1 becomes equal t o zero a t pl.15 k b a r . A t t h e same time t h e o s c i l l a t i o n frequency .Q:ax c o r r e s - ponding t o t h e maximum c r o s s - s e c t i o n of t h e EFS
(HII C2) d e c r e a s e s a b r u p t l y by approximately a fac- t o r of two (Figure l a ) . Hence a t p = pc t h e change of the EFS c o n n e c t i v i t y t a k e s p l a c e .
For p r e s s u r e s pl.12-I3 k b a r , when t h e neck c r o s s - s e c t i o n i s a l r e a d y q u i t e s m a l l , o s c i l l a t i o n frequency .Q:ax diminishes by a f a c t o r of two i n high magnetic f i e l d s H235 kOe. This dependence of
on H i s a r e s u l t of t h e change of t h e EFS c o n n e c t i v i t y induced by magnetic f i e l d and o c c u r s when t h e Fermi l e v e l moving down t h e conduction band due t o t h e r e d i s t r i b u t i o n of e l e c t r o n s and h o l e s between d i f f e r e n t p o c k e t s i n h i g h magnetic f i e l d s c o i n c i d e s w i t h t h e s a d d l e p o i n t E ~ .
By s t u d y i n g p r e s s u r e dependences o f t h e extremal c r o s s - s e c t i o n s S(HI
I
CS) and S(HII
Cl) of p u r e Bi EFS t h e change of t h e EFS c o n n e c t i v i t y h a s been found a t p = p, = (13.52
0.8) kbar141.
Hence a m e t a l - i n s u l a t o r phase t r a n s i t i o n occurs i n B i a t p%26 kbar /5/, corresponding t o t h e p o i n t e l e c t r o n and h o l e FS, t a k i n g p l a c e not by t h esimilar decrease of the three EFS under pressure
but by the decrease of the six surfaces formed as
a
result of the change of the EFS connectivity at
P
=Pc.
Fig. 1
:la) The de endence of ShdH oscillation
frequency
gax
(H\PC2) on pressure. Solid line
is the calculation of
g,,
on the basis of McClu-
re's model with corrections taking into conside-
ration Fermi level shift in high magnetic fields.
Dotted line represents the calculation of the ex-
tremal cross-sections.
Ib) Pressure dependence of the EFS cross-
sections in Bi-Te,
HI
]Cl. Solid lide shows calcu-
lation on the basis of McClure's dispersion law.
Calculations on the basis of McClure's
model /6/ agree with the experimental data if the
energy spectrum of Bi at the L-points of the Bril-
louin zone is considered to be inverse
(E 0)EL
References
/l/ Abrikosov, A.A., Falkovskii, L.A., Zh ETF,
43
(1962) 1089.
/2/
Brandt, N.B., Chudinov, S.M., Karavaev,
V.G.,Zh ETF,
2
(1976) 2296.
/ 3 /
