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Submitted on 1 Jan 1981
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PHONON SPECTROSCOPY OF THE
ELECTRON-HOLE-LIQUID
W. Dietsche, S. Kirch, J. Wolfe
To cite this version:
JOURNAI, DE PHYSIQUE
CoZZoque C6, suppZe'ment
au
nOl
2,Tome
42,de'cembre 1981
page
C6-447PHONON SPECTROSCOPY OF THE ELECTRON-HOLE-LIQUID
W. ~ i e t s c h e j S.J. Kirch and J.P. Wolfe
Physics Department and Materials Research ihboratory, University of IZZinois
a t Urbana-Champaign, Urbana,
I L .61 801,
U. S . A.Abstract.-We have observed t h e 2kF cut-off i n t h e phonon a b s o r p t i o n of e l e c t r o n - h o l e d r o p l e t s i n Ge and measured t h e deformation p o t e n t i a l .
Photoexcited c a r r i e r s i n Ge a t low t e m p e r a t u r e s condense i n t o m e t a l l i c drop- l e t s of e l e c t r o n - h o l e l i q u i d (EHL)
.'
These d r o p l e t s p r o v i d e a unique, t a i l o r a b l e system f o r studying t h e electron-phonon i n t e r a c t i o n i n a Fermi l i q u i d . The i n t e r -2
a c t i o n of phonons w i t h EHL was considered t h e o r e t i c a l l y by Keldysh and h a s been s t u d i e d e x p e r i m e n t a l l y u s i n g h e a t I n c o n t r a s t , we have employed mono- chromatic phonons5 t o examine t h e frequency dependence of t h e a b s o r p t i o n over t h e range of 150
- 500
GHz. The c o n s e r v a t i o n of momentum and energy i n t h e e l e c t r o n - phonon s c a t t e r i n g p r o c e s s i m p l i e s t h a t o n l y phonons w i t h wave v e c t o r s up t o t w i c e t h e Fermi wave v e c t o r a r e absorbed--
l e a d i n g t o a 2k c u t - o f f . One unique f e a t u r eF
of t h e e l e c t r o n - h o l e l i q u i d i s t h a t k can be changed by applying c r y s t a l s t r e s s , a F
f e a t u r e which we have e x p l o i t e d .
The i n s e t i n Fig. 1 shows our experimental set-up. Two superconducting t u n n e l j u n c t i o n s , a PbBi g e n e r a t o r (G) and an A 1 d e t e c t o r (D),were placed on o p p o s i t e f a c e s of t h e u l t r a - p u r e Ge c r y s t a l n e a r one edge. A cloud of EHL d r o p l e t s was c r e a t e d a t t h a t f a c e using a cw Nd: YALG l a s e r ( A = 1.06um). The p o s i t i o n , s i z e , and shape of t h e cloud was determined by d i r e c t l y imaging i t s recombination luminescence. 6
We s t u d i e d phonons propagating in t h e [ I l l ] d i r e c t i o n , and found a measurable a b s o r p t i o n only f o r l o n g i t u d i n a l phonons (LA). I n t h e [ I l l ] d i r e c t i o n , phonon a b s o r p t i o n i s expected t o be dominated by t h e s i n g l e [ l l l ] v a l l e y , because a l l t h e o t h e r v a l l e y s (and t h e h o l e s ) have much s m a l l e r cut-off f r e q u e n c i e s . A p p l i c a t i o n of s t r e s s a l o n g t h e [ l l i ] d i r e c t i o n g r a d u a l l y d e p o p u l a t e s t h e [ I l l ] v a l l e y . T h i s l e a d s t o a r e d u c t i o n of k along [ I l l ] and t h u s t o a r e d u c t i o n i n t h e cut-off
F frequency of t h e phonons.
Two LA phonon s p e c t r a taken a t zero s t r e s s a r e shown i n Fig. 1. The
frequency i s v a r i e d by sweeping t h e g e n e r a t o r b i a s v o l t a g e , w h i l e t h e monochromatic s i g n a l i s provided by a n a d d i t i o n a l p u l s e modulation. Time of f l i g h t s e p a r a t i o n allowed r e s o l u t i o n of t h e d i f f e r e n t modes. Two f e a t u r e s were t y p i c a l of a l l t h e d a t a : a r i s e i n i n t e n s i t y which begins a t 150 Qiz ( F l ) due t o t h e d e t e c t o r t h r e s h o l d and a d e c r e a s e which ends a t 530 GHz (F2) due t o i s o t o p e s c a t t e r i n g . "Present a d d r e s s : Physik Department, TU Miinchen, F.R.G.
JOURNAL DE PHYSIQUE PHONON E N E R G Y ( m r V ) F i g . 1: Phonon s i g n a l v s . f r e q u e n c y , z e r o s t r e s s . L I I I 1 0 200 400 600
PHONON FREQUENCY IGHr)
Between F1 and F2, t h e s i g n a l c o n s i s t s of a monochromatic p a r t and a background. T h i s background i s a common f e a t u r e i n t u n n e l - j u n c t i o n s p e c t r o s c o p y and i s a t t r i b u t e d t o 2A-phonons and i n e l a s t i c decay p r o d u c t s . Below F1 and above F2 o n l y background phonons a r e d e t e c t e d . Between F1 and F2 t h e background w i l l l i e between t h e i n t e r p o l a t i o n s (1) and (2) a s i n f e r r e d from e a r l i e r s p e c t r o s c o p i c work. 5 The a c t u a l cloud-on and cloud-off phonon i n t e n s i t i e s c a n now be compared. Assuming a phonon a b s o r p t i o n of t h e form I = I exp ( - d / l ) , where d i s t h e e f f e c t i v e EHL t h i c k n e s s and 1 is t h e a b s o r p t i o n l e n g t h , t h e r e s u l t i n g d / l a r e p l o t t e d i n F i g . 2a. The e n d s o f t h e e r r o r b a r s i n d i c a t e t h e r e s u l t s o b t a i n e d by u s i n g t h e two a l t e r - n a t i v e backgrounds. A s i m i l a r p r o c e d u r e l e d t o t h e p l o t s i n F i g . 2 (b) and ( c ) f o r two m o d e r a t e s t r e s s e s .
PHONON ENERGY (msVI
F i g . 2: d ( e f f
.
EHL t h i c k n e s s ) / l ( a b s o r p t i o n l e n g t h ) v s . f r e q u e n c yThe dashed l i n e s i n F i g . 2 a r e f i t s t o d e f o r m a t i o n p o t e n t i a l s c a t t e r i n g t h e o r y f o l l o w i n g t h e p r o c e d u r e of
on well.^
The t h e o r e t i c a l cut-of f s a r e r a t h e r broad b e c a u s e t h e sound v e l o c i t y i s comparable t o t h e F e r m i v e l o c i t y i n t h e EHL. The f r e q u e n c y dependence o f our d a t a a g r e e s remarkably w e l l w i t h t h e t h e o r y . At z e r ostress t h e e x p e r i m e n t a l c u t - o f f was o b s c u r e d by t h e i s o t o p e s c a t t e r i n g . A t i n c r e a s i n g s t r e s s t h e cut-off i s observed t o move t h r o u g h t h e e x p e r i m e n t a l f r e q u e n c y r a n g e .
An e f f e c t i v e t h i c k n e s s , d z l l y m , was determined from a n a n a l y s i s of t h e imaging d a t a . T h i s v a l u e i s s u f f i c i e n t l y l a r g e r t h a n a t y p i c a l d r o p l e t r a d i u s of about 2um. With t h i s v a l u e of d , t h e a b s o r p t i o n d a t a of Fig. 2 y i e l d t h e d e f o r -
2 m a t i o n p o t e n t i a l
Z
= (+
Z
)' = (15f?)
eV independent of s t r e s s . u d Our v a l u e o f t h e phonon d e f o r m a t i o n p o t e n t i a l is c l o s e t o t h e s t a t i c d e f o r m a t i o n 2 p o t e n t i a l , 8 49 eV f o r s i n g l e e l e c t r o n s i n Ge. I n c o n t r a s t , a r e c e n t t h e o r e t i c a l 2 p r e d i c t i o n 9 f o r t h e s c r e e n e d e l e c t r o n s i n t h e EHL y i e l d e d 149 eV.
I n summary, by u s i n g t h e method of phonon s p e c t r o s c o p y we have o b t a i n e d t h e f i r s t e x p e r i m e n t a l measurement of t h e phonon d e f o r m a t i o n p o t e n t i a l of EHL i n Ge and d e m o n s t r a t e d a fundamental p r o p e r t y o f t h i s Fermi l i q u i d
--
t h e 2kF c u t - o f f .T h i s work was s u p p o r t e d by NSF u n d e r t h e ?lRL Grant PMR-77-23999. REFERENCES
1. T. M. R i c e and J. C. H e n s e l , T. G. P h i l l i p s , and G. A. Thomas, S o l i d S t a t e P h y s i c s
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