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The Coulomb Anomaly in Strongly Disordered FiiA4
' Shih-Ying Hsu and J.M. Valles, Jr.
Department of Physics, Brown University, Providence, Rhode Island 02912
Electron tunneling measurements of the Coulomb anomaly in the density of states in strongly
-
disordered quench condensed granular films are presented. The strength of this anomaly grows
with increasing sheet resistance, RN, at low RN but saturates at high RN. We suggest that the
granular morphology of these films is responsible for the saturation.
1. INTRODUCTION 2. SAMPLES
r Increases in the static disorder in metal The disordered films were deposited onto
films degrades the screening capabilities of cooled substrates (-' 8K) on which an oxi-
the conduction e-, increases spatial correla- dized Al strip had been previously deposited.
tions among them and thus, increases the ef- The disordered film and Al strip served as
fective e- - e- interactions. This leads to a the tunnel junction electrodes. Four termi-
decrease of the density of states about EF. nal measurements of G,(V) were performed
[1 - 3] In two dimensional weakly disordered at 8K in situ. In fact the normal state con-
systems, this decrease is given by [4]: ductance Gj(V) does not depend on temper-
ature for eV > kIT. Wehave measured Gi IV)
5N ) I 1-of granular Pb and Sn films with RN ranging
6N(E) = ,n)l( IE - EFTeL) (1) from 10fl (kpl ; 1) up to 70kfl (kF "- .04).
No h Gj(V) can be written
where A, depends on the strength and form 0= N f(B + eV) P(E)dF
of the effective e- - e- interactions, I is the Gj(V) f 0f0 +(eV)
mean free path, e is the localization length
and (cid:127)r.-' is the rate of elastic collisions. This a ..
density of states anomaly appears as an n where E is the energy relative to EF, f is the 0_1
maly in the conductance as a function of volt- Fermi distribution, V is the voltage across a
age, G,(V) of tunnel junctions with a disor- junction, NA, is the density of states for the
dered film as one of the electrodes. Here, we Al strip and NFpi, is the density of states
present preliminary studies of this anomaly for the investigated film. P(E) is the tun-
in films that range from the weakly disor- neling probability. We normalized all curves '.
dered limit, where this theory applies, to the by the lowest RN film for each experimental 2
strongly disordered limit, where it does not. run to eliminate the effects of NAI and P(E),
We find that film morphology plays an im- so the normalized junction conductance, GN, a
portant role in determing the strength of this reveals corrections to NFiim due to disorder
anomaly and thus, the strength of the e - - effects.
interactions in strongly disordered films.
Supported by ONR N00014-92-J-1341and the A.P.Sloan Foundation
DEFENSE TECHNICAL INFORMATION CENTER
9324535
I S
3. RESULTS V(MV)
In Fig. 1 we show GN(V) vs. In(V) 5 10 15 20
for a series of granular Sn films. The dotted [3
lines are data and the solid lines show lin-
e"salro preesg igornosw. wTihthes ein creregaiosinnsg sRhrNin. k Tahned ftuhnecir- 5' ..
tional form of GN(V) at high voltages is un- E ..
clear.
We plot the slope vs. RN for Pb and ...............
Sn films in Fig. 2. At low RN these slopes
grow, but at high RN they saturate. The 1.0
sheet resistance at which they saturate, RP;,
and the saturation value are both higher in
Sn than in Pb. This saturation value appears 0.900 0.5 1.0 1.5 2.0 2.5 3.0
to scale with the inverse of the film thickness. In( V(mV) )
According to Eq.(1) the slope of this In(V) Fig. 1 granular Sn 3tOfl 970kk"
dependence corresponds to the strength of 0.14 *-."-.-
the e- - e- interactions and RN represents SC0.12
the degree of the disorder. Disorder enhances 40
the effective e--e- interactions, so the slopes >0.10 -
should grow with increasing RN. We believe S 0.08
that this observed saturation results from a 0.0"
morphology change ("granular" to "uniform") S0
that occurs near R,;. Above RN, films are 0.04
made of isolated grains and the transport prop- .30.02
erties are dominated by intergrain tunneling 0.00_1
___ _____I________
processes. Below R(cid:127), the grains start to cou- 0 10 20 30 40 50 60 70
ple together and the film becomes more uni- Sheet Resistance (kQ)
form. For the granular morphology the effec- Fig. 2 O:Sn A:Pb
tive e- - e- interactions are dominated by
grain charging effects. These depend only on REFERENCES
the intergrain capacitances which are inde-
pendent of RN. For the uniform morphology, 1. Y.Imry and Z.Ovadyahu, Phys. Rev. Lett.
where the theory applies, the effective inter- 4 841 (1982)
actions depend on RN. 2. A.E.White,R.C.Dynes and J.P.Garno, Phys.
4. SUMMARY Rev. B31, 1174 (1985)
We have measured the density of states 3 D.S.Pyun and T.R.Lemberger, Phys. Rev.
of granular Pb and Sn films with RN up to Lett. 63, 2132 (1989)
70kfl. The strength of the coulomb anomaly 4. B.L.Altshuler and A.G.Aronov, in Modem
saturates at high RN. We attribute this effect Problems in Condensed Sciences, edited by
to the granular morphology of the films. A. Efros and M. Pollak (1986)
FINAL TECHNICAL REPORT
ONR Grant N00014-92-J-1344
Principal Investigator: James M. Valles, Jr.
Work supported by this grant has resulted in five manuscripts. These manuscripts de-
scribe in detail the technical progress made. They are:
1. "Electron Tunneling Determination of the Order-Parameter Amplitude at the
Superconductor-Insulator Transition in 2D," by J.M. Valles, Jr., R.C. Dynes, and J.P.
Garno, Phys. Rev. Lett. 69, 3567 (1992).
2. "Perpendicular Upper Critical Field of Granular Pb Films Near the Superconductor-
to-Insulator Transition," by Shih-Ying Hsu and J.M. Valles, Jr., Phys. Rev. B47, 334
(1993).
3. "Magnetic-Field-induced Pair-Breaking Effects in Granular Pb Films Near the
Superconductor-to-Insulator Transition," by Shih- Ying Hsu and J.M. Valles, Jr., Phys.
Rev. B48, 4164 (1993).
4. "The Proximity Effect in Ultrathin Granular Pb Films," by Shih-Ying Hsu, J.M. Valles,
Jr., P.W. Adams, and R.C. Dynes, to be published in the Proceedings of LT20.
5. "The Coulomb Anomaly in Strongly Disordered Films," Shih-Ying Hsu and J.M.
Valles, Jr., to be published in the Proceedings of LT20.
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