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Optical properties and superconductivity of NbSe2
Solid State Communications
Vol. 9, pp. 57—60, 1971.
Pergaom Press.
Printed in Great Britain
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2* R. Bachmann, H.C. Kirsch,t and T.H. Geballe* Bell Telephone Laboratories, Allentown, Pa. and Murray Hill, N.J.
(Received 18 October 1970 by J.L.Olsen)
The optical absorption of NbSe2 was measured by a scanning calorimetric technique in the spectral range of 0.38 to 3.2 eV. Freeelectron-like behavior is observed below 1 eV and the plasma frequency is determined by fitting the reflectance with Drude functions. Using this plasma frequency and the d.c. resistivity a value for the electron—phonon coupling constant, A, can be estimated.
THE STRUCTURAL, optical and electrical properties of the transition metal dichalcogenides TX2 have been comprehensively described by Wilson and Yoffe.’ Recently, the superconducting TaX 2 and NbX2 have attracted renewed interest because it was found that these layered compounds can be intercalated with organic molecules forming stoichiometric organometallic compounds with somewhat different superconducting transition temperatures.2 Presently we are carrying Out a series of optical measurements on these new materials with particular emphasis on their infrared properties. It seemed appropriate to use NbSe 2 as a standard within the group of NbX2 and TaX2 compounds. It can easily be grown by iodine *
transport as large single crystals with natural surfaces of good optical quality and chemical stability. Also, its reflection spectrum has 3 already been measured at energies above 1 eV. The optical absorption A = 1 R of NbSe2 was measured at 2 K by a scanning calorimetric technique, similar to methods which 4and have by Beaglehole~ been used by Biondi and Rayne Measuring the absorption by such calorimetric techniques is superior to standard reflection measurements both in case of highly reflecting —
samples (R 1) and in case of macroscopically uneven surfaces. The apparatus is shown schematically in Fig. 1. Two silicon bolometers are mounted below the two holes in the bottom of the light pipe.’ The low-temperature-sensitive resistor is a thin layer diffused on one side of an otherwise insulating Si wafer. This sensitive side
The research at Stanford was sponsored by the U.S. Air Force Office of Scientific Research, Office of Aerospace Research, under Grant No. AFOSR 68—1510C.
is cut diagonally through the contact pads into two halves, thus making two bolometer elements on each wafer. One half of each wafer is connected into an s.c. bridge, and the absorbed light power can be measured by the resistance change. The same change can be produced by shutting of the
t Predoctoral fellow sponsored by Bell Telephone
Laboratories, Allentown, Pa. * Also at Bell Telephone Laboratories, Murray
Hill, N.J. 57
58
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe
MONOCHROMATOR
then replaced by the sample, whose absorption is
L
measured with reference to the black bolometer. In order to test the system we have measured the / i
________
________
BoF, WINDOW
________
LIGHT PIPE
—
SAMPLE
—
COPPER BLOCK
I
I
‘\
absorption spectrum of a thick (5000 A) gold film
evaporated on a sapphire slide. The results were in excellent agreement with published data.7 Figure 2 shows the results of a measurement on a single-crystal of NbSe 2 as grown (surface .L c-axis). In order to compare measurements 3 weour have plotted the directly with existing data reflectance. For different crystals this spectrum
- -
I —
Vol. 9, No. 1
—
‘~
L~~~11~J —
—T
reproduced within about 10 per cent. This
—
reproducibility assures us that surface effects play a minor role. In the region of interband
—_
LIQUID HELIUM
transitions above 1 eV the reflection spectrum is quite similar to that measured by Antonova et a1.~ at room temperature, except that the peak in our data near 2.5eV is shifted to higher energies by about 0.15eV. Such a shift is expected in view
FIG. 1. Apparatus for measuring calorimetrically
of the large temperature coefficients of the
the optical absorption of metals at low temper-
absorption edges and reflectance peaks of the semi
atures.
conducting TX
8 2 compounds.
In their transmission measurements on NbSe
light and passing a d.c. current through the other half of the wafer. The corresponding electrical power is then equal to the light power absorbed. For calibration of the system the exposed insulating sides of the bolimeters are blackened with carbon black. At a few wavelengths we verified that the light powers coming through the two holes are equal within 1 per cent. For the scanning measurement the bolometers are
2 Wilson and Yoffe observed free-carrier absorption below 1 eV. The reflectance increase below 1 eV shown in Fig. 2 also looks typical of free-carrier behavior. Below 0.8eV the reflectance (2 + E2)l + — ~‘2 ( + ( 2~ 62)i)
R
I
=
2
+
(2
+
2)2 2
1
~/2 (
+
2
I
+ (2 1
+ ¶
2)
i)
2
was fitted with the Drude dielectric functions. 2
2
C,)
connected in series with a load resistor to a battery. Chopping light givesabsorbed two a.c. by signals, proportional to thethe light powers the two bolometers. These signals are measured by
2+ 1/r2 wr(w2+ 1/r2) is the W plasma frequency, r the relaxation time, and Cub represents a polarizability due to virtual
two P.A.R. HR—8 amplifiers, their ratio is taken by a P.A.R. multiplier, model 230, and plotted out on an XY—recorder as a function of wavelength. With both bolometers blackened, this ratio is constant within 1 per cent over the whole spectral spectral range.
interband transitions and was held constant over this energy range (see e.g. Feinleib et a!.).9 A least square fit of better than 1 per cent was obtained over the whole energy range.
The black side of one of the bolometers is
~
=
1
—
_________
+
.
~
3
=
______________
Using standard techniques ~ reflectance of a single crystal NbSe 2 was measured out to 0.1 eV at room temperature.” Since no accurate
Vol. 9, No. 1
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2
p
59
that the superconducting transition temperature T0 does not depend significantly on m*. He
0.8’-
expressed T,, in terms of A, a typical phonon frequency ~ and an effective repulsive Coulomb interaction M*;
0~L 0
0.5
.0
.5
2~
~,c
2.5
h~(eV)
)
1.04(1+A) A — ~i~’ (1 + 0.62A) * was shown to be about 0.13 for transition 5showed that in simple metals. cases the Lately, d.c. resistivity Hopfield ‘ and the plasma frequency can be used to determine A: kT
/
=li&iexp
(— ‘,
FiG. 2. Reflectance of NbSe
Debye temperature)
0D’
2.
A
= 477
27rk~ dp/dT (T>
absolute value could be determined, the results
In the case of NbSe
were normalized to the curve shown in Fig. 2 ifl the region of overlap (0.6—0.38 eV). These results show that R can be linearly extrapolated from 0.4eV to 0.1eV.
2 the application of this formula is complicated by the peculiar break of dp/dT near 150°Kobserved by Lee et a!. l~and also present in our samples. Using a value of 0.65 10~Zcm/°Kfor dp/dT from a smooth
The resulting parameters of the Drude
extrapolation of the resistance below 150cK to higher temperatures we obtain A 0.36. From McMillan’s formula for T0 (7°K), taking 0D ~0D 210°K)it follows p” that 0.13 and F~ci k view of the basic problems introduced A 0.57. In by the extremely high anisotropy of layered structured compounds like NbS;, the agreement between these two values of A seems reasonably good. =
functions are;
=
=
(1.5 ±0.2)eV, Elib
=
1/T=
(1.9 ±0.3)
~14
sec -,
1.7 ±0.4.
The most prominent result of course is the low plasma edge, indicating an unusually high effective mass. With n 1.55. 10~cm3 (i.e. 1 electron per Nb atom) m’~ is calculated from c~= 4 7Tne2/m*
=
‘=
=
In conclusion, in NbSe 2 the free-electron part
as 9.7 me. With this m* the electronic heat capacity Cei V T can be calculated. The value 2 as compared to anof V comes out as iS mJ/mol experimental valuedeg of 20.5 mJ/mol deg2.12 Note, that the mass derived from w is ‘bare’,13 whereas the mass in y is the thermal mass, i.e. * mth m * (1 + A), where A is the electron phonon coupling constant. From the difference of the y- values one would estimate A as 0.36 which agrees excellently with the value calculated =
=
below. However, this agreement may be somewhat accidental, considering that no anisotropy effects have been taken into account. In terms of the original BCS theory the high density of states at the Fermi energy corresponding to the above m* is favorable for superconductivity,4 However, more recently it was shown by McMillan’
of the spectrum is separated well enough from the interbandof part as to frequency. allow a reliable determination thesoplasma The correspond-
ing effective mass correlates well with the experimental electronic specific heat. Following Hopfield’s suggestions c~,was used to estimate the electron phonon coupling constant A, which governs the superconductivity. In this context it will be most interesting to study the optical spectrum in the near IR of NbSe 2 intercalated with with organic molecules. Acknowledgements We are indebted to F.J. DiSalvo and F.R. Gamble (Synvar Research Institute) for supplying the crystals and for helpful discussions. We have greatly profited from discussions with P.M. Platzmanofand P.W. Anderson. The able technical assistance H.-U. Thomas is gratefully acknowledged. —
60
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2
Vol. 9, No. 1
REFERENCES 1. 2.
WILSON J.A. and YOFFE A.D., 4.dv. Phys. 18, 193 (1969). GAMBLE F.R., DISALVO F.J., KLEMM R.A. and GEBALLE T.H., Science 168, 568 (1970).
3. 4. 5.
ANTONOVA E.A., VOROB’EV V.G., KALYUZHNAYA G.A. and SOBOLEV V.V., Soy. Phys. —Solid State 3, 777 (1969). BlOND! R.A. and RAYNE J.A., Phys. Rev. 115, 1522 (1959). BEAGLEHOLE D., Appi. Opt. 7, 2218 (1968).
6.
BACHMANN R., KIRSCH H.C. and GEBALLE T.H., Rev. scient. Instrum. 41, 547 (1970).
7.
BEAGLEHOLE D. and HENDRICKSON T.J., Phys. Rev. Leit. 22, 133 (1969).
8.
GREENAWAY D.L. and NITSCHE R., J. Phys. Chem. Solids 26, 1445 (1965).
9.
FEINLEIB
10.
J.,
SCOULER W.J. and FERRETTI A., Phys. Rev. 165, 765 (1968).
We are greatly indebted to R. Buchanan, Lockheed Research Center, Palo Alto, for doing these measurements.
11.
The light~energiesin the near i.r. being much greater than kT, the free electron part of the spectrum will not be temperature dependent up to room temperature (r.t.). Within the limited accuracy of the .r.t. reflectance measurements the optical conductivity of NbSe2 was indeed found to be the same at 300°Kas at 2°K.The importance of the energy dependence of r is also demonstrated by a comparison of the optical and the d.c. resistivity: 4flcm, pd.c. (300°K) 1.7 lO4clcm. 4.3 lO 12. VAN MAAREN M.H. and HARLAND H.B., Phys. Leti. 29A, 571 (1969). =
=
.
.
13.
PRANGE R.E. and KADANOFF L.P., Phys. Rev. 134, 566 (1964).
14.
MCMILLAN W.L., Phys. Rev. 167, 331 (1968).
15.
HOPFIELD
16.
LEE H.N.S., MCKINZIE H., TANNHAUSER D.S. and WOLD A., J. app!. Phys. 40, 602 (1969).
J.J.,
private communication, to be published in Comments on Solid State Physics.
Die optische Absorption von NbSe 2 wurde kalorimetrisch zwischen 0.38 und 3.2 eV gemessen. Unterhain 1 eV wurde freie Ladungstraeger Absorption beobachtet, und die Plasma Frequenz konnte durch Anpassung der Reflexion mit Drude Funktionen bestimmt werden, Mit Hilfe der Plasma Frequenz und des Gleichstromwiderstandes kann die Elektron—Phonon Wechselwirkungskonstante A abgeschaetzt werden.
Vol. 9, pp. 57—60, 1971.
Pergaom Press.
Printed in Great Britain
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2* R. Bachmann, H.C. Kirsch,t and T.H. Geballe* Bell Telephone Laboratories, Allentown, Pa. and Murray Hill, N.J.
(Received 18 October 1970 by J.L.Olsen)
The optical absorption of NbSe2 was measured by a scanning calorimetric technique in the spectral range of 0.38 to 3.2 eV. Freeelectron-like behavior is observed below 1 eV and the plasma frequency is determined by fitting the reflectance with Drude functions. Using this plasma frequency and the d.c. resistivity a value for the electron—phonon coupling constant, A, can be estimated.
THE STRUCTURAL, optical and electrical properties of the transition metal dichalcogenides TX2 have been comprehensively described by Wilson and Yoffe.’ Recently, the superconducting TaX 2 and NbX2 have attracted renewed interest because it was found that these layered compounds can be intercalated with organic molecules forming stoichiometric organometallic compounds with somewhat different superconducting transition temperatures.2 Presently we are carrying Out a series of optical measurements on these new materials with particular emphasis on their infrared properties. It seemed appropriate to use NbSe 2 as a standard within the group of NbX2 and TaX2 compounds. It can easily be grown by iodine *
transport as large single crystals with natural surfaces of good optical quality and chemical stability. Also, its reflection spectrum has 3 already been measured at energies above 1 eV. The optical absorption A = 1 R of NbSe2 was measured at 2 K by a scanning calorimetric technique, similar to methods which 4and have by Beaglehole~ been used by Biondi and Rayne Measuring the absorption by such calorimetric techniques is superior to standard reflection measurements both in case of highly reflecting —
samples (R 1) and in case of macroscopically uneven surfaces. The apparatus is shown schematically in Fig. 1. Two silicon bolometers are mounted below the two holes in the bottom of the light pipe.’ The low-temperature-sensitive resistor is a thin layer diffused on one side of an otherwise insulating Si wafer. This sensitive side
The research at Stanford was sponsored by the U.S. Air Force Office of Scientific Research, Office of Aerospace Research, under Grant No. AFOSR 68—1510C.
is cut diagonally through the contact pads into two halves, thus making two bolometer elements on each wafer. One half of each wafer is connected into an s.c. bridge, and the absorbed light power can be measured by the resistance change. The same change can be produced by shutting of the
t Predoctoral fellow sponsored by Bell Telephone
Laboratories, Allentown, Pa. * Also at Bell Telephone Laboratories, Murray
Hill, N.J. 57
58
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe
MONOCHROMATOR
then replaced by the sample, whose absorption is
L
measured with reference to the black bolometer. In order to test the system we have measured the / i
________
________
BoF, WINDOW
________
LIGHT PIPE
—
SAMPLE
—
COPPER BLOCK
I
I
‘\
absorption spectrum of a thick (5000 A) gold film
evaporated on a sapphire slide. The results were in excellent agreement with published data.7 Figure 2 shows the results of a measurement on a single-crystal of NbSe 2 as grown (surface .L c-axis). In order to compare measurements 3 weour have plotted the directly with existing data reflectance. For different crystals this spectrum
- -
I —
Vol. 9, No. 1
—
‘~
L~~~11~J —
—T
reproduced within about 10 per cent. This
—
reproducibility assures us that surface effects play a minor role. In the region of interband
—_
LIQUID HELIUM
transitions above 1 eV the reflection spectrum is quite similar to that measured by Antonova et a1.~ at room temperature, except that the peak in our data near 2.5eV is shifted to higher energies by about 0.15eV. Such a shift is expected in view
FIG. 1. Apparatus for measuring calorimetrically
of the large temperature coefficients of the
the optical absorption of metals at low temper-
absorption edges and reflectance peaks of the semi
atures.
conducting TX
8 2 compounds.
In their transmission measurements on NbSe
light and passing a d.c. current through the other half of the wafer. The corresponding electrical power is then equal to the light power absorbed. For calibration of the system the exposed insulating sides of the bolimeters are blackened with carbon black. At a few wavelengths we verified that the light powers coming through the two holes are equal within 1 per cent. For the scanning measurement the bolometers are
2 Wilson and Yoffe observed free-carrier absorption below 1 eV. The reflectance increase below 1 eV shown in Fig. 2 also looks typical of free-carrier behavior. Below 0.8eV the reflectance (2 + E2)l + — ~‘2 ( + ( 2~ 62)i)
R
I
=
2
+
(2
+
2)2 2
1
~/2 (
+
2
I
+ (2 1
+ ¶
2)
i)
2
was fitted with the Drude dielectric functions. 2
2
C,)
connected in series with a load resistor to a battery. Chopping light givesabsorbed two a.c. by signals, proportional to thethe light powers the two bolometers. These signals are measured by
2+ 1/r2 wr(w2+ 1/r2) is the W plasma frequency, r the relaxation time, and Cub represents a polarizability due to virtual
two P.A.R. HR—8 amplifiers, their ratio is taken by a P.A.R. multiplier, model 230, and plotted out on an XY—recorder as a function of wavelength. With both bolometers blackened, this ratio is constant within 1 per cent over the whole spectral spectral range.
interband transitions and was held constant over this energy range (see e.g. Feinleib et a!.).9 A least square fit of better than 1 per cent was obtained over the whole energy range.
The black side of one of the bolometers is
~
=
1
—
_________
+
.
~
3
=
______________
Using standard techniques ~ reflectance of a single crystal NbSe 2 was measured out to 0.1 eV at room temperature.” Since no accurate
Vol. 9, No. 1
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2
p
59
that the superconducting transition temperature T0 does not depend significantly on m*. He
0.8’-
expressed T,, in terms of A, a typical phonon frequency ~ and an effective repulsive Coulomb interaction M*;
0~L 0
0.5
.0
.5
2~
~,c
2.5
h~(eV)
)
1.04(1+A) A — ~i~’ (1 + 0.62A) * was shown to be about 0.13 for transition 5showed that in simple metals. cases the Lately, d.c. resistivity Hopfield ‘ and the plasma frequency can be used to determine A: kT
/
=li&iexp
(— ‘,
FiG. 2. Reflectance of NbSe
Debye temperature)
0D’
2.
A
= 477
27rk~ dp/dT (T>
absolute value could be determined, the results
In the case of NbSe
were normalized to the curve shown in Fig. 2 ifl the region of overlap (0.6—0.38 eV). These results show that R can be linearly extrapolated from 0.4eV to 0.1eV.
2 the application of this formula is complicated by the peculiar break of dp/dT near 150°Kobserved by Lee et a!. l~and also present in our samples. Using a value of 0.65 10~Zcm/°Kfor dp/dT from a smooth
The resulting parameters of the Drude
extrapolation of the resistance below 150cK to higher temperatures we obtain A 0.36. From McMillan’s formula for T0 (7°K), taking 0D ~0D 210°K)it follows p” that 0.13 and F~ci k view of the basic problems introduced A 0.57. In by the extremely high anisotropy of layered structured compounds like NbS;, the agreement between these two values of A seems reasonably good. =
functions are;
=
=
(1.5 ±0.2)eV, Elib
=
1/T=
(1.9 ±0.3)
~14
sec -,
1.7 ±0.4.
The most prominent result of course is the low plasma edge, indicating an unusually high effective mass. With n 1.55. 10~cm3 (i.e. 1 electron per Nb atom) m’~ is calculated from c~= 4 7Tne2/m*
=
‘=
=
In conclusion, in NbSe 2 the free-electron part
as 9.7 me. With this m* the electronic heat capacity Cei V T can be calculated. The value 2 as compared to anof V comes out as iS mJ/mol experimental valuedeg of 20.5 mJ/mol deg2.12 Note, that the mass derived from w is ‘bare’,13 whereas the mass in y is the thermal mass, i.e. * mth m * (1 + A), where A is the electron phonon coupling constant. From the difference of the y- values one would estimate A as 0.36 which agrees excellently with the value calculated =
=
below. However, this agreement may be somewhat accidental, considering that no anisotropy effects have been taken into account. In terms of the original BCS theory the high density of states at the Fermi energy corresponding to the above m* is favorable for superconductivity,4 However, more recently it was shown by McMillan’
of the spectrum is separated well enough from the interbandof part as to frequency. allow a reliable determination thesoplasma The correspond-
ing effective mass correlates well with the experimental electronic specific heat. Following Hopfield’s suggestions c~,was used to estimate the electron phonon coupling constant A, which governs the superconductivity. In this context it will be most interesting to study the optical spectrum in the near IR of NbSe 2 intercalated with with organic molecules. Acknowledgements We are indebted to F.J. DiSalvo and F.R. Gamble (Synvar Research Institute) for supplying the crystals and for helpful discussions. We have greatly profited from discussions with P.M. Platzmanofand P.W. Anderson. The able technical assistance H.-U. Thomas is gratefully acknowledged. —
60
OPTICAL PROPERTIES AND SUPERCONDUCTIVITY OF NbSe2
Vol. 9, No. 1
REFERENCES 1. 2.
WILSON J.A. and YOFFE A.D., 4.dv. Phys. 18, 193 (1969). GAMBLE F.R., DISALVO F.J., KLEMM R.A. and GEBALLE T.H., Science 168, 568 (1970).
3. 4. 5.
ANTONOVA E.A., VOROB’EV V.G., KALYUZHNAYA G.A. and SOBOLEV V.V., Soy. Phys. —Solid State 3, 777 (1969). BlOND! R.A. and RAYNE J.A., Phys. Rev. 115, 1522 (1959). BEAGLEHOLE D., Appi. Opt. 7, 2218 (1968).
6.
BACHMANN R., KIRSCH H.C. and GEBALLE T.H., Rev. scient. Instrum. 41, 547 (1970).
7.
BEAGLEHOLE D. and HENDRICKSON T.J., Phys. Rev. Leit. 22, 133 (1969).
8.
GREENAWAY D.L. and NITSCHE R., J. Phys. Chem. Solids 26, 1445 (1965).
9.
FEINLEIB
10.
J.,
SCOULER W.J. and FERRETTI A., Phys. Rev. 165, 765 (1968).
We are greatly indebted to R. Buchanan, Lockheed Research Center, Palo Alto, for doing these measurements.
11.
The light~energiesin the near i.r. being much greater than kT, the free electron part of the spectrum will not be temperature dependent up to room temperature (r.t.). Within the limited accuracy of the .r.t. reflectance measurements the optical conductivity of NbSe2 was indeed found to be the same at 300°Kas at 2°K.The importance of the energy dependence of r is also demonstrated by a comparison of the optical and the d.c. resistivity: 4flcm, pd.c. (300°K) 1.7 lO4clcm. 4.3 lO 12. VAN MAAREN M.H. and HARLAND H.B., Phys. Leti. 29A, 571 (1969). =
=
.
.
13.
PRANGE R.E. and KADANOFF L.P., Phys. Rev. 134, 566 (1964).
14.
MCMILLAN W.L., Phys. Rev. 167, 331 (1968).
15.
HOPFIELD
16.
LEE H.N.S., MCKINZIE H., TANNHAUSER D.S. and WOLD A., J. app!. Phys. 40, 602 (1969).
J.J.,
private communication, to be published in Comments on Solid State Physics.
Die optische Absorption von NbSe 2 wurde kalorimetrisch zwischen 0.38 und 3.2 eV gemessen. Unterhain 1 eV wurde freie Ladungstraeger Absorption beobachtet, und die Plasma Frequenz konnte durch Anpassung der Reflexion mit Drude Funktionen bestimmt werden, Mit Hilfe der Plasma Frequenz und des Gleichstromwiderstandes kann die Elektron—Phonon Wechselwirkungskonstante A abgeschaetzt werden.