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The superconducting energy gap of NbSe2
Solid State Communications, Vol. 9, PP. 1881—1884, 1971.
Pergamon Press.
Printed in Great Britain
THE SUPERCONDUCTING ENERGY GAP OF NbSe
2
B.P. Clayman and R.F. Frindt Department of Physics, Simon Fraser University, Burnaby 2, British Columbia, Canada
(Received 17 August 1971 by R.H. Silsbee)
The energy gap of NbSe2, a superconducting layer structure, has been measured to be 2.15meV at 1°Kby observing its far-infrarad transmission spectrum. The temperature dependence of the gap is found to be consistent with B.C.S. predictions.
NIOBIUM Selenide, a superconductor, is one of the family of transition metal dichalogenides whose electrical properties range from insulating 1 They are all layered crystals to superconducting. with strong, largely covalent bonds within the layers and weak, largely van der Waals bonds between the layers. The superconducting species, including NbSe, have recently attracted considerable superconductivity in a purely two-dimensional system2 and because tunneling devices such as SQUID’S can be constructed3 from single, thin crystals. Knowledge of the energy gap is crucial to a full understanding of the properties of NbSe 2.
and cleaved by peeling away overlying layers until the desired thickness was reached (typically 200—600 The disc the sample sample holder attached was then A). mounted in awith special in the cryostat, ensuring that no path existed for leakage of radiation around the sample. This point is crucial because of the high attenuation of radiation (“ 10~)caused by the sample. Sample temperature could be varied from 1.5°Kto 25°K by a conventional resistance bridge.7 The transmission spectrum 13 (i.~)was measured for several temperatures from 1.5°K to 7°K for each sample. This was compared with the normal state transmission spectrum l1~(~ for each sample, obtained while maintaining the sample at 10°K.
We have determined the energy gap frequency of NbSe2 single crystals by measuring their transmission spectra from 3 to lOOcm’. This technique is the only optical approach to gap measurements in NbSe2 its high critical field and critical current make direct absorption measurements and the the expected anisotropy the gapimpossible severely reduces value of multiple-in reflection methods where the angle of incidence cannot be controlled. The spectrometer4 and He3 cryostat5 used are described elsewhere. The samples were prepared by iodine vapour transport from high purity (99.93% Nb; 99.999%Se) reagents. All were the two-layer form of NbSe with T~ with measured to be 6.95 ±0.05°K upon 2agreement published6 values of T~ 7°K. The resistance ratio was r(300°K/r(7.5°K) 19 ±2. Samples were mounted on crystal quartz discs with epoxy ~
In Fig. la typical results (i~/1\) are shown for unpolarized radiation in normal incidence.2 The NbSe2 sample had abeam. circular exposed to the infrared Thearea pack32inmm 13 /1~. occurs at 17.2 ±0.4cm~ when T = 1.6°K and shifts ~o 14.6 ±1.Ocm’ when T = 5.0°K. In previous studies of the transmission spectra of superconductors~ it was found that the peak 1N occurs at a frequency about 2% greater in !~/I~’~this was in accordance with the theoretical than predictions9 based on B.C.S. theory. Because the experimental uncertainty is greater than this, we shall take the frequency at the peak to be equal
1881
1882
SUPERCONDUCTING ENERGY GAP OF NbSe
2
PHOTOP~ ENERGy 20
the Fermi surface and the phonon density of states. This should cause anisotropy in the superconducting
(‘~
4.0
Vol. 9, No. 22
6.0
energy gap.” To detect it optically requires radiation at oblique incidence. NORMAL 20
a)
It should first be noted that the ‘normal incidence’ results described above really refer to radiation incident at half-angles less than 14°, due to the f/2.0 far-infrared optics. The angular distribution of the radiation incident on the sample is not known quantitatively, but is known to be
INCIDENCE Nb$,4
peaked at true normal incidence. This range of angles of incidence produces an average gap, weighted strongly at normal incidence. b)NbS.2
20
OBLIQUE
To see whether anisotropy could be detected optically, a technique was devised to sample the gap in crystallographic directions further than 14°
INCIDENCE i0~
0
8
16
24 32 WAVENUMBIR
40
(~)
48
~é
from normal incidence. Light cones 12 were placed above and below the quartz disc; they increased the spread of the radiation from 14°to 90° halfangle and after it passed through the sample, returned it to the 14° appropriate to the detector optics. Because of the 4mm thickness of the quartz disc, much of the high-angle radiation was lost, but enough reached the detector to produce the
FIG. 1. Ratio of superconducting to normal transmission as a function of frequency in wavenumbers. Instrumental resolution is indicated by (b) Oblique components increased by arrows. (a) incidence Two temperatures at normal incidence, using light cones.
to z~. We see then that at T = l.6°K, h~g/kT~ = 3.7 ~0.1 and at T = 5.0°K, h~ ~k T,~ = 3.1 ±0.2. The results for all temperatures masured are summarized in Fig. 2. The large uncertainties in temperatures for the high temperature runs are due to poor thermal coupling between the thermometer and the thin crystal sample. Agreement between these data and the B.C.S. prediction’° of the temperature dependence of the gap energy is good over the limited range of T/TC which is accessible. At higher temperatures, no peak in ‘8
“N
change in the transmission ratio evident in Fig. lb. The peak location shiftsthe to centroid lower frequency 1) while of the peak shifts ~to0.6cm a higher frequency (18.6 ±0.6cm1) than (16.6 the centroid at ‘normal’ incidence (17.8 ±0.6crn1). In addition, I~/1~does not fall smoothly toward zero at low frequencies as it does in Fig. la. Instead, a shoulder appears at about 10cm~.
The changes in gap frequency and in the shape of the peak could be interpreted as evidence of gap anisotropy. However, we feel that, although they are suggestive of anisotropy, they should not be interpreted as conclusive evidence for it. Other mechanisms, particularly cavity modes in the sample holder, could account for the observed differences. Work is underway on a new sample configuration which will permit unambiguous determination of the gap at a variety of angles of mcidence.
was discernable from the background noise.
Because of the extreme anisotropy of the crystal structure, anisotropy is expected in both
There is no additional structure in ‘$/‘N at high frequencies (~100 cm~). In Pb, Joyce and Richards’3 found additional absorption well above
Vol. 9, No. 21
SUPERCONDUCTING ENERGY GAP OF NbSe
1883
2
~
yTc
FIG. 2. Temperature dependence of the gap frequency. The measured value of equal to i..~(O),and T~ = 7°K. The solid curve is the B.C.S. prediction.
i~, deduced that it was due to the Holstein process 14 and were able to measure the phonon density of states. Little is known about either the phonon or the electron distributions in NbSe2, so it is especially unfortunate that this process does not occur here. Its absence is probably due to weaker electron—phonon coupling in NbSe2 than in Pb. There have been several theoretical approaches to the problem of gap anisotropy. However, for a given system it is still not possible to predict a priori the relative importance of the three possible sources of anisotropy: (a) an interaction 15, (b) matrix element Vkk, which is not constant a non-spherical Fermi surfac&6, (c) the real phonon spectrum17. Our data are insufficient to determine which, if any, of the mechanisms are important in NbSe 2, so we will not consider this point further.
i-~at
T
=
1.6°Kis taken
Our results have important implications for the experiments on pure and intercalated NbSe2 mentioned above. The infrared radiation in normal incidence samples the gap for electron pairs with velocities largely parallel to the plane of the layers, so we predict that if two dimensional superconductivity is being observed in the intercalated systems, the associated energy gap will be h’frg/kTc = 3.7 or ~ = 2.15meV. This relatively high gap energy also predicts that detectors employing NbSe2 weak links will be useful at relatively high far-infrared frequencies.
Acknowledgements We gratefully acknowledge helpful discussions with Dr. R.R. Haering Dr. —
L.H. Palmer, and
J.
Edwards. This work was
supported in part by the National Research Council of Canada and the Research Corporation.
REFERENCES 1.
WILSON J.A. and YOFFE A.D., Ad~.Phvs. 18, 193 (1969).
2.
GAMBLE F.R., DISALVO F.J., KLEMM R.A. and GEBALLE T.H., Science, .\‘.Y. 168, 568 (1970).
3.
CONSADORI F., FIFE A.A., FRINDT R.F. anf GYGAX S., Appl. Phys. Lest. 18, 233 (1971).
4.
A modified R.I.I.C. LR—l00. Details of the modifications are to be published in Rev. Sciens. Instrum.
5.
CLAYMAN B.P., KIRBY R.D. and SIEVERS A.J., Phys. Rev. 83, 1351 (1971).
6.
REVOLINSKY E., SPIERING G.A. and BEERNTSEN D.J., J. Chem. Phys. Solids 26, 1029 (1965).
7.
Oxford Instruments Resistance Bridge.
8.
PALMER LEIGHT HUNT and TINKHAM M., Phys. Rev. 165, 588 (1968).
1884
SUPERCONDUCTING ENERGY GAP OF NbSe2
Vol. 9, No. 22
9. 10.
MATTIS D.C. and BARDEEN J., Phys. Rev. 111, 412 (1958). BARDEEN J., COOPER L.N. and SCHRIEFFER J.R., Phys. Rev. 108, 1175 (1957).
11.
A review of gap anisotropy is: SHEPELEV A.G., Usp. Fiz. Nauk. 96, 217 (1968) [ English transi:
Soviet Physics, Uspekhi 11, 690 (1969)].
Opt.
12.
WILLIAMSON D.E., J.
13.
JOYCE R.R. and RICHARDS P.L., Phys. Rev. Let!. 24, 1007 (1970).
14. 15.
HOLSTEIN T., Phys. Rev. 96, 535 (1954). POKROVSKII V.L., Zh. Eksp. Teor. Fiz. 40, 641 (1961) [ English transl: Soviet Physics
16.
13, 447 (1961)]. GEILIKMAN B.T. and KRESIN
Physics 17.
—
Soc. Am. 42, 712 (1952).
V.Z. Fiz. Tverd. Tela 5, 3549 (1963) Solid State 5, 2605 (1964)].
[ English
—
JETP
transl: Soviet
BENNET A.J., Phys. Rev. 140, A1902 (1965); 153, 482 (1967).
Das Transmissionsspecktrum im langwelligen Infrarot des supraleitenden Schichtkristalles NbSe2 wurde gemessen. Der Bandabstand bei 1°Kist 2.15 meV. Die Temperaturabh~ngigkeit des Bandabstandes wurde bestimmt. Sie verh~ltsich gemäss der B.C.S. Theorie.
Pergamon Press.
Printed in Great Britain
THE SUPERCONDUCTING ENERGY GAP OF NbSe
2
B.P. Clayman and R.F. Frindt Department of Physics, Simon Fraser University, Burnaby 2, British Columbia, Canada
(Received 17 August 1971 by R.H. Silsbee)
The energy gap of NbSe2, a superconducting layer structure, has been measured to be 2.15meV at 1°Kby observing its far-infrarad transmission spectrum. The temperature dependence of the gap is found to be consistent with B.C.S. predictions.
NIOBIUM Selenide, a superconductor, is one of the family of transition metal dichalogenides whose electrical properties range from insulating 1 They are all layered crystals to superconducting. with strong, largely covalent bonds within the layers and weak, largely van der Waals bonds between the layers. The superconducting species, including NbSe, have recently attracted considerable superconductivity in a purely two-dimensional system2 and because tunneling devices such as SQUID’S can be constructed3 from single, thin crystals. Knowledge of the energy gap is crucial to a full understanding of the properties of NbSe 2.
and cleaved by peeling away overlying layers until the desired thickness was reached (typically 200—600 The disc the sample sample holder attached was then A). mounted in awith special in the cryostat, ensuring that no path existed for leakage of radiation around the sample. This point is crucial because of the high attenuation of radiation (“ 10~)caused by the sample. Sample temperature could be varied from 1.5°Kto 25°K by a conventional resistance bridge.7 The transmission spectrum 13 (i.~)was measured for several temperatures from 1.5°K to 7°K for each sample. This was compared with the normal state transmission spectrum l1~(~ for each sample, obtained while maintaining the sample at 10°K.
We have determined the energy gap frequency of NbSe2 single crystals by measuring their transmission spectra from 3 to lOOcm’. This technique is the only optical approach to gap measurements in NbSe2 its high critical field and critical current make direct absorption measurements and the the expected anisotropy the gapimpossible severely reduces value of multiple-in reflection methods where the angle of incidence cannot be controlled. The spectrometer4 and He3 cryostat5 used are described elsewhere. The samples were prepared by iodine vapour transport from high purity (99.93% Nb; 99.999%Se) reagents. All were the two-layer form of NbSe with T~ with measured to be 6.95 ±0.05°K upon 2agreement published6 values of T~ 7°K. The resistance ratio was r(300°K/r(7.5°K) 19 ±2. Samples were mounted on crystal quartz discs with epoxy ~
In Fig. la typical results (i~/1\) are shown for unpolarized radiation in normal incidence.2 The NbSe2 sample had abeam. circular exposed to the infrared Thearea pack32inmm 13 /1~. occurs at 17.2 ±0.4cm~ when T = 1.6°K and shifts ~o 14.6 ±1.Ocm’ when T = 5.0°K. In previous studies of the transmission spectra of superconductors~ it was found that the peak 1N occurs at a frequency about 2% greater in !~/I~’~this was in accordance with the theoretical than predictions9 based on B.C.S. theory. Because the experimental uncertainty is greater than this, we shall take the frequency at the peak to be equal
1881
1882
SUPERCONDUCTING ENERGY GAP OF NbSe
2
PHOTOP~ ENERGy 20
the Fermi surface and the phonon density of states. This should cause anisotropy in the superconducting
(‘~
4.0
Vol. 9, No. 22
6.0
energy gap.” To detect it optically requires radiation at oblique incidence. NORMAL 20
a)
It should first be noted that the ‘normal incidence’ results described above really refer to radiation incident at half-angles less than 14°, due to the f/2.0 far-infrared optics. The angular distribution of the radiation incident on the sample is not known quantitatively, but is known to be
INCIDENCE Nb$,4
peaked at true normal incidence. This range of angles of incidence produces an average gap, weighted strongly at normal incidence. b)NbS.2
20
OBLIQUE
To see whether anisotropy could be detected optically, a technique was devised to sample the gap in crystallographic directions further than 14°
INCIDENCE i0~
0
8
16
24 32 WAVENUMBIR
40
(~)
48
~é
from normal incidence. Light cones 12 were placed above and below the quartz disc; they increased the spread of the radiation from 14°to 90° halfangle and after it passed through the sample, returned it to the 14° appropriate to the detector optics. Because of the 4mm thickness of the quartz disc, much of the high-angle radiation was lost, but enough reached the detector to produce the
FIG. 1. Ratio of superconducting to normal transmission as a function of frequency in wavenumbers. Instrumental resolution is indicated by (b) Oblique components increased by arrows. (a) incidence Two temperatures at normal incidence, using light cones.
to z~. We see then that at T = l.6°K, h~g/kT~ = 3.7 ~0.1 and at T = 5.0°K, h~ ~k T,~ = 3.1 ±0.2. The results for all temperatures masured are summarized in Fig. 2. The large uncertainties in temperatures for the high temperature runs are due to poor thermal coupling between the thermometer and the thin crystal sample. Agreement between these data and the B.C.S. prediction’° of the temperature dependence of the gap energy is good over the limited range of T/TC which is accessible. At higher temperatures, no peak in ‘8
“N
change in the transmission ratio evident in Fig. lb. The peak location shiftsthe to centroid lower frequency 1) while of the peak shifts ~to0.6cm a higher frequency (18.6 ±0.6cm1) than (16.6 the centroid at ‘normal’ incidence (17.8 ±0.6crn1). In addition, I~/1~does not fall smoothly toward zero at low frequencies as it does in Fig. la. Instead, a shoulder appears at about 10cm~.
The changes in gap frequency and in the shape of the peak could be interpreted as evidence of gap anisotropy. However, we feel that, although they are suggestive of anisotropy, they should not be interpreted as conclusive evidence for it. Other mechanisms, particularly cavity modes in the sample holder, could account for the observed differences. Work is underway on a new sample configuration which will permit unambiguous determination of the gap at a variety of angles of mcidence.
was discernable from the background noise.
Because of the extreme anisotropy of the crystal structure, anisotropy is expected in both
There is no additional structure in ‘$/‘N at high frequencies (~100 cm~). In Pb, Joyce and Richards’3 found additional absorption well above
Vol. 9, No. 21
SUPERCONDUCTING ENERGY GAP OF NbSe
1883
2
~
yTc
FIG. 2. Temperature dependence of the gap frequency. The measured value of equal to i..~(O),and T~ = 7°K. The solid curve is the B.C.S. prediction.
i~, deduced that it was due to the Holstein process 14 and were able to measure the phonon density of states. Little is known about either the phonon or the electron distributions in NbSe2, so it is especially unfortunate that this process does not occur here. Its absence is probably due to weaker electron—phonon coupling in NbSe2 than in Pb. There have been several theoretical approaches to the problem of gap anisotropy. However, for a given system it is still not possible to predict a priori the relative importance of the three possible sources of anisotropy: (a) an interaction 15, (b) matrix element Vkk, which is not constant a non-spherical Fermi surfac&6, (c) the real phonon spectrum17. Our data are insufficient to determine which, if any, of the mechanisms are important in NbSe 2, so we will not consider this point further.
i-~at
T
=
1.6°Kis taken
Our results have important implications for the experiments on pure and intercalated NbSe2 mentioned above. The infrared radiation in normal incidence samples the gap for electron pairs with velocities largely parallel to the plane of the layers, so we predict that if two dimensional superconductivity is being observed in the intercalated systems, the associated energy gap will be h’frg/kTc = 3.7 or ~ = 2.15meV. This relatively high gap energy also predicts that detectors employing NbSe2 weak links will be useful at relatively high far-infrared frequencies.
Acknowledgements We gratefully acknowledge helpful discussions with Dr. R.R. Haering Dr. —
L.H. Palmer, and
J.
Edwards. This work was
supported in part by the National Research Council of Canada and the Research Corporation.
REFERENCES 1.
WILSON J.A. and YOFFE A.D., Ad~.Phvs. 18, 193 (1969).
2.
GAMBLE F.R., DISALVO F.J., KLEMM R.A. and GEBALLE T.H., Science, .\‘.Y. 168, 568 (1970).
3.
CONSADORI F., FIFE A.A., FRINDT R.F. anf GYGAX S., Appl. Phys. Lest. 18, 233 (1971).
4.
A modified R.I.I.C. LR—l00. Details of the modifications are to be published in Rev. Sciens. Instrum.
5.
CLAYMAN B.P., KIRBY R.D. and SIEVERS A.J., Phys. Rev. 83, 1351 (1971).
6.
REVOLINSKY E., SPIERING G.A. and BEERNTSEN D.J., J. Chem. Phys. Solids 26, 1029 (1965).
7.
Oxford Instruments Resistance Bridge.
8.
PALMER LEIGHT HUNT and TINKHAM M., Phys. Rev. 165, 588 (1968).
1884
SUPERCONDUCTING ENERGY GAP OF NbSe2
Vol. 9, No. 22
9. 10.
MATTIS D.C. and BARDEEN J., Phys. Rev. 111, 412 (1958). BARDEEN J., COOPER L.N. and SCHRIEFFER J.R., Phys. Rev. 108, 1175 (1957).
11.
A review of gap anisotropy is: SHEPELEV A.G., Usp. Fiz. Nauk. 96, 217 (1968) [ English transi:
Soviet Physics, Uspekhi 11, 690 (1969)].
Opt.
12.
WILLIAMSON D.E., J.
13.
JOYCE R.R. and RICHARDS P.L., Phys. Rev. Let!. 24, 1007 (1970).
14. 15.
HOLSTEIN T., Phys. Rev. 96, 535 (1954). POKROVSKII V.L., Zh. Eksp. Teor. Fiz. 40, 641 (1961) [ English transl: Soviet Physics
16.
13, 447 (1961)]. GEILIKMAN B.T. and KRESIN
Physics 17.
—
Soc. Am. 42, 712 (1952).
V.Z. Fiz. Tverd. Tela 5, 3549 (1963) Solid State 5, 2605 (1964)].
[ English
—
JETP
transl: Soviet
BENNET A.J., Phys. Rev. 140, A1902 (1965); 153, 482 (1967).
Das Transmissionsspecktrum im langwelligen Infrarot des supraleitenden Schichtkristalles NbSe2 wurde gemessen. Der Bandabstand bei 1°Kist 2.15 meV. Die Temperaturabh~ngigkeit des Bandabstandes wurde bestimmt. Sie verh~ltsich gemäss der B.C.S. Theorie.