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Electron and phonon effects in superconducting FCC lead-based alloys
Volume 24A, number 8
PHYSICS
tion as the site axes acd transforming the external magnetic field into these axes. For the case E > H one obtains for the S=s three sets of Kramers The center Kramers doublet, the mainly cllblej;. 2s-z states, give the most isotropic and consistently strong spectra. It is from this pair of levels that the reported data are obtained. We have been able to fit gZ exactly and g, andgy quite well with E/D=O.45 and E =2 000 gauss. The full spectra, when the spectrometer is operated in a more sensitive mode, shows many lines. The further data are found to be in qualitative agreement with this general strong zero-field splitting picture and “+ = -6” and “-$= -z” lines are observed as well as the hyperfine “forbidden”
ELECTRON
LETTERS
10
April 1967
transitions [6]. Work is in progress at this time to complete the analysis. References
1. W.A.Deer et al., Rock Forming Minerals,
2. 3* 4 5:
Vol. 1 (Longmans, Green and Co., Ltd., London, 1962): The replacement of OH for F (for Utah Topaz) occurs only to a cery limited extent with 1.94 percent of the (F, OH) group being taken up with OH. T . Castner , Jr. , G.S.Newell, W.C.Ho1tonandC.P. Slichter, J.Chem.Phys.32 (1960) 668. H. Wickman, M.P.Klein and D.A.Shirley, J. Chem. Phys.42 (1965) 2113. F.Holuj, Ca.n.J. of Phys.44 (1966) 503. B. Bleaney and R.S.Rubins, Proc. Phys.Soc. (London) 77 (1961) 103.
AND PHONON EFFECTS IN SUPERCONDUCTING FCC LEAD-BASED ALLOYS * J. G. ADLER, J. E. JACKSON and T. A. WILL ** Department of Physics and Condensed State Center, Case Institute of Technology and Western Reserve University, Cleveland, Ohio 44106, U.S.A. Received
Electron tunneling measurements have been carried electron-phonon coupling strengths.
Using alloys of bismuth, thallium, and indium in lead, one can study fee lead-based alloys over a wide range of electron concentration. Since the atomic masses of bismuth and thallium are about the same as that of lead, changes in the electronphonon interaction in Pb-Bi and Pb-Tl arise primarily from changes in the electron concentration. On the other hand the atomic mass of indium is about half that of lead; thus in Pb-In alloys both the solute mass and electron concentration play an important role in determining the electronphonon interaction and phonon spectra. In this letter we report electron tunneling measurements in fee alloys of Pb with Bi, Tl, and In (over the range from 4.1 electrons/atom (e/a) to 3.3 e/a) and relate these measurements to * Work supported by the U.S. Air Force Office of Scientific Research through grant 565-66. ** National Aeronautics and Space Administration Predoctoral Trainee.
4 March
196’7
out in fee lead-based
alloys
over a wide range of
Table 1 Alloy Pb Ph Pb Pb Pb
e/a
A0 (meV)
2Ao/kT,
+ 20 at% Tl + 40 at% Tl + 60 at% Tl $
4.1 4.0 3.8 3.6 3.4
1.42 1.35 1.14 0.94 0.68
4.40 4.34 3.96 3.71 3.4
2at%In 3 at% In 5 at% In 12 at% In 15 at% In 16 at% In 26 at% In 27 at% In 50 a& In 70 at% In
3.98 3.97 3.95 3.88 3.85 3.84 3.74 3.73 3.50 3.30
1.36 1.36 1.35 1.33 1.32 1.32 1.29 1.28 1.20 1.18
4.34 4.38 4.37 4.35 4.33 4.34 4.36 4.35 4.20 4.20
+ 10 at% Bi
Pb+ Pb+ Pb + Pb + Pb + Pb + Pb f Pb + Pb + Pb +
OTh e gap for the Pb4Tl6 specimen was found by comparing the end point of the phonon spectrum observed by Ng and Brockhouse [8] with the corresponding singularity in da/d V.
407
PHYSICS
Volume 24A, number 8
LETTERS
10 April 1967
determined by the two methods agreed with each other within 2 to 3 at%. The tunneling experiments were carried out below 1°K. The relative dynamic conductance u = (dV/dZ)./(dV/dZ), (where dV/dZ is the dynamic resistance of the tunnel junction, n and s denote the normal and superconducting states of the alloy, respectively) and du/dV were measured using a harmonic detection technique described elsewhere
PI.
-
Pb
--
Pb+ IO at.“/. Bi ..
Pb+20ot.%
000
Pb+4Oot.%TI
-
Pb+60ot.%TI
-
TI
-.IC
Fig. 1. du/dV as a function of energy for various alloy junctions. the phonon spectrum and electron-phonon interaction. The tunnel junctions were prepared by standard techniques [l]. Our determination of superconducting transition temperatures, along with chemical analysis of one of the evaporated films, shows that Pb-Bi and Pb-Tl films may be evaporated with negligible shift in stoichiometry. In contrast to this, Pb-In films exhibit considerable change in composition on evaporation so that it was necessary to determine the composition of these films from residual resistance ratio measurements [l]. Six samples were also analyzed by flame spectroscopy *. The compositions 408
The Pb-Tl and Pb-Bi alloys. We consider first those alloys in which the effects are primarily due to changing electron concentration because of the small mass difference between solvent and solute atoms. In table 1 we see that both the gap, A,, and 2Ao/kTc decrease with decreasing electron concentration. These results are in good agreement with recent measurements by Claeson [3]. The small differences between the sets of results may be due to uncertainties of a few atomic percent in the compositions of the films **. These data indicate a decrease in the strength of the electron-phonon interaction, and can be accounted for qualitatively by the fact that as e/a decreases the ion cores are less well screened, which results in a decrease in magnitude of the net attractive interaction which gives rise to superconductivity. A similar conclusion may be reached by examining the deviations of the tunneling density of states from its predicted BCS (weak coupling) value near the end of the phonon spectrum [4]. Some of the features of the phonon spectrum can be inferred from fig. 1 in which do/dV is shown as a function of energyfor five alloys. do/dV is related to cy2(o)F(w), where (Y(W) is the electron-phonon coupling coefficient and F(o) is the phonon density of states [5-‘71. Examining fig. 1 in the region between 8 meV and 10 meV, which is associated predominantly with longitudinal phonons one can see a shift to higher frequencies with decreasing electron concentration. This is in good agreement with the neutron data of Ng and Brockhouse [8]. The broadening of the structure seen in the 3 meV to 6 meV range reflects the shift of the T[.$[.$] phonons to lower energies and the T[
* We are indebted to Dr. J. W. Rowe11for arranging to have the spectroscopic analysis done for us at the Bell Telephone Laboratories. ** We should like to note for the higher Tl concentrations (at 40 at% and above) we do not always obtain films which show a single sharp energy gap. The reason for this has not yet been determined but it may be due to compositional films.
inhomogeneity
of the
Volume
24A, number
PHYSICS
8
The Pb-Zn alloys. From table 1 we see that ZA,/kT, is almost independent of e/a for these alloys. Previous measurements [l, 9] on these alloys show that, because of the light mass of the indium atom, a localized mode appears in the phonon spectrum at low indium concentrations and grows into a phonon impurity band as the indium concentration increases. In these alloys, as in the Pb-Tl alloys, the decreasing electron concentration must result in a decrease in the magnitude of the net attractive interaction leading to superconductivity. But unlike the Pb-Tl case the light solute mass gives rise to higher phonon frequencies, thus extending the energy range of the phonon damping which leaves 2A,kT, almost unchanged. The observed results show that this ratio decreases only slightly with higher In concentration, T, decreasing less rapidly than A,. We wish to thank B. S. Chandrasekhar, W. N. Mathews, Jr. , and T. M. Wu for valuable dis-
UBER
DAs
10 April
LETTERS
1967
cussions. We are grateful to B. N. Brockhouse, S. C. Ng and T. Claeson for communicating their results to us prior to publication.
References 1. J. G.Adler, J. E. Jackson and B.S. Chandrasekhar, Phys.Rev. Letters 16 (1966) 53. 2. J.G.Adler and J. E. Jackson, Rev.Sci. In&r. 37 (1966) 1049. 3. T. Claeson, to be published. 4. J.G.Adler, J.S.RogersandS.B.Woods, Can.J. Phys.43 (1965) 557. 5. D. J.Scalapino, J.R.Schrieffer and J. W. Wilkins, Phys.Rev. 148 (1966) 263. 6. D. J.Scalapino and P.W.Anderson, Phys.Rev. 133 (1964) A921. 7. W.L.McMillan and J.M.Rowell, Phys.Rev.Letters 14 (1965) 108. 8. S.C. Ng’and N. N.Brockhouse, to be published. 9. J.M.Rowell, W.L.McMillan and P.W.Anderson, Phys.Rev.Letters 14 (1965) 633.
SPEETRALE EMIsSI~NSVERRALTEN V0N GEPULSTEN GaAs-LASERDIODEN
NANOSEEUNDEN-
F. W. LINDNER Lehrstuhl
ftir Angewandte
Physik
der
Technischen
Eingegangen
Time integrated and time resolved of temperature effects on spectral
Hochschule
Germany
am 7. MLrz 1967
spectra of nanosecond-pulsed emission far above threshold.
Mittels eines Jarell-Ash-O.5 m-Ebert-Monochromators wurde bei einer Auflijsung von ca. 0.6 A sowohl das zeitintegrierte als such das zeitaufgelbste Spektrum von GaAs-Laserdioden [l] bei Stromimpulsbreiten zwischen 25 ns und 100 ns untersucht. Es wurde gefunden, dass der Aufbau der Spektren stark von Diode zu Diode variiert, dass jedoch die Abhlngigkeiten des Spektrums von Strom, Temperatur und Impulsbreite qualitativ bei allen Dioden den gleichen Verlauf besitzen. Zwei Dioden wurden besonders eingehend totersucht: eine (#2) bei der Erregung in Liniengruppen erfolgte, d. h. Erregung von je 2-4 benachbarten Moden in einer Gruppe bei einem Abstand von ca. acht theoretischen Modenabstanden zwischen zwei Gruppen, die andere (#l) mit Erre-
Darmstadt,
GaAs-diode-lasers
show the influence
von Linien im konstanten Abstand von drei theoretischen Modenabstanden. Im Bereich des superlinearen Laseranstieges, der bei der Diode #2 im Gegensatz zur Diode #l sehr ausgedehnt war, konnte keine Erregung zusatzlicher Moden zu denen bei 10% oberhalb der Schwelle erregten Moden nachgewiesen werden. Erst zu Beginn des linearen Laserbereiches konnte die zusatzliche Erregung sowohl langwelligerer als such kurzwelligerer Linien beobachtet werden. In ijbereinstimmung mit der Literatur [2] wurde oberhalb der Schwelle ein schnelleres Wachsen der kurzweiligen Moden gegeniiber den langwelligen mit einer Verschiebung des Intensitatsmaximums des Spektrums bei Stromerhtihung gung
409
PHYSICS
tion as the site axes acd transforming the external magnetic field into these axes. For the case E > H one obtains for the S=s three sets of Kramers The center Kramers doublet, the mainly cllblej;. 2s-z states, give the most isotropic and consistently strong spectra. It is from this pair of levels that the reported data are obtained. We have been able to fit gZ exactly and g, andgy quite well with E/D=O.45 and E =2 000 gauss. The full spectra, when the spectrometer is operated in a more sensitive mode, shows many lines. The further data are found to be in qualitative agreement with this general strong zero-field splitting picture and “+ = -6” and “-$= -z” lines are observed as well as the hyperfine “forbidden”
ELECTRON
LETTERS
10
April 1967
transitions [6]. Work is in progress at this time to complete the analysis. References
1. W.A.Deer et al., Rock Forming Minerals,
2. 3* 4 5:
Vol. 1 (Longmans, Green and Co., Ltd., London, 1962): The replacement of OH for F (for Utah Topaz) occurs only to a cery limited extent with 1.94 percent of the (F, OH) group being taken up with OH. T . Castner , Jr. , G.S.Newell, W.C.Ho1tonandC.P. Slichter, J.Chem.Phys.32 (1960) 668. H. Wickman, M.P.Klein and D.A.Shirley, J. Chem. Phys.42 (1965) 2113. F.Holuj, Ca.n.J. of Phys.44 (1966) 503. B. Bleaney and R.S.Rubins, Proc. Phys.Soc. (London) 77 (1961) 103.
AND PHONON EFFECTS IN SUPERCONDUCTING FCC LEAD-BASED ALLOYS * J. G. ADLER, J. E. JACKSON and T. A. WILL ** Department of Physics and Condensed State Center, Case Institute of Technology and Western Reserve University, Cleveland, Ohio 44106, U.S.A. Received
Electron tunneling measurements have been carried electron-phonon coupling strengths.
Using alloys of bismuth, thallium, and indium in lead, one can study fee lead-based alloys over a wide range of electron concentration. Since the atomic masses of bismuth and thallium are about the same as that of lead, changes in the electronphonon interaction in Pb-Bi and Pb-Tl arise primarily from changes in the electron concentration. On the other hand the atomic mass of indium is about half that of lead; thus in Pb-In alloys both the solute mass and electron concentration play an important role in determining the electronphonon interaction and phonon spectra. In this letter we report electron tunneling measurements in fee alloys of Pb with Bi, Tl, and In (over the range from 4.1 electrons/atom (e/a) to 3.3 e/a) and relate these measurements to * Work supported by the U.S. Air Force Office of Scientific Research through grant 565-66. ** National Aeronautics and Space Administration Predoctoral Trainee.
4 March
196’7
out in fee lead-based
alloys
over a wide range of
Table 1 Alloy Pb Ph Pb Pb Pb
e/a
A0 (meV)
2Ao/kT,
+ 20 at% Tl + 40 at% Tl + 60 at% Tl $
4.1 4.0 3.8 3.6 3.4
1.42 1.35 1.14 0.94 0.68
4.40 4.34 3.96 3.71 3.4
2at%In 3 at% In 5 at% In 12 at% In 15 at% In 16 at% In 26 at% In 27 at% In 50 a& In 70 at% In
3.98 3.97 3.95 3.88 3.85 3.84 3.74 3.73 3.50 3.30
1.36 1.36 1.35 1.33 1.32 1.32 1.29 1.28 1.20 1.18
4.34 4.38 4.37 4.35 4.33 4.34 4.36 4.35 4.20 4.20
+ 10 at% Bi
Pb+ Pb+ Pb + Pb + Pb + Pb + Pb f Pb + Pb + Pb +
OTh e gap for the Pb4Tl6 specimen was found by comparing the end point of the phonon spectrum observed by Ng and Brockhouse [8] with the corresponding singularity in da/d V.
407
PHYSICS
Volume 24A, number 8
LETTERS
10 April 1967
determined by the two methods agreed with each other within 2 to 3 at%. The tunneling experiments were carried out below 1°K. The relative dynamic conductance u = (dV/dZ)./(dV/dZ), (where dV/dZ is the dynamic resistance of the tunnel junction, n and s denote the normal and superconducting states of the alloy, respectively) and du/dV were measured using a harmonic detection technique described elsewhere
PI.
-
Pb
--
Pb+ IO at.“/. Bi ..
Pb+20ot.%
000
Pb+4Oot.%TI
-
Pb+60ot.%TI
-
TI
-.IC
Fig. 1. du/dV as a function of energy for various alloy junctions. the phonon spectrum and electron-phonon interaction. The tunnel junctions were prepared by standard techniques [l]. Our determination of superconducting transition temperatures, along with chemical analysis of one of the evaporated films, shows that Pb-Bi and Pb-Tl films may be evaporated with negligible shift in stoichiometry. In contrast to this, Pb-In films exhibit considerable change in composition on evaporation so that it was necessary to determine the composition of these films from residual resistance ratio measurements [l]. Six samples were also analyzed by flame spectroscopy *. The compositions 408
The Pb-Tl and Pb-Bi alloys. We consider first those alloys in which the effects are primarily due to changing electron concentration because of the small mass difference between solvent and solute atoms. In table 1 we see that both the gap, A,, and 2Ao/kTc decrease with decreasing electron concentration. These results are in good agreement with recent measurements by Claeson [3]. The small differences between the sets of results may be due to uncertainties of a few atomic percent in the compositions of the films **. These data indicate a decrease in the strength of the electron-phonon interaction, and can be accounted for qualitatively by the fact that as e/a decreases the ion cores are less well screened, which results in a decrease in magnitude of the net attractive interaction which gives rise to superconductivity. A similar conclusion may be reached by examining the deviations of the tunneling density of states from its predicted BCS (weak coupling) value near the end of the phonon spectrum [4]. Some of the features of the phonon spectrum can be inferred from fig. 1 in which do/dV is shown as a function of energyfor five alloys. do/dV is related to cy2(o)F(w), where (Y(W) is the electron-phonon coupling coefficient and F(o) is the phonon density of states [5-‘71. Examining fig. 1 in the region between 8 meV and 10 meV, which is associated predominantly with longitudinal phonons one can see a shift to higher frequencies with decreasing electron concentration. This is in good agreement with the neutron data of Ng and Brockhouse [8]. The broadening of the structure seen in the 3 meV to 6 meV range reflects the shift of the T[.$[.$] phonons to lower energies and the T[
* We are indebted to Dr. J. W. Rowe11for arranging to have the spectroscopic analysis done for us at the Bell Telephone Laboratories. ** We should like to note for the higher Tl concentrations (at 40 at% and above) we do not always obtain films which show a single sharp energy gap. The reason for this has not yet been determined but it may be due to compositional films.
inhomogeneity
of the
Volume
24A, number
PHYSICS
8
The Pb-Zn alloys. From table 1 we see that ZA,/kT, is almost independent of e/a for these alloys. Previous measurements [l, 9] on these alloys show that, because of the light mass of the indium atom, a localized mode appears in the phonon spectrum at low indium concentrations and grows into a phonon impurity band as the indium concentration increases. In these alloys, as in the Pb-Tl alloys, the decreasing electron concentration must result in a decrease in the magnitude of the net attractive interaction leading to superconductivity. But unlike the Pb-Tl case the light solute mass gives rise to higher phonon frequencies, thus extending the energy range of the phonon damping which leaves 2A,kT, almost unchanged. The observed results show that this ratio decreases only slightly with higher In concentration, T, decreasing less rapidly than A,. We wish to thank B. S. Chandrasekhar, W. N. Mathews, Jr. , and T. M. Wu for valuable dis-
UBER
DAs
10 April
LETTERS
1967
cussions. We are grateful to B. N. Brockhouse, S. C. Ng and T. Claeson for communicating their results to us prior to publication.
References 1. J. G.Adler, J. E. Jackson and B.S. Chandrasekhar, Phys.Rev. Letters 16 (1966) 53. 2. J.G.Adler and J. E. Jackson, Rev.Sci. In&r. 37 (1966) 1049. 3. T. Claeson, to be published. 4. J.G.Adler, J.S.RogersandS.B.Woods, Can.J. Phys.43 (1965) 557. 5. D. J.Scalapino, J.R.Schrieffer and J. W. Wilkins, Phys.Rev. 148 (1966) 263. 6. D. J.Scalapino and P.W.Anderson, Phys.Rev. 133 (1964) A921. 7. W.L.McMillan and J.M.Rowell, Phys.Rev.Letters 14 (1965) 108. 8. S.C. Ng’and N. N.Brockhouse, to be published. 9. J.M.Rowell, W.L.McMillan and P.W.Anderson, Phys.Rev.Letters 14 (1965) 633.
SPEETRALE EMIsSI~NSVERRALTEN V0N GEPULSTEN GaAs-LASERDIODEN
NANOSEEUNDEN-
F. W. LINDNER Lehrstuhl
ftir Angewandte
Physik
der
Technischen
Eingegangen
Time integrated and time resolved of temperature effects on spectral
Hochschule
Germany
am 7. MLrz 1967
spectra of nanosecond-pulsed emission far above threshold.
Mittels eines Jarell-Ash-O.5 m-Ebert-Monochromators wurde bei einer Auflijsung von ca. 0.6 A sowohl das zeitintegrierte als such das zeitaufgelbste Spektrum von GaAs-Laserdioden [l] bei Stromimpulsbreiten zwischen 25 ns und 100 ns untersucht. Es wurde gefunden, dass der Aufbau der Spektren stark von Diode zu Diode variiert, dass jedoch die Abhlngigkeiten des Spektrums von Strom, Temperatur und Impulsbreite qualitativ bei allen Dioden den gleichen Verlauf besitzen. Zwei Dioden wurden besonders eingehend totersucht: eine (#2) bei der Erregung in Liniengruppen erfolgte, d. h. Erregung von je 2-4 benachbarten Moden in einer Gruppe bei einem Abstand von ca. acht theoretischen Modenabstanden zwischen zwei Gruppen, die andere (#l) mit Erre-
Darmstadt,
GaAs-diode-lasers
show the influence
von Linien im konstanten Abstand von drei theoretischen Modenabstanden. Im Bereich des superlinearen Laseranstieges, der bei der Diode #2 im Gegensatz zur Diode #l sehr ausgedehnt war, konnte keine Erregung zusatzlicher Moden zu denen bei 10% oberhalb der Schwelle erregten Moden nachgewiesen werden. Erst zu Beginn des linearen Laserbereiches konnte die zusatzliche Erregung sowohl langwelligerer als such kurzwelligerer Linien beobachtet werden. In ijbereinstimmung mit der Literatur [2] wurde oberhalb der Schwelle ein schnelleres Wachsen der kurzweiligen Moden gegeniiber den langwelligen mit einer Verschiebung des Intensitatsmaximums des Spektrums bei Stromerhtihung gung
409