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Collective excitations in narrow superconducting strips
COLLECTIVE
EXCITATIONS CONDUCTING
IN NARROW STRIPSt
K. W. SHEPARD Department of Physics, Stanford University, Stanford,
SUPER-
California,
USA
Synopsis
Thin aluminum films scribed into strips several microns wide and a few mm long have been irradiated with microwaves of wavelength comparable to the length of the strips. The microwave source is an electron cyclotron maser, of the sort devised by Bott, tunable in wavelength from 12 to 2 mm, and with output power on the order of 100 mW. The aluminum strips constitute dipole antennas with a resonance corresponding to a highly relaxed plasmon excitation which can be made to lie within the superconducting energy gap. Effects of excitation of the plasmon mode upon the condensate will be described.
Plasmons are usually considered as charge density oscillations of a high frequency with an energy more or less independent of wavenumber. When the wavenumber becomes extremely small, comparable to the inverse of the longest dimension of the conductor being considered, the longitudinal charge density oscillations are mediated by fields extending through free space and the dispersion relation for such excitations approaches o = ck. These are shape resonances, such as occur in a dipole antenna. With a superconducting dipole such modes may constitute excitations within the energy gap. When Little first suggested the possibility of an organic superconducting molecule’), Onsager mentioned that such highly relaxed plasmons would punctuate any superconducting energy gap in a long molecule and possibly destroy the superconductivity. The work reported here is preliminary results of a study of relaxed plasmons in a metallic superconductor. The object is to determine what effect, if any, the density oscillations have upon superconductivity. The system studied is thin film, narrow strips of aluminum, the length of which is varied to place the dipole resonance at various positions within the gap. The dimensions of the strips are film thickness I = 200 A, width o = 2 F and length I = 0.5-2 mm. The width of these strips is less than the effective penetration depth so that currents should be uniformly distributed across the width. Also the inductance of the strips will be modified by the kinetic inductance of the superfluid which is proportional to the square of t Work supported by the US Office of Naval Research. 786
COLLECTIVE
EXCITATIONS
IN AI STRIPS
787
the penetration depth. This should cause a further decrease in the frequency of density oscillations and introduce a temperature dependence. The experiment is to excite the dipole resonance with microwave radiation and observe the response. The microwave generator used was developed several years ago by Bott2T3). An over-moded cavity is placed in a strong magnetic field and the cavity filled with weakly relativistic electrons in cyclotron orbits. When the cavity field is adjusted so that the cyclotron resonance frequency coincides with a favorable mode of the cavity oscillation occurs. The output, (fig. l), is not continuously tunable, but consists of a closely spaced series of modes. No absolute power measurements have been made, but the crystal outputs correspond roughly with the Bott’s result of power levels on the order of 100 mW. -
2 2
.1
+
h
2 m
f F ”
.Ol
-
I
I
I
III
40
80
Frequency
GHz
Fig. 1. Electron cyclotron maser output as a function of frequency. Only the stronger modes are shown. Above 114 GHz, a continuous output is obtained.
To observe the dipole resonance resistive leads are attached to an aluminum strip and the dc critical current measured simultaneously with irradiation by microwaves. The microwave power necessary to reduce the critical current to zero is taken as a measure of the dipole response. The power is measured with a Ge bolometer in the same dewar as the sample. Only the most preliminary experimental results have been obtained. Figure 2 shows the response of a dipole exhibiting a marked resonance the width of which is rough!y what one would expect from radiation damping of a dipole antenna resonance. The vertical lines are calculated resonance frequencies for a dipole of the given length, taking into account the dielectric properties of the substrate and the kinetic inductance of the superfluid which produces the observed temperature dependence of the resonant frequency. Since the kinetic inductance depends strongly on film thickness the agreement obtained here is reasonable.
788
K. W. SHEPARD
t ‘0.63
40
50
Frequency
60 GHz
Fig. 2. Dipole response as a function of applied microwave frequency. Response R a l/P, where P, is the microwave power necessary to drive the dipole normal. R is in arbitrary units. The above resonance is for an Al strip 1.53 mm long.
The dependence of the dc critical current on microwave power has an interesting feature displayed in fig. 3. For a considerable range of microwave power the critical current is increased. This effect has been seen in nearly all the dipoles studied. The magnitude and structure of the effect depend upon sample geometry, temperature, and microwave frequency.
2 ‘C
2
4
MIcrowave
Fig. 3. Normalized
6-8 Power
critical current VS. applied microwave power for a thin-film strip of Al 2.6 CC wide.
The charge-density oscillation provides a simple mode1 for the enhancement effect4). If we represent tHe plasmon by a dipole moment, Peiwt, then the timeaverage energy associated with the excitation will have the form F, = KP2 -&EP,
COLLECTIVE
EXCITATIONS
IN Al STRIPS
789
where E is the maximum value of the microwave field and K is a parameter which depends upon sample geometry and microwave frequency. The first term on the right is the self-energy of the excitation and the second term the interaction energy with the applied field which is negative so long as the dipole is driven below resonance. The above situation holds only in the superconducting state because in the normal state the plasmon is heavily damped. There will be a change in the condensation energy of the form F, - F, = KP= - 3EP,
and we see that when the interaction term dominates, the condensation energy will be increased by application of the microwave field. One feature of this model is that as the width of the superconducting strip increases beyond the effective penetration depth, the response is confined to the edges of the strip. The dipole interaction with the applied field will not increase as does the total condensation energy. For strips more than a few microns in width the enhancement should be very small. A similar enhancement effect has been noticed5,6) in Dayem bridges which is not observable for constriction widths of more than a few microns. Although the more complex geometry and non-linear behavior of such structures would make the application of this model less straightforward, it possibly applies to these systems. The model suggested is certainly not established with the present data and further work is being done. REFERENCES 1) Little, W.A.,
Phys.
2) Bott, I. B., Phys. 3) Beasley,
J., P., C.V.D.
4) Suggested 5) Wyatt, 6) Dayem,
Rev.,134(1964)A1416.
Letters,
14 (1965) 293. Terminal
Report:
RP8-38,
Mullard
by W. A. Little.
A. F. G. er al., Phys. Rev. Letters, A. H. and Wiegand,
J. J., Phys.
16
(1966) Id166. ( 1967) 4 19.
Rev. 155
Research
Laboratories
(1967).
EXCITATIONS CONDUCTING
IN NARROW STRIPSt
K. W. SHEPARD Department of Physics, Stanford University, Stanford,
SUPER-
California,
USA
Synopsis
Thin aluminum films scribed into strips several microns wide and a few mm long have been irradiated with microwaves of wavelength comparable to the length of the strips. The microwave source is an electron cyclotron maser, of the sort devised by Bott, tunable in wavelength from 12 to 2 mm, and with output power on the order of 100 mW. The aluminum strips constitute dipole antennas with a resonance corresponding to a highly relaxed plasmon excitation which can be made to lie within the superconducting energy gap. Effects of excitation of the plasmon mode upon the condensate will be described.
Plasmons are usually considered as charge density oscillations of a high frequency with an energy more or less independent of wavenumber. When the wavenumber becomes extremely small, comparable to the inverse of the longest dimension of the conductor being considered, the longitudinal charge density oscillations are mediated by fields extending through free space and the dispersion relation for such excitations approaches o = ck. These are shape resonances, such as occur in a dipole antenna. With a superconducting dipole such modes may constitute excitations within the energy gap. When Little first suggested the possibility of an organic superconducting molecule’), Onsager mentioned that such highly relaxed plasmons would punctuate any superconducting energy gap in a long molecule and possibly destroy the superconductivity. The work reported here is preliminary results of a study of relaxed plasmons in a metallic superconductor. The object is to determine what effect, if any, the density oscillations have upon superconductivity. The system studied is thin film, narrow strips of aluminum, the length of which is varied to place the dipole resonance at various positions within the gap. The dimensions of the strips are film thickness I = 200 A, width o = 2 F and length I = 0.5-2 mm. The width of these strips is less than the effective penetration depth so that currents should be uniformly distributed across the width. Also the inductance of the strips will be modified by the kinetic inductance of the superfluid which is proportional to the square of t Work supported by the US Office of Naval Research. 786
COLLECTIVE
EXCITATIONS
IN AI STRIPS
787
the penetration depth. This should cause a further decrease in the frequency of density oscillations and introduce a temperature dependence. The experiment is to excite the dipole resonance with microwave radiation and observe the response. The microwave generator used was developed several years ago by Bott2T3). An over-moded cavity is placed in a strong magnetic field and the cavity filled with weakly relativistic electrons in cyclotron orbits. When the cavity field is adjusted so that the cyclotron resonance frequency coincides with a favorable mode of the cavity oscillation occurs. The output, (fig. l), is not continuously tunable, but consists of a closely spaced series of modes. No absolute power measurements have been made, but the crystal outputs correspond roughly with the Bott’s result of power levels on the order of 100 mW. -
2 2
.1
+
h
2 m
f F ”
.Ol
-
I
I
I
III
40
80
Frequency
GHz
Fig. 1. Electron cyclotron maser output as a function of frequency. Only the stronger modes are shown. Above 114 GHz, a continuous output is obtained.
To observe the dipole resonance resistive leads are attached to an aluminum strip and the dc critical current measured simultaneously with irradiation by microwaves. The microwave power necessary to reduce the critical current to zero is taken as a measure of the dipole response. The power is measured with a Ge bolometer in the same dewar as the sample. Only the most preliminary experimental results have been obtained. Figure 2 shows the response of a dipole exhibiting a marked resonance the width of which is rough!y what one would expect from radiation damping of a dipole antenna resonance. The vertical lines are calculated resonance frequencies for a dipole of the given length, taking into account the dielectric properties of the substrate and the kinetic inductance of the superfluid which produces the observed temperature dependence of the resonant frequency. Since the kinetic inductance depends strongly on film thickness the agreement obtained here is reasonable.
788
K. W. SHEPARD
t ‘0.63
40
50
Frequency
60 GHz
Fig. 2. Dipole response as a function of applied microwave frequency. Response R a l/P, where P, is the microwave power necessary to drive the dipole normal. R is in arbitrary units. The above resonance is for an Al strip 1.53 mm long.
The dependence of the dc critical current on microwave power has an interesting feature displayed in fig. 3. For a considerable range of microwave power the critical current is increased. This effect has been seen in nearly all the dipoles studied. The magnitude and structure of the effect depend upon sample geometry, temperature, and microwave frequency.
2 ‘C
2
4
MIcrowave
Fig. 3. Normalized
6-8 Power
critical current VS. applied microwave power for a thin-film strip of Al 2.6 CC wide.
The charge-density oscillation provides a simple mode1 for the enhancement effect4). If we represent tHe plasmon by a dipole moment, Peiwt, then the timeaverage energy associated with the excitation will have the form F, = KP2 -&EP,
COLLECTIVE
EXCITATIONS
IN Al STRIPS
789
where E is the maximum value of the microwave field and K is a parameter which depends upon sample geometry and microwave frequency. The first term on the right is the self-energy of the excitation and the second term the interaction energy with the applied field which is negative so long as the dipole is driven below resonance. The above situation holds only in the superconducting state because in the normal state the plasmon is heavily damped. There will be a change in the condensation energy of the form F, - F, = KP= - 3EP,
and we see that when the interaction term dominates, the condensation energy will be increased by application of the microwave field. One feature of this model is that as the width of the superconducting strip increases beyond the effective penetration depth, the response is confined to the edges of the strip. The dipole interaction with the applied field will not increase as does the total condensation energy. For strips more than a few microns in width the enhancement should be very small. A similar enhancement effect has been noticed5,6) in Dayem bridges which is not observable for constriction widths of more than a few microns. Although the more complex geometry and non-linear behavior of such structures would make the application of this model less straightforward, it possibly applies to these systems. The model suggested is certainly not established with the present data and further work is being done. REFERENCES 1) Little, W.A.,
Phys.
2) Bott, I. B., Phys. 3) Beasley,
J., P., C.V.D.
4) Suggested 5) Wyatt, 6) Dayem,
Rev.,134(1964)A1416.
Letters,
14 (1965) 293. Terminal
Report:
RP8-38,
Mullard
by W. A. Little.
A. F. G. er al., Phys. Rev. Letters, A. H. and Wiegand,
J. J., Phys.
16
(1966) Id166. ( 1967) 4 19.
Rev. 155
Research
Laboratories
(1967).