PACS numbers: r, Ad,85.25.Cp,74.25-q

Transcription

1 Microwave resonant activation in hybrid single-gap/two-gap Josephson tunnel junctions Steve Carabello, 1, a) Joseph G. Lambert, 2 Jerome Mlack, 2 Wenqing Dai, 3 Qi Li, 3 Ke Chen, 4 Daniel Cunnane, 4 X. X. Xi, 4 and Roberto C. Ramos 5 1) Penn State Harrisburg, Middletown, PA 1757, USA 2) Drexel University, Philadelphia, PA 1914 USA 3) The Pennsylvania State University, University Park, PA 1682, USA 4) Temple University, Philadelphia, PA 19122, USA 5) University of the Sciences, Philadelphia, PA 1914, USA (Dated: 4 August 216) Microwave resonant activation is a powerful, straightforward technique to study classical and quantum systems, experimentally realized in Josephson junction devices cooled to very low temperatures. These devices typically consist of two single-gap superconductors separated by a weak link. We report the results of the first resonant activation experiments on hybrid thin film Josephson junctions consisting of a multi-gap superconductor (MgB 2 ) and a single-gap superconductor (Pb or Sn). We can interpret the plasma frequency in terms of theories both for conventional and hybrid junctions. Using these models, we determine the junction parameters including critical current, resistance, and capacitance and find moderately high quality factors of Q 1 for these junctions. PACS numbers: r, 74.7.Ad,85.25.Cp,74.25-q a) Electronic mail: sac13@psu.edu; Drexel University, Philadelphia, PA 1914 USA 1

2 I. INTRODUCTION The current-biased Josephson junction has long been used as a test bed for studying resonant activation, which is the escape of a Brownian motion particle from a potential well in the presence of a source of fluctuations 1,2. Increasing the bias current through the junction is analogous to tilting the associated washboard potential and lowering the potential barrier height. This results in the escape of a fictitious phase particle from the well, experimentally realized as a switch from the superconducting to the normal state of the junction. Microwaves resonant with the well s plasma frequency can facilitate this escape 2,3 - a process known as microwave resonant activation (MRA). Such switching experiments have been widely performed on purely single-gap junctions with electrodes made with conventional superconductors (e.g. Nb, Al) or high-t c superconductors (e.g. 4 ). With the advent of the multi-gap superconductors magnesium diboride (MgB 2 ) 5,6 and iron pnictides 7 9, there has been a growing theoretical interest in the switching dynamics of junctions that incorporate multi-gap superconductors In these theories, the simplest hybrid junction consists of Josephson-coupled single-gap and two-gap superconducting electrodes, where the tunneling current is the parallel sum of two Josephson currents between the electrodes. Within the two-gap electrode is a Josephson-like interband coupling between the Cooper pair condensates, as proposed by Leggett 14. This is known as the Josephson-Leggett (JL) mode. The dynamics of a hybrid junction system has been theoretically described in terms of a particle in a two-dimensional washboard potential with axes consisting of the center-of-mass phase (θ) and relative phase (ψ), which are transformations of the phase differences between the two different Cooper pair condensates in the two-gap superconductor and that of the single-gap superconductor 1. We report the first microwave resonant activation (MRA) experiments on hybrid Josephson junctions, with magnesium diboride and Pb or Sn as the dual-gap and single-gap superconducting electrodes, respectively. We have observed the enhancement of escape rates under microwave excitation, as predicted by theory, and which demonstrates MRA in hybrid junctions. By manipulating microwave frequency and power, we demonstrate good control over the escape of the phase particle. As a guide to this paper, we first briefly discuss aspects of hybrid junction theory rele- 2

3 vant to microwave resonant activation measurements. We find that the plasma frequency predicted by hybrid junction theory has the same form as that predicted by conventional theory, except for a scaling factor. As a result, switching experiments on a single hybrid junction can be analyzed, to some extent, as a conventional junction. Next, we describe our samples and experimental details. We follow this with our results, which describe the details of the microwave resonant activation measurements and escape rate enhancement peaks which suggest quantum behavior with a moderately high quality factor 1. II. THEORY The RCSJ (Resistively and Capacitively Shunted Junction) model 15,16, shown schematically in the inset of Figure 1, provides useful insights for understanding the behavior of Josephson junctions. The model illustrates that the junction obeys the same dynamics as a phase particle in a tilted washboard potential. m=c Φ 2π ω 2 I b = U U(γ) E J -4 I b ω p I b = I /2-8 I R C I f I b = I γ/π FIG. 1. The washboard potential for an ideal tunnel junction. Here, γ is the phase difference across the junction. When I b < I, the phase particle may be trapped in the well, oscillating about the local minimum. As the bias current increases, the barrier height U and resonant frequency ω p decrease, until, at the critical current I, U = and the junction must exhibit a finite resistance. Inset: The RCSJ model of a Josephson junction, consisting of an ideal junction in parallel with resistive and capacitive channels. Fluctuations to the current may be provided by thermal and/or microwave excitations. As shown in Figure 1, local minima exist which may trap the phase particle, leading 3

4 to zero voltage across the junction (for relatively slow ramp rates), when the bias current I b < I. The phase particle may escape from this minimum either by gaining sufficient thermal energy to move classically over the barrier, or by tunneling quantum-mechanically through it. In a system with small damping, once the phase particle escapes, its velocity must remain nonzero, which is manifested physically by a finite voltage across the junction. The phase particle may resonantly escape when microwave excitations match the resonant frequency of this system, described as the plasma frequency 15 ω p = 2eI hc ( 1 (Ib /I ) 2) 1/4 (1) which is a function of bias current I b. Therefore, the bias current at which the junction switches can be used to calculate the resonant frequency. In conventional junctions, where both electrodes have a single energy gap, these resonances have been used to obtain the junction parameters, and to distinguish between classical and quantum escape (e.g. 3,17 ). For hybrid junctions incorporating one electrode with two superconducting energy gaps (such as MgB 2 ), additional effects must be considered. As discussed in Asai et al. 11,12, the DC current through the junction controls the tilt along the center-of-mass phase (θ) axis of the two-dimensional potential. In 11, the authors consider the in-phase case with small oscillations of the relative phase difference coordinate about ψ =. In this framework, the system is described by a modified one-dimensional washboard potential coupled to a harmonic oscillator bath arising from fluctuations in ψ (the JL mode). The JL mode modifies the conventional washboard potential of a purely single-gap system in two ways: first, there is an effective lowering of the barrier height, and second, the JL bath provides a source of dissipation. Considering these effects, they derive an effective plasma frequency for this system 11 ω eff p = 2eI (1 ε) ( 1 (Ib / [I (1 ε)]) 2) 1/4 hc (2) where ε is a small dimensionless constant related to the coupling of the Josephson-plasma and Josephson-Leggett modes. 4

5 III. EXPERIMENT DESIGN The junctions used in this study incorporate high purity MgB 2 thin films grown by hybrid physical-chemical vapor deposition (HPCVD) on single-crystal SiC substrates 18,19. An insulating cement is painted, leaving a roughly.3 mm-wide strip exposed. A native oxide formed by exposing the MgB 2 film to air serves as the insulating barrier. Finally, a strip of Pb or Sn is thermally evaporated perpendicular to the exposed film, forming the superconducting counter-electrode. The MgB 2 /I/Pb junction used for this study has an area.59 mm 2 ; the MgB 2 /I/Sn junction has an area of.15 mm 22. Magnesium diboride is chosen because of its two well-characterized energy gaps 21, with the σ gap associated with two-dimensional bonds localized in the Boron planes and the π gap associated with three-dimensional bonds derived from the Boron p z orbitals 6. These contribute to substantial anisotropy in the tunneling behavior, with different samples exhibiting varying amounts of tunneling from these two gaps. Conductance measurements of the same devices demonstrate that tunneling for the MgB 2 /I/Pb junction is along the c-axis with minimal contribution from the σ band (σ gap weighting factor w σ < 1%), as expected for a film grown on SiC. The film of the MgB 2 /I/Sn junction is grown on a SiC substrate tilted 8 from the c-axis, allowing moderate tunneling along the a b plane (w σ 6%) 22. A typical current vs. voltage curve is shown in Figure 2(a). These junctions were cooled in a Helium dilution refrigerator with a base temperature 2 mk. To minimize noise, the current bias lines were thermalized to each stage and heavily filtered using Thermocoax lines and copper powder filters that yield a total attenuation in excess of 8 db across the frequency range investigated. Further information about these junctions, their current-voltage characteristics, and the measurement system, may be found in 22. We seek to analyze the switching dynamics. Because the phase escape is stochastic, we must repeatedly measure the switching current to obtain a distribution. We achieve this by ramping the current from to beyond I to ensure an escape, which is detected by a corresponding jump in the voltage across the junction, as indicated in Figure 2. The current is then reduced to slightly negative values to ensure that the phase particle is retrapped. Finally, leaving the current at zero allows the system to equilibrate. This cycle is repeated 5

6 I (µa) (a) -4 4 V (mv) I (µa) V (mv) (b) I (i) (ii) (iii) (c) V trigger level t (s) (d) FIG. 2. (a) A current-voltage characteristic of the MgB 2 /I/Sn junction. The strong hysteresis and high subgap resistance indicate a good tunnel barrier. (b) When conducting switching experiments, a far smaller portion of the I-V curve is explored. (c) Measured current vs. time. The current ramp proceeds in three stages: (i) a linear increase from through the critical current (ii) a smooth reduction to slightly negative values, to ensure retrapping of the phase particle (iii) the current remains zero, to allow the system to equilibrate. (d) Measured voltage vs. time. The voltage across the junction suddenly jumps to a finite value at the switching current. This signals the timer to stop, allowing us to compute the switching current to high precision. at a frequency of 9 Hz. During the entire ramp, we apply a constant-frequency RF current, coupled to the junction by an antenna close to the sample. The resulting resonant escapes are then detected and analyzed through histograms of many escape events, as shown in Figures 3(b) and 4. At low RF power, the phase particle is unlikely to absorb a photon during any given ramp in the current. In this case, only one peak is observed at a current slightly smaller than I (e.g. the -32 dbm curve of Figure 3(b)). This is the primary peak at current I p < I, that reflects premature switching due to a combination of quantum tunneling through the barrier, thermal activation, and perturbations in the washboard potential due to the applied microwaves. At high RF power, resonant escape is very likely, resulting in escape at a lower current (e.g. the -26 dbm curve of Figure 3(b)). At an intermediate power, both the higher-current primary peak and the lower-current resonant peak are observed simultaneously (e.g. 4,23 ). I p and the resonant current I r are chosen at the local maxima of 6

7 (a) I r Γ(s -1 ) Counts (b) I p -32 dbm -3 dbm -29 dbm -28 dbm -26 dbm Switching Current (µa) FIG. 3. (Color online) Histograms and escape rates at five different nominal microwave powers (i.e. power at the microwave source), for the MgB 2 /I/Pb junction at T = 22 mk, when driven by microwaves at 1.35 GHz. At low powers, the distributions are effectively the same as those in the absence of microwaves. As the power is increased, the phase particle is more likely to escape via resonant activation, which eventually becomes the dominant process. The resonant current I r is defined as the current of the resonant peak for the power at which it is the same height as the primary peak. This coincides with a local maximum in the escape rate. the histogram peaks when these two peaks are equal heights 24,25. The escape rate as a function of bias current, Γ(I), is computed from the switching current distributions 26. As indicated in Figure 3(a), I r coincides with a local maximum in the escape rate, which is often more practical than using the histogram peaks of Figure 3(b). We used the time-of-flight technique to collect switching current distributions as indicated in Figure 3. While increasing the bias current from zero, we precisely measure the time between the start of the ramp until the junction switches to the finite voltage state. We detect the switch when the voltage threshold of a Schmitt trigger is reached (at roughly 2/3 of the gap voltage V g = 1+ 2 e where i are the superconducting energy gaps of the two electrodes). We achieve good statistics with 1 na bin width using an SR62 frequency counter with 25 ps resolution. We convert the time to current using the known current ramp 7

8 FIG. 4. (Color online) Perspective plot of switching histograms for the MgB 2 /I/Pb junction at T = 23mK, when driven by microwaves at 1.35GHz. The transition from primary peak to resonant peak is even more apparent. Within a narrow range of powers, the primary and resonant peaks coexist. rate. IV. RESULTS When the bias current I b is equal to the resonant current I r, the frequency of the applied microwaves f is equal to the effective plasma frequency of the junction f eff p = ωp eff /2π in the harmonic limit. Therefore, measuring I r over a range of applied frequencies allows us to fit the resulting f vs. I curve using Equation 2. An example is shown in Figure 5. We point out that Equation 2 is equivalent to Equation 1 if I is replaced by I eff = I (1 ε). When fitting using Equation 2 alone, I and ε cannot be independently constrained. As a result, we treat I eff as one of the two fit parameters (the other being the junction capacitance C). Additional resonances were observed at higher harmonics and subharmonics of the resonant frequency; these further assisted in constraining the fit parameters. For the MgB 2 /I/Pb junction used for this study, the f vs. I fits give I eff = 19.93±.4 µa and C = ± 18.6 pf. For the MgB 2 /I/Sn junction, I eff = ±.5 µa and C = 1523 ± 14 pf. 8

9 f (GHz) I r (µa) FIG. 5. Microwave driving frequency f vs. resonant current I r for the MgB 2 /I/Sn junction for T 25mK, fit according to Equation 2. Only two parameters, I eff and C, are needed to generate the fit. In this case, I eff = ±.5 µa and C = 1523 ± 14 pf. Additional information about the junctions may be extracted from MRA results using the enhancement in the escape rate due to the microwaves normalized to the case with no microwaves Γ = Γ RF On Γ RF Off 17 Γ Γ RF Off. When the enhancement is plotted as a function of current, a Lorentzian peak at I r is observed if the system is dominated by quantum-mechanical tunneling through the barrier. However, when thermal escape over the barrier is the dominant process, the enhancement exhibits a nearly flat shelf below the resonant current I r, instead of a peak 17,27,28. This enhancement peak provides a measure of the quality factor Q. Converting the current axis to frequency using Equation 2, the quality factor is calculated as the applied microwave frequency divided by the half width at half maximum of the Lorentzian fit 27. The quality factor extracted in this way from the enhancement is commonly taken to be a lower bound or conservative estimate of Q 27,28. As shown in the inset of Figure 6, we observed a peak in the escape rate enhancement. We fit these data to a three-parameter Lorentzian curve to extract conservative estimates of the quality factors of these junctions. Accordingly, for the MgB 2 /I/Pb junction, Q(I = µa) 45 and Q(I = ) Q 9. For the MgB 2 /I/Sn junction, Q(I = µa) 3 and Q 1. The remainder of this section presents additional results unrelated to microwave resonant activation that we used to gain confidence in the results of these fits. We can verify the quality factor, and thereby extract a resistance, by fitting the escape rate in the absence of microwaves, in the thermal regime. We determined the minimum 9

10 1 7 RF Off RF On 1 6 Γ (s -1 ) FWHM =.85 µa I peak = µa Area =.99 µa 1 4 Γ/Γ (µa) (µa) FIG. 6. Escape rates in the presence and absence of microwaves, for the MgB 2 /I/Pb junction at 21 mk. For this plot, the microwaves were applied at.8 GHz at a nominal power of -51 dbm. Inset: Enhancement in the escape rate due to microwave excitation. The Lorentzian fit to the enhancement gives Q(I = µa) 45, or Q 9. temperature at which this applies by plotting the standard deviation vs. temperature, as shown in Figure 7. For both junctions, the standard deviation decreases approximately linearly with temperature down to 1 mk. Therefore, we conclude that thermal energy is the dominant source of phase escape above this temperature. The escape rate of a conventional junction with low damping, when thermal rather than quantum escape is the dominant process, was found by Büttiker, Harris and Landauer 29 ( ω p Γ BHL = a t 2π exp U ) k B T esc (3) where a t = [ 4 ] 2, Q = ω p RC is the quality factor of the junction, and 1+5Qk B T esc /(9 U)+1 T esc is the escape temperature of the junction, which is expected to match the physical temperature of the junction in the thermal regime 27. To our knowledge, there are currently no equations for the escape rate in the thermal regime for hybrid junctions. The escape rate expressions found in 1 and 11 are in the quantum (T ) limit. Therefore, in the following discussion, we assume that the conventional 1

11 σ (µa) T (K) FIG. 7. Standard deviation of the switching histogram vs. temperature for the MgB 2 /I/Pb junction. Dashed lines are guides for the eye. The standard deviation decreases approximately linearly with temperature down to 1 mk. Therefore, we conclude that thermal energy was the dominant process for phase escape above this temperature. equation (Equation 3) for thermal escape applies, although corrective factors may be needed to account for hybrid junction behavior. With these considerations in mind, we use the I eff and C values determined from microwave resonant activation, and fit the escape rate in the absence of microwaves to Equation 3. Representative results are shown in Figure mk K Γ (s -1 ) 1 6 Fit: 1 5 R = 9. Ω C = 1523 pf 1 4 T esc =.226 K I = µa (µa) Fit: R = 9. Ω C = 1523 pf T esc = K I = µa (µa) FIG. 8. Fit of the escape rate in the absence of microwaves for the MgB 2 /I/Sn junction. Data were taken from 23 mk through 3.45 K; the resulting escape rates were fit according to Equation 3 above 1 mk - i.e. when the system is in the thermal regime. From these, we conclude that R = 9 ± 4 Ω for this junction. From these fits, we find, for the MgB 2 /I/Pb junction, R = 46 ± 24 Ω 3 and Q = 11

12 R 2eI C h = 25 ± 14. For the MgB 2 /I/Sn junction, R = 9 ± 4 Ω and Q = 2 ± 9. For each, the relatively high percentage uncertainty in the resistance (compared with that in the critical current and the capacitance) is due to the relative insensitivity to changes in resistance of the thermally-fitted escape rate. This fit also depends strongly on the critical current, so small variations in I eff produce large variations in R. These results compare favorably with the conservative estimates of the quality factor determined from the escape rate enhancement, described above. This suggests that our application of the conventional equation may be reasonable. However, over most of the temperature range, there is a consistent factor of 1.3 discrepancy between the measured temperature and the fitted temperature T esc, obtained from Equation 3. We have not determined the source of this discrepancy, although it may be related to the effective suppression of the washboard due to coupling to the Josephson-Leggett mode, as described in 1. V. CONCLUSIONS We have performed the first microwave resonant activation experiments on hybrid singlegap/two-gap junctions based on MgB 2. We have demonstrated good control of the escape of the phase particle describing the dynamics of the junction, by manipulating frequency and microwave power. We have observed the primary and resonant escapes in these devices. Our resonant activation results are consistent with theory for the plasma frequency for hybrid junctions, in which the I of conventional junctions is replaced by I eff = I (1 ε) for hybrid junctions. Using these methods, we have determined junction parameters for two junctions (MgB 2 /I/Pb and MgB 2 /I/Sn) with different film geometries, critical currents, resistances and capacitances. Additionally, both proved to be highly underdamped Josephson junctions (quality factor Q 1), reflecting low dissipation. This is consistent with our highly hysteretic I V curves (e.g. Figure 2(a)). Additional exploration of switching behavior may further elucidate the influence of the Josephson-Leggett mode on the switching dynamics of hybrid two-gap junctions, including a deeper analysis of escape rates in the thermal regime. 12

13 ACKNOWLEDGMENTS This research has been supported by a grant in aid from Sigma Xi, the Scientific Research Society. We acknowledge partial support from National Science Foundation Grant # DMR (R. C. R.), DOE DE-FG2-8ER46531 (Q.L.). The work at Temple University was supported by ONR under Grant No. N REFERENCES 1 H. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7, (194). 2 M. H. Devoret, D. Esteve, J. M. Martinis, A. Cleland, and J. Clarke, Resonant activation of a Brownian particle out of a potential well: Microwave-enhanced escape from the zerovoltage state of a Josephson junction, Phys. Rev. B 36, (1987). 3 M. H. Devoret, J. M. Martinis, D. Esteve, and J. Clarke, Resonant activation from the zero-voltage state of a current-biased Josephson junction, Phys. Rev. Lett. 53, (1984). 4 T. Bauch, T. Lindström, F. Tafuri, G. Rotoli, P. Delsing, T. Claeson, and F. Lombardi, Quantum dynamics of a d-wave Josephson junction, Science 311, 57 6 (26), 5 J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature 41, (21). 6 X. X. Xi, Two-band superconductor magnesium diboride, Rep. Prog. Phys. 71, (28). 7 Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor La[O1-xFx]FeAs (x =.5.12) with Tc = 26 K, J. Am. Chem. Soc. 13, (28), pmid: , 8 H. Takahashi, K. Igawa, K. Arii, Y. Kamihara, M. Hirano, and H. Hosono, Superconductivity at 43 K in an iron-based layered compound LaO1-xFxFeAs, Nature 453, (28). 9 J. Paglione and R. L. Greene, High-temperature superconductivity in iron-based materi- 13

14 als, Nat. Phys. 6, (21). 1 Y. Ota, M. Machida, and T. Koyama, Macroscopic quantum tunneling in multigap superconducting Josephson junctions: Enhancement of escape rate via quantum fluctuations of the Josephson-Leggett mode, Phys. Rev. B 83, 653 (211). 11 H. Asai, Y. Ota, S. Kawabata, M. Machida, and F. Nori, Theory of macroscopic quantum tunneling with Josephson-Leggett collective excitations in multiband superconducting Josephson junctions, Phys. Rev. B 89, (214). 12 H. Asai, S. Kawabata, Y. Ota, and M. Machida, Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions, J. Phys. Conf. Ser. 568, 226 (214). 13 H. Asai, Y. Ota, S. Kawabata, and F. Nori, Inter-band phase fluctuations in macroscopic quantum tunneling of multi-gap superconducting Josephson junctions, Physica C 54, (214), proceedings of the 26th International Symposium on Superconductivity. 14 A. J. Leggett, Number-Phase Fluctuations in Two-Band Superconductors, Progr. Theoret. Phys. 36, (1966). 15 M. Tinkham, Introduction to Superconductivity: Second Edition (Dover Publications, 1996). 16 A. Barone and G. Paternò, Physics and Applications of the Josephson Effect (Wiley-VCH Verlag GmbH & Co. KGaA, 25). 17 J. M. Martinis, M. H. Devoret, and J. Clarke, Energy-level quantization in the zerovoltage state of a current-biased Josephson junction, Phys. Rev. Lett. 55, (1985). 18 K. Chen, Y. Cui, Q. Li, C. G. Zhuang, Z.-K. Liu, and X. X. Xi, Study of MgB 2 /I/Pb tunnel junctions on MgO (211) substrates, Appl. Phys. Lett. 93, 1252 (28). 19 Y. Cui, K. Chen, Q. Li, X. X. Xi, and J. M. Rowell, Degradation-free interfaces in MgB 2 /insulator/pb Josephson tunnel junctions, Appl. Phys. Lett. 89, (26). 2 Although these junctions are relatively large, junctions of similar size fabricated in the same way exhibited good uniformity of the barrier K. Chen, W. Dai, C. Zhuang, Q. Li, S. Carabello, J. G. Lambert, J. T. Mlack, R. C. Ramos, and X. X. Xi, Momentum-dependent multiple gaps in magnesium diboride probed by electron tunnelling spectroscopy, Nat. Commun. 3, 619 (212). 22 S. Carabello, J. G. Lambert, J. Mlack, W. Dai, Q. Li, K. Chen, D. Cunnane, C. G. Zhuang, 14

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16 m=c Φ 2π ω 2 I b = U U(γ) E J -4 I b ω p I b = I /2-8 I R C I f I b = I γ/π

17 I (µa) (a) -4 4 V (mv) I (µa) V (mv) (b) I (i) (ii) (iii) (c) V trigger level t (s) (d)

18 (a) I r Γ(s -1 ) Counts (b) I p -32 dbm -3 dbm -29 dbm -28 dbm -26 dbm Switching Current (µa)

19

20 f (GHz) I r (µa) 1 11

21 1 7 RF Off RF On 1 6 Γ (s -1 ) FWHM =.85 µa I peak = µa Area =.99 µa 1 4 Γ/Γ (µa) (µa)

22 σ (µa) T (K)

23 mk K Γ (s -1 ) 1 6 Fit: 1 5 R = 9. Ω C = 1523 pf 1 4 T esc =.226 K I = µa (µa) Fit: R = 9. Ω C = 1523 pf T esc = K I = µa (µa)