Transport phenomena in single crystal superconducting niobium

Physica B 169 (1991) 445-446 North-Holland

TRANSPORT R.J.GAITSKELL,

PHENOMENA D.J.GOLDIE,

IN SINGLE

CRYSTAL

SUPERCONDUCTING

NIOBIUM

N.E.BGQTH,C.PATELandG.L.SALMON

Department of Physics, University of Oxford, Nuclear Physics Laboratory, Keble Road, Oxford OX1 3RH, United Kingdom Following recent interest in niobium as a superconducting detector for possible astronomical dark matter, we have extended previous measurements of phonon propagation in high purity single crystal niobium below 1K. We have also, for the first time, observed the propagation of quasiparticles in bulk niobium, with a characteristic diffusion time an order of magnitude slower than that of the phonons. _ 1. INTRODUCTION

Considerable interest has been shown ln the possibility of using niobium, with its large nuclear spin of 9/2, as a bulk superconducting detector in the search for and identification of dark matter candidates (1). The nuclear recoil from the interaction of such a particle will lead to the creation of an excess of quasiparticles and phonons in the superconductor. In order to establish the feasibility of such a detector we have studied the transport properties of phonons and quasiparticles in 3-g single crystals of niobium. At low temperatures, the recombination rate of quasiparticles, which is determlned by the thermal density, decreases as exp(-A/kT). The scattering rate of the quasiparticles from the phonons is also reduced and the mean free path of the quasiparticles becomes limited solely by impurity scattering. The subgap (R<2A) phonons and quasiparticles become decoupled. The phonons propagate ballistically limited only by impurity scattering. The quasiparticles propagate in mixed mode” where 2A phonons emitted by quasiparticle recombination propagate only a limited distance before re-creating two quasiparticles. The rate of the phonon pair breaking process is roughly independent of temperature. For a bulk superconductor the effective quasiparticle loss mechanism is the occasional breakup of a 2A phonon via an anharmonic process. As a result of the large energy gap in niobium (2A=3050 ueV) the theoretical lifetime, due to this loss mechanism, of quasiparticle signals becomes much greater than one second below about 1K (2,3). 2. EXPERIMENT Figure 1 shows a schematic of three superconducting tunnel junctions (STJs), used in the investigation, which were fabricated on the surface of chemically polished Nb single crystals of nominal five 9’s purity. Quasiparticle and

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phonon excitations were generated using a low power pulsed laser incident on the opposite face of the crystal via optical fibres. Measurements of the STJ response to direct illumination by laser light could also be made. The use of a range of STJ geometries allowed the separate study of the phonon and quasipartlcle signals ln the Nb. lndivldual junction areas were 0.5 mm* with I&N of lOm0 - lOOn. The upper probe film was 300 nm of Pb. The lower electrode of the junction was formed in one of three ways: by the crystal itself, with the glow discharge oxidized surface of the Nb acting as the tunnelling barrier; by a 1- 100 nm Al film deposited directly on the the crystal prior to oxidation; or by a 100 nm Al film electrically isolated from the crystal surface by 200 nm of SiO. The junctions were current biased and the signals were amplified and recorded using signal averaging. The crystals were 10 mm in diameter and l-3 mm thick with the faces lying perpendicular to the [ 1001 direction. The isolation of a STJ (see Rg. lc) from the crystal by a layer of SiO prevents any quasipartlcles from directly entering the junction films thereby making this contiiation insensitive to any direct quasiparticle signal in the Nb. However, each STJ geometry is sensitive to phonons of energy n 2 2Arttm which are able to create quasiparticles in the probe films by pair breaking. 3. PHONON DIFFUSION The inset of Fig. 2 shows the prompt phonon pulse observed in the STJ of Fig. Ic at 360 mK. The dotted line is a calculation using a diffusion function. Small additional structure was present at the leading edge of the pulses which was consistent w&h ballistic phonon transport at the known velocities of sound in Nb. A value for the diffusion coefficient can be calculated from the pulse shape and the propagation distance in the crystal. This was performed for

Schematic of 3 different Su

FIGURE 1

446

RJ. Gaitskell et al. I Single crystal superconducting niobium

a number of crystal samples and the results are plotted in the main body of Fig. 2. The solid line is a calculation assuming that the phonon mean free path A is determined by the sum of two contributions: quasiparticle AS and impurity scattering Ai. The elecnonic contribution is calculated assuming I\N = 25 nm (4). These results are consistent with the work of Pannetier et al(5). The pulse shape appears best described by a simple 3-dimensional diffusion function with no boundary conditions, suggesting little contribution from phonons reflected from the crystal surfaces. r

longer effective lifetime prediction of the Rothwarf-Taylor equations (2). The mechanism determining the quasiparticle loss rate is not clear, although the possibility that they are being trapped into regions driven normal by trapped flux or relaxing into a damage layer at the boundary of the crystal cannot be eliminated.

0

8

100

200 Tiie(ms) 1

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0

0

20

40

Time@ J

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10 15 20 TC/T FIGURE 2 Phonon diffusion coefficient as a function of TJT for a number of different devices on Nb crystals 4. QUASIPARTICLE SIGNAL Figure 3a shows the signal observed in the STJ of Fig. 1a which has an energy threshold for phonon detection of R ~2Apb (2680 ueV). This high threshold significantly reduces the magnitude of the prompt phonon peak as compared to the signal in a junction which contains an Al fti (Fig. lb or c). A second pulse with a peak arrival time about 30 times later than the prompt phonon peak is observed which we attribute to quasiparticle diffusion, Some improvement of the quasiparticle diffusion coefficient in the crystals was achieved by a short period of vacuum out-gassing at 1000 “C. A comparison of the signals observed in the STJs of Figs. lb and c is shown in Fig.3b and c. Both traces show a large initial phonon contribution, having thresholds for phonon detection of n 2 2Ati (400 ueV). The small signal at subsequent times in the STJ of Fig. lc is related to the emission of phonons by the quasiparticle decay mechanism. The sensitivity of the STJ of Fig. 1b to quasiparticles requires the existence of a proximity layer effect between the Nb and the Al film to allow transmission of quasiparticles to the junction interface (6). The influence of the proximity effect is observed in the STJ I- V characteristics. Quasiparticle transmission is exhibited by the improved sensitivity of this STJ to the quasiparticle signal relative to the prompt phonon signal. Figure 3d shows the DC coupled voltage signal in the STJ of Fig.lb over a much longer time base. The signal decays exponentially with a characteristic time of 6Oms, well in excess of any previously measured quasiparticle lifetimes. There appears to be little temperature dependence of the signal decay time for TslK. At 1K the observed decay time is between the estimate of Kaplan et al. (3) for the thermal recombination time of quasiparticles, and the

100

200 300 400 Tile (us) FIGURE 3 Signals detected in the STJs of Fig.1 at 360mK showing the prompt phonon pulse and the slower quasiparticle contribution. 4. CONCLUSIONS The absorption of photons in single crystal superconducting Nb creates a local non-equilibrium density of both phonons and quasiparticles. The subgap phonons and quasiparticles diffuse independently at temperatures below 2K where quasiparticle-phonon scattering ceases to dominate their diffusion. Unexpectedly the phonon signal precedes the quasiparticle signal in time. The impurity limited mean free path for the phonons is of the order of 100 urn. The diffusion coefficient for the quasiparticle propagation is low at around 60 cm% 1. The mean free path is of the order of 0.1 urn and was lengthened by a factor of two by out-gassing. The quasiparticle lifetime is longer than any previously observed although it appears to be saturated below 1K. A comparison of the magnitudes of the phonon and quasiparticle signals at low temperatures indicates that a very significant fraction of the initial interaction energy resides in the long-lived quasiparticle gas. REFERENCES and D.N.Spergel, Phys. Rev. (1) A.K.D&er,K.Freese D33 (1986) 3495; P.F.Smith and J.D.Lewin, Phys. Reports 187 (!990) 204 (2) A. Rothwarf and B.N.Taylor, Phys. Rev. Len., 19 (1967) 27 J.J.Chang, (3) S.B.Kaplan, C.C.Chi, D.N.Langenberg, S.Jafarey and D.J.Scalapino, Phys. Rev. B 14 (1976) 4854 Phys. Rev., 136, (1964), 1535 (see (4) V.M.Bobetic, particularly eq. 3) F.R.Ladan, J.P.Maneval, Heat pulse (5) B.Pannetier, determination of phonon mean free paths in niobium, Groupe de Physique des Solides de 1’Ecole Normale Superieure, 24 rue Lhomond, Paris 05, France (unpublished) N.E.Booth. C.Patel and G.L.Salmon. (6) D.J.Goldie. Phys. Rev. ‘Len., 64 (1990) 964