Pis'ma v ZhETF, vol.96, iss.ll, pp.830-837
© 2012 December 10
ПО ИТОГАМ ПРОЕКТОВ РОССИЙСКОГО ФОНДА ФУНДАМЕНТАЛЬНЫХ ИССЛЕДОВАНИЙ Проект РФФИ # 08-02-00935
THz phonon spectroscopy of doped superconducting cuprates
Ya. G. Ponomarev, H. H. Van, S. A. Kuzmichev, S. V. Kulbachinskii, M. G. Mikheev, M. V. Suclakova,
S. N. Tchesnokov
Department of Low Temperature Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Submitted 19 October 2012
Facts are presented evidencing a strong electron-phonon interaction in doped BSCCO superconductors. A pronounced fine structure in dl/dF-characteristics of Josephson junctions has been observed which is caused by interaction of AC Josephson current with Raman-active optical phonon modes. "Quantization" of the "gap" voltage for natural nanosteps on the cryogenically cleaved surfaces of BSCCO proves the existence of the intrinsic Josephson effect. A sharp extra structure in the current-voltage characteristics of nanosteps is attributed to the presence of the extended van Hove singularity.
Introduction. According to Abrikosov [1] a high transition temperature Tc in layered cuprates is caused by the presence of an extended van Hove singularity (EVHS) near the Fermi level. In Abrikosov's model, optical phonons with small wave vectors play a dominant role in pairing. The electron-phonon coupling in high-temperature superconductors (HTSC) was confirmed experimentally via the pump-probe optical spectroscopy [2], the effect of renormalization of the quasiparticle density of states [3-8], the effect of generation of optical phonons by AC Josephson current [9-12], the photoemission spectroscopy [13,14], and the isotope effect [15].
It is well known that the transition temperature % for cuprates varies with the hole concentration, p, according to a parabolic law: Tc = TCjmax[l — 82.6(p — ^0.16)2] (the doping levelp is defined as the hole density per Cu site normalized to one C11O2 plane) [16,17]. At the same time there is a contradictory information about a doping dependence of a superconducting gap A (p).
In the present investigation a transition from over-doped (OD) to underdoped (UD) samples was achieved by substituting Sr with La [18]. The intrinsic Joseph-son effect in nanosteps on cryogenically cleaved surfaces of doped Bi-2212(La) single crystals, Bi-2212 whiskers and Bi-2223 polycrystals has been studied. A discreet character of the "gap" voltage Vgn = n(2A/e) for natural nanosteps (j||c) was observed (n is the number of contacts in a nanostep). The obtained results support a previously observed scaling of the superconducting gap A with the critical temperature Tc on doping [19]. In addition, we have registered a sharp extra structure
i
-80 -40 0 40 V (mV)
Fig. 1. dl/dF-characteristics of a single tunneling SIS-contact (1) and a single Andreev SnS-contact (2) in underdoped Bi-2212(La) at T = 4.2 K (Tc = 78 ± 2K, A = 24 ± 0.5 meV, 2A/ikTc = 7.1 ± 0.4)
in the current-voltage characteristics (CVC's) of perfect Bi-2212 nanosteps which could be caused by the presence of the EVHS [20-23] close to the Fermi level in both slightly overdoped and slightly underdoped samples. An interaction between AC Josephson current and Raman-active optical phonon modes in the entire range of phonon frequencies (up to 25 THz) was observed in
Bi-2212, samp. B11A, OVD, " T= 4.2 K, T' = 88 K, A = 25 meV
-400 -200 0 200 400 V (mV)
Fig. 2. dl/dF-characteristics of a Bi-2212(La) nanostep (8 contacts) at T = 4.2 K (a) shunted by a single SIS contact (b) (slightly overdoped sample, Tc = 88 K, A = = 25.0 ± 0.5 meV)
doped Bi-2212 and Bi-2223 samples, pointing to a strong electron-phonon coupling in HTSC [24-26]. A giant instability in I(V) - characteristics of Bi-2223 nanos-teps is explained by a resonant emission of 2A - optical phonons in a process of recombination of nonequilibrium quasiparticles (Krasnov-Schnyder model [27,28]).
Experimental. A break-junction technique [29] has been used to generate contacts of SIS-type (tunnelling spectroscopy) and SnS-type (Andreev spectroscopy) in Bi-2212(La) single crystals, Bi-2212 whyskers, and Bi-2223 polycrystals. To protect Bi-2212 whiskers from damaging at room temperature additional transitive substrates of thin tissue paper were used. Four strips of liquid indium-gallium solder were painted on substrates, and whiskers were located across these strips. At cooling of a sample holder an indium-gallium solder froze and fixed whiskers. Calibration of measuring channels of multifunctional I/O board AT-MIO-16X (National Instruments) was performed by a high-precision digital voltmeter.
For temperature measurements a calibrated germanium thermometer was used. A typical error of measurements of a dynamic conductance of junctions didn't exceed one percent.
The magnitude of the gap measured by tunnelling and Andreev spectroscopies on the same sample usually coincided within experimental errors (Fig. 1). In addi-
1
-40 0 40 V (mV)
Fig. 3. dl/dV-curves for SIS contacts in underdoped Bi-2212
tion, using the same technique we have studied the current - voltage characteristics (CVC's) of natural nanos-teps with a height from 1.5 to 30 nm which are always present on cryogenically cleaved surfaces of bismuth cuprates. In most cases these nanosteps were shunted by a single SIS contact, which allowed to estimate the number of contacts n in a stack (Fig. 2, dl/dV-characteristic of a Bi-2212(La) nanostep (8 contacts) at T = 4.2 K (a) shunted by a single SIS contact (b)).
We have used the data of tunneling, intrinsic tunneling and Andreev spectroscopies to derive the dependence of a superconducting gap A on the impurity hole concentration p (Figs. 1-4). It should be noted, that for underdoped samples of bismuth cupratrs it becomes progressively difficult to prepare true single SIS contacts with the current in c-direction. The layered structure of the material and weakening of bonding between superconducting blocks causes the formation of complicated network of contacts in the vicinity of the surface. In the present investigation the electron-phonon resonances were used as reliable calibration marks, which helped to judge a single SIS contact from a stack Dotted lines in Fig. 3 indicate the position of electron-phonon resonances Fres, corresponding to a nonlinear interac-
-40 0 40
V (mV)
Fig. 4. Resistive transitions R{T) and gaps A (T) in under-doped Bi-2212 samples
tion of AC Josephson current with Raman-active optical phonon modes [30]. For an apical oxygen phonon mode 0Sr: -Ephon = 2eKes « 80meV [9].
In all cases the superconducting gap A(T = 4.2K) was found to scale with the transition temperature % (Figs. 5 and 6) in the entire doping range (the ratio 2/AkTc is close to 7). The flattening of the "gap" parabola in the vicinity of optimal doping (Fig. 6 ) is probably an indication of pinning of the Fermi level to the EVHS [31].
We have found, that La substitution (red solid circles in Fig. 6) does not affect the character of scaling of A and Tc (empty squares correspond to as grown crystals without La). A similar dependence was reported in [19], though a conflicting experimental information can also be found [32]. Recently scaling of superconducting gap A and Tc was also observed in [33].
The results obtained in the present investigation and in [19,33] support the conclusion that the frequency range of HTSC Josephson contacts (important for THz applications) is maximal for optimal doping.
Direct measurements done by the scanning tunneling microscopy (STM) method showed that the height of nanosteps on cryogenically cleaved surfaces is pro-
20 40 60 80 100 T (K)
Fig. 5. Resistive transitions R{T) and gaps A(T) in under-doped Bi-2212 samples
portional to half the height of the unit cell: 1.5 nm (the cleavage surface is located between two neighbouring BiO planes) [18,19]. Note that half a unit cell in the c-direction corresponds to a single Josephson junction. According to Kaneko et al. [34] and Mitchell et al. [35], the nanostep width does not exceed 1/tm. This result coincides with the estimates made in Ref. [19]. By tuning the junction with a micrometric screw in a single experiment it was possible to move from one nanostep to another and record their CVC's individually.
The gap voltage for nanosteps with different number of SIS contacts n is "quantized" : Vgn = n(2A/e) (Figs. 7 and 8), which proves the applicability of the "intrinsic Josephson effect" scenario for cuprates [36]. The sharpness of the gap structure is typical for Bi-2212(La) and Bi-2223 nanosteps and allows to estimate Vgn with sufficient accuracy. No signs of overheating at biase voltages V « Vgn were observed. For slightly underdoped Bi-2212(La) single crystal in Fig. 7 an elementary gap voltage 2A/e equals 50 mV at T = 4.2 K.
The gap feature in the CVC's has a shape typical for an "s-symmetry" (isotropic) gap parameter. At the first glance it is difficult to match this result with the photoemission spectroscopy data, according to which the gap parameter in the ab plane is highly anisotropic [37]. However, the situation changes when there is a van Hove
100.0
83.3
66.7
50.0
33.3
16.7
Fig. 6. Doping dependence of Д and Tc for Bi-2212
singularity at the Fermi level. Wei et al. [38] had found that a van Hove singularity enhances the gap structure in the CVC's of junctions even when the gap parameter in the ab plane is highly anisotropic. For slightly overdoped and slightly underdoped samples a sharp extra structure in the CVC's of Bi-2212 nanosteps was observed (Figs. 9 and 10), which we attribute to the presence of the extended van Hove singularity (EVHS) close to the Fermi level [1,20,21,23,39]. This extra structure is absent in the CVCs of optimally doped samples (Fig. 2) where it falls into a 2A-region. For strongly underdoped and strongly overdoped samples the extra structure is also not detectable. The latter effect could be the result of a pronounced drop o
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