{'fraction_non_alphanumeric': 0.042838898011311806, 'fraction_numerical': 0.025031928480204343, 'mean_word_length': 4.226163234172388, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 3, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Oxygen-isotope effect on the in-plane penetration depth in cuprate superconductors

Muon-spin rotation (muSR) studies of the oxygen isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic field penetration depth lambda_{ab} in cuprate high-temperature superconductors (HTS) are presented. First, the doping dependence of the OIE on the transition temperature T_c in various HTS is briefly discussed. It is observed that different cuprate families show a similar doping dependence of the OIE on T_c. Then, bulk muSR, low-energy muSR, and magnetization studies of the total and site-selective OIE on lambda_{ab} are described in some detail. A substantial OIE on lambda_{ab} was observed in various cuprate families at all doping levels, suggesting that cuprate HTS are non-adiabatic superconductors. The experiments clearly demonstrate that the total OIE on T_c and lambda_{ab} arise from the oxygen sites within the superconducting CuO_2 planes, demonstrating that the phonon modes involving the movement of planar oxygen are dominantly coupled to the supercarriers. Finally, it is shown that the OIE on T_c and lambda_{ab} exhibit a relation that appears to be generic for different families of cuprate HTS. The observation of these unusual isotope effects implies that lattice effects play an essential role in cuprate HTS and have to be considered in any realistic model of high-temperature superconductivity.


Introduction
Although the discovery of the cuprate high-temperature superconductors (HTS) [1] in 1986 triggered world-wide an enormous effort to understand these novel materials, there is at present still no convincing microscopic theory describing the mechanism of superconductivity. Due to the high values of the superconducting transition temperature T c and the early observation of a tiny oxygen-isotope effect in optimally doped YBa 2 Cu 3 O 7−δ [2,3,4], many theoreticians came to the conclusion that the electronphonon interaction cannot be responsible for high-temperature superconductivity. As a result, alternative pairing mechanisms of purely electronic origin were proposed. However, the assumption that T c cannot be higher than 30 K within a phonon-mediated pairing mechanism is not justified [5]. A prominent example is the recent discovery of superconductivity in MgB 2 [6] with a T c ≈ 39 K which is accepted to be a purely phononmediated superconductor. There is increasing experimental evidence from recent work, such as neutron scattering [7,8], angle resolved photoemission spectroscopy [9,10], and isotope effect studies (this work) that lattice effects play an essential role in the basic physics of HTS and have to be considered in reliable theoretical models [11,12].
It is well known that the observation of an isotope effect on T c in conventional superconductors was crucial in the development of the microscopic BCS theory. The isotope shift may be quantified in terms of the relation where M is the isotope mass, and α is the isotope-effect exponent. In the simplest case of weak-coupling BCS theory T c ∝ M −1/2 and α BCS ≃ 0.5, in agreement with a number of experiments on conventional metal superconductors. However, there are exceptions of this rule such as Zr and Ru for which α ≃ 0. The conventional phonon-mediated theory is based on the Migdal adiabatic approximation in which the density of states at the Fermi level N(0), the electronphonon coupling constant λ ep , and the effective supercarrier mass m * are all independent of the mass M of the lattice atoms. However, if the interaction between the carriers and the lattice ions is strong enough, the Migdal approximation is no more valid [13]. Therefore, in contrast to ordinary metals, unconventional isotope effects on various quantities, such as the superconducting transition temperature and the magnetic penetration depth are expected for a non-adiabatic superconductor.
In 1990 the University of Zurich group started a project on isotope effect on cuprates that was initiated by K. Alex Müller. Here we briefly review some of our results. They include unconventional oxygen isotope ( 16 O/ 18 O) effects (OIE) in HTS on the transition temperature and the in-plane magnetic penetration depth. For a detailed description of our work we refer to Refs. [14,15,16,17,18,19,20,21,22]. In this review it is demonstrated that the muon spin rotation (µSR) technique is a very powerful and unique tool to investigate the OIE on the magnetic penetration depth in HTS. In particular, the novel low-energy µSR technique (LEµSR) [23] allows a direct and very accurate measurement of the magnetic penetration depth in HTS and with that a reliable measurement of the OIE on λ.
The paper is organized as follows. In Sec. 2 we describe the sample preparation and the oxygen exchange procedure. Some results of the OIE on the transition temperature T c obtained for different cuprate families are presented in Sec. 3. Sec. 4 comprises studies of the OIE on the in-plane penetration depth λ ab in Y 1−x Pr x Ba 2 Cu 3 O 7−δ and La 2−x Sr x CuO 4 by means of bulk µSR and in optimally doped YBa 2 Cu 3 O 7−δ by means of LEµSR . Furthermore, results of the site-selective OIE on λ ab in Y 0.6 Pr 0.4 Ba 2 Cu 3 O 7−δ obtained by bulk µSR are reported. In Sec. 5 we discuss implications of the OIE on λ ab and the empirical relation between the isotope effect on T c and λ ab observed for different HTS families. The conclusions follow in Sec. 6.

Sample preparation and oxygen isotope exchange
For isotope effect studies it is important to have isotope substituted samples of the same quality. In the case of 16  isotope exchange is shown in Fig. 1 [24]. In order to ensure that the substituted samples are subject to the same thermal history, the annealing (in 16  The procedure to prepare completely oxygen substituted and site-selective oxygen substituted Y 1−x Pr x Ba 2 Cu 3 O 7−δ samples (which are mostly described in this review) is schematically shown in Fig. 2 18 O pac ) were simultaneously annealed in the same atmosphere as before in order to have the reference samples following the same thermal history. The results of the oxygen exchange can be checked by Raman spectroscopy. Fig. 2(b) shows Raman spectra with zz and xx polarizations of completely and siteselective oxygen substituted Y 0.6 Pr 0.4 Ba 2 Cu 3 O 7−δ samples [21]. In the 18 O pac sample, the Raman lines are all shifted to lower frequencies in agreement with the results of Zech et al. [25], indicating a nearly complete exchange of 16    After [21].
The importance of phonons for the pairing mechanism of conventional superconductors (including doped fullerenes [26] and MgB 2 [27]) was provided by measurements of the isotope effect (IE) on T c . The BCS theory predicts that where ω is a typical phonon frequency (e.g. the Debye frequency ω D ). The electron phonon coupling is given by the product of the electron-phonon interaction constant V and the electronic density of states at the Fermi surface N(0), both of which are assumed to be independent of the ion mass M. Eq. (2) implies an isotope-mass , characterized by the isotope effect exponent α = 1/2. This is in agreement with isotope effect results reported for many nontransition metal superconductors (e.g. Hg, Sn and Pd). However, as mentioned above, there are exceptions as Zr and Ru with α ≃ 0.
Since 1987 a number of oxygen isotope effect investigations on T c were performed in most families of HTS. The first OIE experiments were done on optimally doped samples, showing no significant isotope shift [2,4]. However later experiments revealed a small but finite dependence of T c on the oxygen isotope mass M O [3,28,29]. It is now well established that the OIE on T c is doping dependent [29,30]. As an example, Fig. 3 shows the temperature dependence of the magnetization in the vicinity of T c in optimally doped 16 It is seen that the isotope shift on T c increases with decreasing doping (increasing Pr concentration) quite substantially: from ∆T c =-0. 25 The oxygen-isotope exponent α O = −d ln T c /d ln M O as a function of doping shows a trend that appears to be generic for all families of cuprate superconductors [15,16,18,28,31]. In the underdoped region α O is large (even exceeding the BCS value α =1/2) and becomes small in the optimally doped and overdoped regime (see Fig. 4). Moreover, the copper-isotope ( 63 Cu/ 65 Cu) exponent α Cu shows a similar trend as α O [34,35,36,37]. Both exponents increase monotonically with decreasing doping [18,35,36,37].
The observation of OIE on T c indicates that lattice vibrations in the CuO 2 planes are relevant for the occurrence of superconductivity. From this point of view, one would expect that the planar oxygen modes give rise to larger OIE on T c than the apical and/or chain oxygen modes. The first reliable site-selective OIE (SOIE) studies of T c were performed by Zech et al. [25]. It was shown that in optimally doped YBa 2 Cu 3 O 7−δ the planar oxygen mainly (≥ 80 %) contribute to the total OIE on T c . These results were confirmed by Zhao et al. [31] and later by Khasanov et al. [21]. Both groups [31,21] found that in underdoped Y 1−x Pr x Ba 2 Cu 3 O 7−δ the predominant contribution (100 % within error bar) arises from the oxygen within the superconducting CuO 2 planes [see  . The open circles are Y 1−x Pr x Ba 2 Cu 3 O 7−δ data from [28]. Open down triangles are data of YBa 2−x La x Cu 3 O 7 taken from [32]. Open stars are data of La 1.85 Sr 0.15 Cu 1−x Ni x O 4 from [33]. Closed circles correspond to Y 1−x Pr x Ba 2 Cu 3 O 7−δ data from [20,22] and unpublished data (this work). The solid line corresponds to

Oxygen isotope effect on the in-plane magnetic penetration depth λ ab
The conventional phonon-mediated theory of superconductivity (standard BCS theory) is based on the Migdal adiabatic approximation in which the effective supercarrier mass m * is independent of the mass M of the lattice atoms. However, if the interaction between the carriers and the lattice is strong enough, the Migdal adiabatic approximation breaks down and m * depends on M (see, e.g. [13]). A significant experiment to explore a possible coupling of the supercarriers to the lattice is an isotope effect study of the magnetic field penetration depth λ.
For a general Fermi surface the zero-temperature magnetic penetration depth λ ii (0) may be written as an integral over the Fermi surface [38]: where i denotes the crystallographic axes (a, b, c) and v F i is the Fermi velocity. For the special cases of spherical or ellipsoidal Fermi surfaces, Eq. 3 leads to the London where n s is the superconducting carrier density and m * ii is the effective mass of the carriers. For a general Fermi surface, it is convenient to parameterize experimental data by means of Eq. 4. It should be noted, however, that in this case m * ii is not directly related the band mass, except for spherical or ellipsoidal Fermi surfaces [38]. For HTS, which are superconductors in the clean limit, we may parameterize the in-plane penetration depth λ ab in terms of the relation: where m * ab is the in-plane effective mass (not band mass) of the charge carriers. According to Eq. 5, this implies that an OIE on λ ab has to be due to a shift in n s and/or m * ab : Therefore a possible mass dependence of m * ab can be tested by investigating the isotope effect on λ ab , provided that the contribution of n s to the total isotope shift is known.
The first observation of a possible OIE on the magnetic penetration depth λ(0) in polycristalline YBa 2 Cu 3 O 6.94 was reported by Zhao and Morris [39]. In another study Zhao et al. [40,16] extracted the isotope dependence on λ(0) in fine grained samples of La 2−x Sr x CuO 4 (0.06 ≤ x ≤ 0.15) from the Meissner fraction. Hofer et al. [41] investigated the OIE on λ −2 ab (0) in tiny single crystals of La 2−x Sr x CuO 4 by means of torque magnetometery. All these experiments showed indeed a pronounced oxygen isotope dependence of the magnetic penetration depth λ.
The µSR technique is a very powerful method to determine the magnetic penetration depth in superconductors. In the following we will discuss in more detail OIE investigations of λ ab in optimally doped and underdoped cuprate HTS by means of bulk µSR and LEµSR, which at present is the most powerful and elegant technique to measure the magnetic penetration depth directly. Detailed bulk µSR investigations of polycrystalline samples of HTS have demonstrated that λ can be obtained from the muon-spin depolarization rate σ(T ) ∼ 1/λ 2 (T ), which probes the second moment of the magnetic field distribution in the mixed state [42]. It was shown [43,44] that in polycrystalline samples of highly anisotropic systems such as the HTS (λ c /λ ab > 5), λ eff (powder awerage) is dominated by the shorter penetration depth λ ab due to the supercurrents flowing in the CuO 2 planes: σ(T ) ∝ 1/λ 2 ab (T ). In LEµSR experiments spin-polarized low-energy muons are implanted in the thin film sample at a known depth z beneath the surface and precess in the local magnetic field B(z). This feature allows to measure directly the profile B(z) of the magnetic field inside the superconducting film in the Meissner state and to make a model independent determination of λ [45]. All the OIE µSR results of T c and λ ab discussed in this review are summarized in Table 1. For comparison the low-field magnetization data are also included.  The first measurements of OIE on λ ab (0) using bulk µSR were performed by Khasanov et al. [20] in underdoped Y 1−x Pr x Ba 2 Cu 3 O 7−δ (x = 0.3 and x = 0.4). The transversefield µSR measurements were performed on the beam-line πM3 at the Paul Scherrer Institute (PSI, Switzerland) using low-momentum muons (29 MeV/c). The samples were field-cooled from far above T c in a magnetic field of 200 mT. The depolarization rate σ was extracted from the µSR time spectra using a Gaussian relaxation function R(t) ∝ exp(−σ 2 t 2 /2). Above T c a small temperature-independent depolarization rate σ nm = 0.15 µs −1 is seen, arising from the nuclear magnetic moments. Below T c , σ increases strongly due to the flux lattice formation. An additional sharp increase of σ(T ) was observed below 10 K which is due to antiferromagnetic ordering of Cu(2) moments [46]. However, zero-field µSR experiments indicate no presence of magnetism above 10 K. Therefore, data points below 10 K were excluded in the analysis. The superconducting contribution σ sc was then determined by subtracting σ nm measured above T c from σ. In Fig. 5 the temperature dependence of σ sc for Y 1−x Pr x Ba 2 Cu 3 O 7−δ (x = 0.3 and x = 0.4) is shown. It is evident that for both concentrations x a remarkable oxygen isotope shift on T c as well as on σ sc (0) is observed. The data in Fig. 5 were fitted to the power law [42] The values of σ sc (0) obtained from the fits were found to be in agreement with previous results [46]. In order to prove that the observed OIE on λ ab is intrinsic, the 18 O sample with x = 0.4 was back exchanged ( 18 O→ 16 O). As seen in Fig. 5 the data points of this sample (crosses) coincide with those of the 16 O sample. From the measured values of σ sc (0) the relative isotope shift of λ ab (0) was found to be ∆λ ab (0)/λ ab (0) = 2.5(1)% and 4.5(1)% for x = 0.3 and x = 0.4 samples, respectively (see Table 1 was kept at plane (p) sites, following the same procedure as described in Refs. [25,24]. The site-selectivity of the oxygen exchange was checked by Raman spectroscopy [see Fig. 2 (b)]. Figure 6 shows the temperature dependence of the µSR depolarization rate   (7)] fitting σ sc (T ) for 16 O pac was subtracted from the experimental data (inset in Fig. 6). It can be seen that the experimental points for the two pairs of samples mentioned above coincide within error bar, indicating that the oxygen site within the CuO 2 planes mainly contribute to the total OIE on T c and λ ab .

OIE on λ ab in optimally doped compounds
Recently, a substantial OIE on λ ab in optimally doped samples of YBa 2 Cu 3 O 7−δ [∆λ ab (0)/λ ab (0) = 2.6(5)%, β O = 0.41 (7)] (see Fig. 7) and La 1.85 Sr 0.15 CuO 4 [∆λ ab (0)/λ ab (0) = 2.2(6)%, β O = 0.35 (9)] was observed by means of bulk µSR [47] (see Table 1  The most direct and model independent way to confirm this result is the determination of λ from the functional dependence of magnetic field profile B(z) penetrating the surface of a superconductor in the Meissner state. Recently, such a measurement of λ ab was performed in a thin film of YBa 2 Cu 3 O 7−δ at the Paul Scherrer Institute (PSI, Switzerland) [45] , by using the novel low-energy µSR (LEµSR) technique [49]. The principle of the measurement is shown schematically in Fig. 8. Polarized muons of energy in the keV range are implanted into the film. By tuning their energy these particles can be stopped at different and controllable depths beneath the surface of the superconductor in the Meissner state. The stopping profile of the muons, shown in the bottom part of Fig. 8(a), depends on the energy and can be reliably simulated [50,51]. From the known value of the mean implantation depth z and the corresponding average field B obtained from the µSR precession spectra, the functional dependence B(z) is determined. By means of this technique, measurements of OIE on λ ab in optimally doped c-axis oriented YBa 2 Cu 3 O 7−δ thin films were recently performed. A weak external magnetic field of 9.2 mT was applied parallel to the sample surface after the sample was cooled in zero magnetic field from a temperature above T c to 4 K. In this geometry (the thickness of the sample is negligible in comparison with the width), currents flowing in the abplanes determine the magnetic field profile along the crystal c-axis inside the film [see Fig. 8 correspondent average value of the stopping distancez were extracted. The value ofB was taken from the fit of the time evolution of the muon-spin polarization spectrum by using the Gaussian relaxation function andz was the first moment of the simulated n(z) distribution. Results of this analysis for the 16 O and 18 O substituted YBa 2 Cu 3 O 7−δ films are shown in Fig. 9. The magnetic penetration at the surface of the superconductor is more pronounced for the 18 O substituted film showing immediately that 18 λ ab > 16 λ ab .
The solid lines represent a fit to theB data by the function: This is the form of the classical exponential field decay in the Meissner state B(z) = B(0) exp(−z/λ ab ) (where B(0) is the field at the surface of the superconductor), modified for a film with thickness 2t with flux penetrating from both sides. The value of z was corrected in order to take into account the surface roughness of the films [45], which was taken equal (8.0(5) nm) for both samples originating from the same batch. In order to prove the intrinsic character of the effect, a backexchange experiment was performed on fine powder samples, where the isotope dependence of λ ab (0) can be determined from that of the Meissner fraction f [22]. Such type of measurements have been previously performed on the La 2−x Sr x CuO 4 system in a wide range of doping (0.06 ≤ x ≤ 0.15) [16,40]. Figure 10 shows the temperature dependence of λ −2 ab calculated from f for the 16 O/ 18 O substituted YBa 2 Cu 3 O 7−δ fine powder samples. The value of f was determined from the FC SQUID magnetization measurements taken at 1 mT . The absence of weak links between grains is confirmed by the linear magnetic field dependence of the FC magnetization measured at 5 K in 0.5 mT, 1 mT, and 1.5 mT. λ ab (T ) can be determined from the measured λ eff (T ) using the relation λ eff = 1.31λ ab which holds for highly anisotropic superconductors (λ c /λ ab > 5) [43,44]. The relative shift at 4 K is found to be ∆λ ab /λ ab = 3.0(1.1)%, in good agreement with the bulk µSR and LEµSR data (see Figs. 7,9 and Table 1). The results of the back exchange experiments shown as crosses in Fig. 10 prove the intrinsic character of the effect.

Implications of the OIE on λ ab and universal correlations between OIE on T c and λ ab
From the present investigations it is evident that there is an OIE on λ ab (0) at all doping levels which appears to be generic for cuprate HTS. Here the fundamental questions arise: Is the observation of an OIE on the zero-temperature penetration depth (superfluid density) a direct signature of strong lattice effects? And what is the relevance of this finding for the pairing mechanism? In order to adequately answer these questions more experimental, and in particular more theoretical, work is needed. In the following we only discuss a few points related to these questions.
Under the assumption that we can parameterize experimental data of λ ab (0) in terms of Eq. (5) it follows from Eq. (6) that the isotope shift of λ ab is due to an isotope shift of n s and/or m * ab . It was demonstrated by a number of independent experiments fine powder samples as obtained from low-field SQUID magnetization measurements. The inset shows the low-temperature region between 10 K and 60 K. The reproducibility of the oxygen exchange procedure was checked by the backexchange (crosses). After [22]. that for La 2−x Sr x CuO 4 [16,18,40,41] and Y 1−x Pr x Ba 2 Cu 3 O 7−δ [20] the change of n s during the oxygen exchange procedure is negligibly small. Recently, Khasanov et al. [22] provided further evidence of this scenario from measurements of the nuclear quadrupole resonance (NQR) frequency of the plane and the chain 63 Cu in 16 O and 18 O substituted optimally doped YBa 2 Cu 3 O 7−δ powder samples. It was found that the change of the hole number per unit cell caused by the isotope substitution is less than ≃ 10 −3 . Since in optimally doped YBa 2 Cu 3 O 7−δ there is approximately one doped hole per unit cell, the relative change of the hole density ∆n/n at the oxygen exchange must be less than 10 −3 . The absence of an observable OIE on n s implies that the change of λ ab (0) is mainly due to a change on m * ab . From Eqs. (5) and (6) it follows that ∆m * ab /m * ab ≃ −∆λ −2 ab (0)/λ −2 ab (0) = 2∆λ ab (0)/λ ab (0).
This implies that in HTS m * ab depends on the oxygen mass M O with ∆m * ab /m * ab ≃ 5 − 10%, depending on doping level (see also Table 1). Note that such an isotope effect on m * ab is not expected for a conventional weak-coupling phonon-mediated BCS superconductor. In fact in HTS the charge carriers are very likely coupled to optical phonons, as indicated by measurements of the static and high-frequency dielectric constants [52], neutron scattering [7,8], photoemission [9,10,53] and tunnelling [54] experiments. Strong interaction between the charge carriers and the lattice ions leads to a break down of the adiabatic Migdal approximation [13], and consequently the effective supercarrier mass m * depends on the mass of the lattice atoms. To our knowledge there are just a few theoretical models which predict an OIE on the effective carrier mass m * (see e.g. Refs. [13,55,56,57]).
Khasanov et al. [20] reported an empirical linear relation between the OIE Fig. 11 we plot ∆λ ab (0)/λ ab (0) ∝ β O versus −∆T c /T c ∝ α O for Y 1−x Pr x Ba 2 Cu 3 O 7−δ and La 2−x Sr x CuO 4 for the data listed in Table 1. It is evident from Fig. 11 that there is correlation between the OIE of T c and λ ab (0) which appears to be universal for cuprate HTS. Different experimental techniques (SQUID magnetization, magnetic torque, bulk µSR, LEµSR) and different types of samples (single crystals, powders, thin films) yield within error bar consisting results, indicating that the observed isotope effects are intrinsic and not artifacts of the particular experimental method or sample used. As indicated by the dashed line, at low doping level ∆λ ab (0)/λ ab (0) ≃ |∆T c /T c |, whereas close to optimal doping ∆λ ab (0)/λ ab (0) is almost constant and considerably larger than |∆T c /T c | (∆λ ab (0)/λ ab (0) ≈ 10|∆T c /T c |). This finding is consistent with the empirical "Uemura relation" [58,59] and with the "parabolic ansatz" proposed in [30] in a differential way for doped cuprate HTS.
It was shown by Schneider and Keller [60,61] that this empirical relation naturally follows from the doping driven 3D-2D crossover and the 2D quantum superconductor to insulator (2D-QSI) transition in the highly underdoped limit. Close to the 2D-QSI transition the following relation holds [61]: where ∆d s /d s is the oxygen-isotope shift of the thickness of the superconducting sheets d s of the sample. The solid line in Fig. 11 represents a best fit of Eq. (10) to the data with ∆d s /d s = 3.3(4)%. Since the lattice parameters are not modified by oxygen substitution [62,63], the observation of an isotope shift of d s implies local lattice distortions involving oxygen which are coupled to the superfluid [61]. As shown in Fig. 12, a similar type of correlation between the OIE on λ ab (0) and OIE on T c is also observed for the site-selective substituted Y 0.6 Pr 0.4 Ba 2 Cu 3 O 7−δ samples [21]. It is evident that the oxygen site within the CuO 2 planes mainly contributes to the total OIE on T c and λ ab (0). Since for fixed Pr concentration the lattice parameters remain essentially unaffected by the isotope substitution [62,63], these results unambiguously demonstrate the existence of a coupling of the charge carriers to phonon modes involving movements of the oxygen atoms in the CuO 2 plane, while suggesting that modes involving apical and chain oxygen are less strongly coupled to the carriers.  (Table 1). Diamonds and stars are LEµSR and Meissner fraction data for optimally doped YBa 2 Cu 3 O 7−δ ( Table 1). Open triangles are torque magnetization data for La 2−x Sr x CuO 4 from [41]. The dashed line corresponds to ∆λ ab (0)/λ ab (0) = |∆T c /T c |. The solid line indicates the flow to 2D-OSI criticality and provides with Eq. (10) an estimate for the oxygen isotope effect on d s , namely ∆d s /d s = 3.3(4)%.

Conclusions
In conclusion, the unconventional isotope effects presented here clearly demonstrate that lattice effects play an important role in the physics of cuprates. The fact that a substantial OIE on λ ab is observed, even in optimally doped cuprates, strongly suggests that cuprate HTS are non-adiabatic superconductors. This is in contrast to the novel high-temperature superconductor MgB 2 for which within experimental error no Boron ( 10 B/ 11 B) isotope effect on the magnetic penetration depth was detected [64]. The site-selective OIE studies of T c and λ ab indicate that the phonon modes involving the movements of oxygen within the superconducting CuO 2 planes are essential for the occurrence of superconductivity in cuprate HTS. This is in agreement with recent inelastic neutron scattering [7,8] and photoemission [9,10] studies, indicating a strong interaction between charge carriers and Cu-O bond-stretching-type of phonons. The generic relation between the OIE on T c and λ ab demonstrates that, in contrast to conventional phonon-mediated superconductors, λ ab (superfluid density) is a key parameter for understanding the role of phonons in cuprates, in particular local lattice distortions involving planar oxygen. The present results rise serious doubts that models, neglecting lattice degrees of freedom, as proposed for instance in [65], are potential candidates to explain superconductivity in HTS.