Pairing and the phase diagram of the normal coherence length ξN(T, x) above Tc of La(2-x)Sr(x)CuO4 thin films probed by the Josephson effect.

The long range proximity effect in high-Tc c-axis Josephson junctions with a high-Tc barrier of lower Tc is still a puzzling phenomenon. It leads to supercurrents in junctions with much thicker barriers than would be allowed by the conventional proximity effect. Here we measured the T - x (Temperature-doping level) phase diagram of the barrier coherence length ξN(T, x), and found an enhancement of ξN at moderate under-doping and high temperatures. This indicates that a possible origin of the long range proximity effect in the cuprate barrier is the conjectured pre-formed pairs in the pseudogap regime, which increase the length scale over which superconducting correlations survive in the seemingly normal barrier. In more details, we measured the supercurrents Ic of Superconducting - Normal - Superconducting SNS c-axis junctions, where S was optimally doped Y Ba2Cu3O(7-δ) below Tc (90 K) and N was La(2-x)Sr(x)CuO4 above its Tc (<25 K) but in the pseudogap regime. From the exponential decay of Ic(T) ∝ exp[-d/ξN(T)], where d is the barrier thickness, the ξN(T) values were extracted. By repeating these measurements for different barrier doping levels x, the whole phase diagram of ξN(T, x) was obtained.

A controversy still exist concerning the nature of the pseudogap regime in the cuprate superconductors12. Some researchers visualize the pseudogap regime as a precursor to superconductivity, where uncorrelated pairs which form below the pseudogap cross-over temperature T*, acquire global phase coherence at T3. Others view the pseudogap regime as a phase or phases which are competing with superconductivity such as in spin and charge density waves and when charge, magnetic and gyrotropic orders occur456789101112. The former group bases its case mostly on tunneling and ARPES measurements21314 of a single energy gap which evolves smoothly while crossing from the superconducting phase into the pseudogap regime. The latter group uses different observations of two distinct energy gaps, obtained by the same techniques, to rest their case1516. The whole picture of the pseudogap regime however, seems to be much more complex as various experiments show precursor superconductivity coexisting with competing orders in the same samples61718. A possible origin for the competing and coexisting orders is the inherent inhomogeneity of the surface of the cuprates, but global measurements which average over these inhomogeneities, still bring up new results which lend support to one or more of the above mentioned scenarios19. Polarized elastic neutron scattering and ultrasound measurements in Y Ba2Cu3O6+ have shown that the pseudogap is bound by a line of a real thermodynamic phase transition rather than by a cross over regime only820. So the controversy on the origin of the pseudogap regime is still ongoing21.

Here we focus on properties of the pseudogap as revealed by supercurrent measurements in superconducting - normal - superconducting SNS Josephson junctions, where N is in the pseudogap regime of a cuprate barrier with a T lower than that of S. The observed results are closely related to the long-range (or “giant”) proximity effect in trilayer c-axis junctions which was investigated previously both experimentally and theoretically22232425. In one of these studies, supercurrents were observed also at temperatures significantly above T of the N-barrier, even when its thickness was two orders of magnitude larger than the expected “normal” coherence length ξ ≈ 0.2 nm for transport in the c-axis direction22. The actual ξ is therefore long ranged compared to that of the conventional proximity effect, and seems to reflect the specific nature of the pseudogap regime with its conjectured preformed pairs. To further substantiate this hypothesis, a systematic study of the supercurrent I dependence on temperature T and barrier doping level x is needed. This was done in the present study using Y Ba2Cu3O7− − La2−Sr4 − Y Ba2Cu3O7− junctions (for x = 0.07, 0.1, 0.18 and 0.24), with the intention of obtaining a phase diagram of ξ(T, x) from the measured I(T, x) data. Since the proportionality constant of the proximity relation I ∝ exp[−d/ξ] is unknown, we had to have I(T, x) data for at least two different d values for each doping level x in order to extract ξ(T, x). Once done, we present a novel phase diagram of ξ(T, x) of La2−Sr4 above its T and in its pseudogap regime, where on the T versus x diagram, the contours of constant ξ(T, x) for T > 55 K have a maximum in the underdoped regime. This provides further supporting evidence for the precursor superconductivity scenario in the cuprates.

Preparation of the junctions

We chose to work with fully epitaxial SS'S thin film junctions of the cuprates that have a conveniently wide temperature range where S' is in the pseudogap regime between the T values of S' and S. In this regime, we shall refer to the junctions as SNS junctions, which is the more commonly used term in such a situation. Optimally doped Y Ba2Cu3O7− (YBCO) with T ≈ 90 K was chosen as the S electrodes, while the S' barrier was chosen to be La2−Sr4 (LSCO-x) with T values of up to about 25 K. A schematic cross-section of a junction is shown in the top inset of Fig. 1. The trilayer film of YBCO/LSCO-x/YBCO was grown epitaxially in-situ by laser ablation deposition on 10 × 10 mm2 wafers of (100) SrTiO3. The trilayer was then patterned by photolithography and Ar ion milling to produce ten base electrodes with their corresponding ramps on the wafer. This was followed by a room temperature deposition of the gold cover electrode, which unlike in our previous ramp junctions26, left the ramp of the base electrode in a highly resistive state, with only a negligible current flow in the a–b plane direction through it for the lack of the high temperature annealing step. This yielded a cross-over junction where the current flows mostly in the c-axis direction via a 5 × 5 µm2 area (defined by a second patterning process) into the gold cover electrode.

Figure 1

Resistance versus temperature of a Josephson junction with a 20 nm thick LSCO-0.07 barrier obtained using a 100 µA current bias.

The top inset shows a schematic cross-section of the junction, and the bottom one is a zoom-in on the resistance below the transition of the YBCO electrodes.

Transport results

Fig. 1 shows a typical resistance versus temperature curve of a Josephson junction with a 20 nm thick La1.93Sr0.07CuO4 barrier with 7% Sr doping (LSCO-0.07). The YBCO electrodes become superconducting at T ≈ 90 K where the junction resistance drops sharply. It doesn't however drop to zero, as can be seen in the bottom inset of Fig. 1 which shows a knee-like structure down to about 50 K on top of an almost constant residual resistance of ~ 0.3 Ω below it. These two resistance components originate in the barrier material in the junction (the LSCO-0.07 layer) and the gold cover electrode. Once the LSCO-0.07 layer becomes superconducting at about 50 K by the proximity effect, the constant residual resistance below it is due to the gold cover electrode only. Thus, as we lower the temperature further, the Josephson current increases but the series resistance of the Au cover electrode remains.

A typical I-V curve at 10 K of this type of Josephson junction is shown in Fig. 2. This curve shows that the junction has a critical current of 0.55 mA as measured by a 5 µV criterion. It also exhibits a resistively shunted junction (RSJ) behavior at higher bias with a normal resistance of 0.8 Ω. The I product of the junction is therefore equal to 0.44 meV which is typical of Josephson junctions in the cuprates27. The inset of Fig. 2 depicts a conductance spectrum of this Josephson junction at 40 K under 10.7 GHz microwave irradiation, showing the AC Josephson effect. The evenly spaced peaks in the curve are due to Shapiro steps in the I-V curve at a somewhat larger than the expected spacing of ΔV = hν/2e due to the series resistance of about 0.3 Ω of the gold cover electrode. On a wafer with 10 junctions, the spread of the measured critical current values was about ±30%. In the following measurements of I versus T on each wafer with a given barrier thickness and doping level, we had chosen to work on the junction whose critical current value is closest to the average value obtained on that wafer.

Figure 2

Current versus voltage at 10 K of a Josephson junction with a 20 nm thick LSCO-0.07 barrier.

A gold series resistance of 0.3 Ω was subtracted from the data. The inset shows the conductance of this junction at 40 K under 10.7 GHz microwave irradiation, where the Shapiro steps in the corresponding I-V curve are seen as evenly spaced peaks.

Next we focus on the temperature dependence of the critical currents which were extracted from the I-V curves using a 5 µV criterion. Fig. 3 shows the temperature dependence of the critical currents in two representative Josephson junctions with LSCO-0.07 barriers on two different wafers. One with a 20 nm thick barrier and the other with a thinner 12 nm thick barrier. At temperatures above 40–50 K, when the critical currents are small, they decay versus temperature as a (T − T)2 power law as predicted by the De-Gennes dirty limit proximity effect formula28. At lower temperatures, as the supercurrents increase, the I-V curves deviate from the weak-link RSJ model and start to show a strong-link flux flow behavior which changes the power law temperature dependence. This may be due to the self field effect when the width of the junction w becomes larger than the Josephson penetration depth λ. A critical current of about 1.5 mA at 40 K with the 12 nm thick barrier, corresponds to a Josephson penetration depth λ of which is of the order of the width of our junctions (w = 5 µm).

Figure 3

Critical current as a function of temperature of two Josephson junctions on two different wafers with LSCO-0.07 barrier thicknesses of 20 nm and 12 nm.

Extraction of ξ(T, x) from the data

We now turn to the main result of this study which shows the normal coherence lengths of the LSCO-x barriers at different doping levels. For any given temperature T and doping level x, the normal coherence length of the barrier can be extracted from the ratio of the critical currents in junctions with two different barrier thicknesses d using the exponential part of the De-Gennes formula (I ∝ exp[−d/ξ]28). To further clarify the procedure of extracting ξ(T) from the data, a detailed description is given in the supplementary material for the case of LSCO-0.24 film and junctions. Fig. 4 shows the normal coherence lengths ξ(T, x) for x = 0.1 and x = 0.18 LSCO-x barriers as a function of temperature. The temperature range of the coherence lengths plots is limited here to 40–60 K. The lower bound of the temperature range is set by the flux flow phenomenon in the junctions with the thinner barrier due to the high I values and rounding of the I-V curves which make the determination of I difficult. The upper bound is set by the low critical currents in the junctions with the thicker barrier which are noisy and therefore hard to measure. Fig. 4 shows that the measured normal coherence length values range between 4–6 nm. These values are much higher than expected from the conventional proximity effect theory28, where the coherence length should be limited by the short c-axis superconductor coherence length ξ and the corresponding mean free path l, both of which are shorter than 1 nm. Previous experiments on SNS cuprate junctions of the type LSCO-LCO-LSCO had also shown very long coherence lengths22. This “giant proximity effect” was explained by a number of theories which took into account superconducting phase fluctuations above T in the barrier2425.

Figure 4

Normal coherence lengths ξ of LSCO-0.1 and LSCO-0.18 as a function of temperature.

The inset shows the normal state resistivity of the corresponding LSCO-x barriers as a function of temperature.

Discussion

Another interesting feature in Fig. 4 is the unexpected crossing of the ξ curves at about 55 K for the two doping levels. At low temperatures, the overdoped LSCO-0.18 barrier has a higher normal coherence length than the underdoped LSCO-0.1. This behavior however is reversed above 55 K, where the coherence length of the LSCO-0.1 barrier becomes higher. In the following we shall try to understand this peculiar dependence of ξ of LSCO-x which is a dirty limit material for transport in the c-axis direction. As we shall calculate only the ratio of coherence lengths ξ(0.18)/ξ(0.1), any effect of the long range proximity effect should cancel out to a first approximation. Moreover, long range proximity effect was obtained using the standard proximity effect while invoking strong superconducting “pockets” in the barrier24, which is similar to the pre-formed pairs scenario3. We shall thus use here the conventional proximity effect theory. In the dirty limit this yields the normal coherence length where D is the diffusion constant. In order to estimate the value of D, we used the normal resistivity values obtained from the I-V curves of our junctions at high bias. The resulting resistivity values ρ(T, x) are plotted in the inset of Fig. 4. In our junctions the current flows in the c-axis direction and therefore these ρ(T, x) results represent inter-layer transport. In the anisotropic cuprates, a prevalent model for the transport mechanisms assumes a strong in-plane coupling where superconductivity occurs, and a weak-link, Josephson coupling between the planes. One such model was discussed by Graf, Rainer and Sauls29, where the normal c-axis, inter-layer conductivity ρ = 1/ρ is given by: where N is the density of states at the chemical potential. This allowed us to calculate the inter-layer diffusion constant D and the corresponding ξ of Eq. (1), using the measured resistivity values while the density of states values were taken from Ino et al30. Using this procedure, we calculated the ratio between the normal coherence lengths of the x = 0.18 and x = 0.1 Sr doped barriers. This yields at 60 K, which disagrees with the measured coherence lengths of Fig. 4 at this temperature. Generally, the diffusion constant D and therefore also ξ, should be larger in the less resistive materials, those with the higher doping level, as is actually seen in the low temperature regime of Fig. 4. The fact that this behavior is reversed at the high temperature regime, must be due to an unconventional proximity effect where the LSCO-0.1 barrier does not behave as a normal metal. Some feature of this barrier should facilitate the long range proximity effect and the preference for higher ξ values in the underdoped regime at higher temperatures. We attribute this behavior to the precursor superconductivity scenario, in which the conjectured uncorrelated pairs (preformed pairs) allow for these phenomena to occur.

The phase diagram of ξ(T, x)

To further elucidate and explain this interpretation of our results, we plot in Fig. 5 a color-map of the full phase diagram of ξ(T, x). All the measured ξ(T) values of the x = 0.07, 0.1, 0.18 and 0.24 doping levels were used (12 × 4 measured values at 12 temperatures per each doping level), and the color-map extrapolates and draws the contours in between these doping levels. The contours in between the measured data points should thus be considered only as guides to the eye. We have data also below 40 K, but this is less reliable due to flux flow effects and we have chosen not to show it here. A clear feature in Fig. 5 is that the contours of constant ξ follow roughly the superconducting dome, but this occurs much above the T values of the LSCO-x barrier. Moreover, above 55 K, the maximum ξ values for each contour occurs at moderate under-doping (x = 0.1). One can see this behavior also by looking at the dashed line which shows the general trend of the contours in the 0.1 < x < 0.18 doping range at high temperatures. Although reminiscent of the pseudogap T* behavior as depicted from ARPES measurements by the dotted line31, the slopes of the two lines are very different, possibly indicating the presence of additional effects such as phase fluctuations or that the two phenomena are unrelated2021. Similar phase diagram trends were observed before in the cuprates in Nernst effect measurements32, in high magnetic field results33, in infrared and terahertz spectroscopy1734, and in higher energy gap results obtained in Andreev conductance spectroscopy measurements35. These previous results, as well as the new one presented here, provide additional support for strong superconducting fluctuation effects and the preformed pairs scenario in the underdoped regime of the cuprates above T, but not necessarily up to the T* transition-line of the pseudogap.

Figure 5

A color-map of the phase diagram of ξ(T, x) representing the normal coherence length of LSCO-x in nm as function of temperature T and doping x.

The dotted line represents the pseudogap T* temperature of Ref. 32, while the dashed line describes the trend of the present data of ξ for 0.18 ≥ x ≥ 0.1 and T > 55 K. For comparison we plot also T(x) measured on LSCO single crystals by Matsuzaki et al.36.

In conclusion, comparative supercurrent measurements in SNS YBCO - LSCO-x - YBCO c-axis junctions at various temperatures and doping levels x, yielded a novel phase diagram of ξ(T, x), which besides the observation of a long range proximity effect, also support the precursor superconductivity scenario in the underdoped regime of the cuprates above T.

Author Contributions

T.K. had initiated this project and made the major part of the experiments. G.K. made some of the experiments and both have written this manuscript.