In-plane tunnel spectroscopy of cuprate superconductors with nano-scale Josephson junctions

Superconducting tunnel spectroscopy¹ is a powerful technique to directly measure the density of states of materials to study their electrical properties. It has provided a wealth of information about the nature of electrical transport in superconductors by measuring the superconducting energy gap, Δ. The energy gap is the most important superconducting parameter used to describe the superconducting state. It can be used to predict most of the observable properties in conventional superconductors such as transition temperature and coherence length.² However, in the enigmatic high-transition temperature (high- $T C$⁠) superconductors, a predictable theory has yet to be established due to the complexity and anisotropy of high- $T C$ materials.

In anisotropic materials, the gap is a function of both temperature and electron momentum $Δ ≡ Δ ( T , p → )$⁠. This anisotropy in momentum space (k-space) can be driven by several factors such as an anisotropic Fermi surface, anisotropic vibrational spectra that change the pairing potential, or pair braking structures such as the copper oxygen chains in cuprates. Furthermore, the effects of gap anisotropy become more pronounced when the superconducting coherence length becomes much smaller than the mean free path, $ξ ≪ l$ which is the case for high- $T C$ superconductors.³ Most of the numerous studies investigating Δ in high- $T C$ superconductors have been along the c-axis direction due to difficulties in engineering tunnel devices oriented in other directions. This is unfortunate as the (high- $T C$⁠) materials are highly anisotropic, and measurements in bulk crystals show that superconductivity is much stronger in the a–b plane.^4,5

The most commonly studied cuprate superconductors crystallize in an orthorhombic unit cell with a distorted perovskite structure: in the center is a single yttrium (or rare earth) atom flanked by two copper oxygen planes, as depicted in Fig. 1(a). It is widely accepted that strong interactions between electrons in these planes are critical to the superconducting state.⁶ Electrons are strongly coupled for k-space directions parallel to the Cu–O–Cu bonds but weakly coupled in k-space directions along the diagonals. This gives rise to the anisotropy in the superconductivity. The superconducting coherence length in YBCO is less than 0.2 nm along the c-axis and 2–3 nm in the a–b plane.⁴ Copper oxide chains run along the top and bottom of the unit cells along the b directions and contribute to electrical transport: the electrical conductivity in the b-direction σ_b is the highest, but parallel to the a and c directions conductivity is 1/3 σ_b and 1/10 σ_b, respectively.⁴ These observations motivate superconducting tunnel spectroscopy within the a–b plane to determine $Δ ( T , p → )$ for the development of a predictable model of high- $T C$ superconductors.

Earlier in-plane tunnel spectroscopy was performed by creating tunnel devices on the facets of bulk single crystals with conventional superconductors and showed good Josephson tunnel characteristics for the $⟨ 100 ⟩$ direction,⁷ and another study mapped the angular dependence of Bi2212 using point contacts with normal wire.⁸ However, all superconductor in-plane tunneling in thin film materials has proved more challenging. Some innovative techniques involved etching ramps and deposition of counter electrodes,^9–11 but in these geometries, the in-plane component is convoluted with an out-of-plane component. Furthermore, the ion beam etching in these processes causes radiation damage, which is well known to reduce the critical temperature and likely suppresses the gap. Other work to get the a–b plane information involved the growth of a-axis orientated films.¹² However, these films are always of poor quality, and this method can only probe one direction and not gather information on angular dependence. Overall the results are inconsistent, and it is difficult to rule out effects from disordered materials, process damage, and trapped vortices, which are known to create zero bias peaks in the density of states.¹³ 

In 2015, Cybart et al. developed a new approach to a–b plane tunneling utilizing a focused helium ion beam (FHIB)¹⁴ to fabricate Josephson tunnel junctions in YBa₂Cu₃O_7−δ thin films with the transport current residing entirely within the a–b plane.¹⁵ Unlike prior-art metallic barrier high- $T C$ Josephson junctions,^16–18 these have insulating barriers¹⁹ and exhibit quasi-particle tunneling with well-described energy gaps.¹⁵ This process relies on the sensitivity of high- $T C$ materials to disorder.^20,21

The cuprate crystal structure is sensitive to point defects caused by ion irradiation.²⁰ Increasing irradiation dosage increases resistivity and $T C$ decreases. The material becomes a disordered insulator for helium irradiation exceeding $3 × 10 15$ ions/cm². The irradiation-induced metal-to-insulator transition (MIT) in the normal state comes about because the electron mean free path is sensitive to the disorder of the oxygen lattice. Disorder shortens the mean free path and increases the resistivity.²⁰ 

To create focused helium ion beam (FHIB) Josephson junctions, a commercial thin film of 40-nm-thick YBCO was grown by Ceraco GMBH by reactive co-evaporation on cerium oxide buffered r-plane sapphire.²² For electrical contacts, a 200-nm-thick Au layer was thermally evaporated in situ subsequently. Laser photolithography was used with Fuji Film OCG825 positive photoresist, and argon ion milling was performed in an Ion tech 21 cm broad beam Kaufman source at 500 V to etch both layers to define the electrodes. Second photolithography and KI⁺ chemical etch were used to remove the Au layer and uncover the YBCO area for FHIB direct writing. Helium ion irradiation was performed in a Zeiss Orion NanoFab He/Ne ion microscope with 32 keV He⁺ ions. An ion dose of $∼ 6 × 10 16 He + /$ cm² was applied to create a very narrow insulating barrier of ∼1–2 nm (Ref. 23) for YBCO in-plane superconducting–insulating–superconducting (SIS) junctions as shown in Fig. 1(b). A dose of $3 × 10 17 He + /$ cm² created the insulating regions to isolate the Josephson junctions for 4-point measurement for the nanoscale experiment depicted in Fig. 3.

The devices were cooled in an evacuated dip probe with a μ-metal magnetic shield vacuum can in a liquid helium Dewar. The measurements presented herein were taken at liquid helium temperature. A Keyence 33500B arbitrary function generator and custom electronics for noise isolation were used to bias the devices, and voltages were measured with SR560 low-noise battery-powered pre-amplifiers and an SR830 lock-in-amplifier to measure dI/dV. All the instruments and Dewar were in an RF-shielded room and connected to a general ground to reduce noise.

A typical current–voltage characteristic (⁠ $I − V$⁠) is shown in Fig. 1(c), and a plot of differential conductance (⁠ $d I − d V$⁠) shows a measurement of the YBCO energy gap Δ in the a–b plane. The inset shows (⁠ $I − V$⁠) of the same junction with a reduced range of 2 mV, highlighting that these junctions are well described by the resistively shunted junction model.^24,25

These junctions provide an accurate measurement of the density of states, because there are no interfaces between different deposited materials. There are also no etched ramps, which eliminate process damage to the electrodes. Furthermore, the conduction is entirely within the plane of a single film that is too thin to form vortices with cores aligned with the tunneling direction. In this work, we study FHIB Josephson junctions oriented along different crystalline directions in the a–b plane and report the anisotropy of the energy gap for micron- and nanoscale-sized structures.

To measure the energy gap Δ anisotropy of YBCO, laser lithography and argon ion milling were used to pattern electrodes oriented along different crystallographic directions that converged into the center of the chip into a 10 μm circle as shown in Fig. 2(a). A Josephson junction was directly written into each of these electrodes as indicated by the red lines in Fig. 2(a). Each Josephson junction can be individually addressed in a four-point transport measurement with an example transport arrangement indicated in Fig. 2(a).

Differential conductance (⁠ $d I − d V$⁠) was measured for each junction at temperatures significantly below the material $T C$⁠, and 2Δ was defined as the peak. Data for the angles of 11°, 34°, 56°, 79°, 101°, 124°, 146°, and 169° are shown in Fig. 2(b), where the angle is defined with respect to the a-axis. The YBCO a–b orientation was determined with transport measurements and Raman spectroscopy. A linear fit of the current–voltage characteristic was used to estimate the conductance. The results as a function of angle are plotted in Fig. 2(c) and show a gap anisotropy with two axes that differ by a factor of roughly 2:1. This is what one would expect from the measurement of bulk detwinned YBCO crystals⁴ that show a similar difference between the a and b crystal axes. This measurement suggests a high-quality orientated YBCO film. Furthermore, the conductance is inversely proportional to the gap. This correlates with measurements in bulk crystals using electrical transport⁵ and infrared spectroscopy.²⁶ 

To mitigate the effects of long-range, non-local film defects and to gain more resolution at the scale of the grains, we created a nano-lithography pattern with 24 Josephson junctions within a $5 × 5 μ$m² area. This experiment probes every 15° within the a–b plane, where each tunnel junction is individually addressable by integrating micro- and nano-lithographic isolation by utilizing the FHIB to directly pattern nanowire electrodes.²⁷  Figure 3(a) shows a helium ion micrograph of the center of a YBCO chip with lines superimposed that represent where FHIB lithography was performed to create Josephson junctions. The white lines were written at a very high dose of FHIB irradiation to ensure that they form insulating boundaries, and the red lines were written at a lower dose, which is typical to create Josephson tunnel junctions. Each Josephson junction can be individually measured as indicated by the four-point measurement scheme depicted in Fig. 3(a) The inset is a zoomed-out picture of the same sample showing the registration of the nanopattern with the photolithographic patterned electrodes.

The gap energies and conductances were measured as described above and are plotted in Fig. 3(b), and they also appear to be inversely proportional to one another. However, compared to the anisotropy of the longer Josephson junctions that are presented in Fig. 2, the patterns are more disordered and deviate from ideality. We attribute this to the granularity of the film, which is shown in a false color helium ion micrograph in Fig. 3(c). In Fig. 3(b), the angle is defined with respect to the micrographs in Figs. 3(a) and 3(c) so that the anisotropy can be related to the imaged film features. The a-axis was found to be along the 135° in this figure. The lithographic pattern can faintly be seen in the lower-left corner of this image, and some of the microstructure can be correlated with the electrical properties.

Our experimental results show that the energy gap of cuprate thin films is suppressed in the same directions where conductivity in the normal state is the highest. This is consistent with the model by Kresin and Wolf²⁸ that vacancies in the Cu–O chain create magnetic moments^29,30 on adjacent copper atoms that serve as pair breakers that suppress the gap. Because the coherence peaks are not sharp with large-scale patterns like those in Fig. 2, local variations average out, and we see well-defined patterns. However, moving to the nanoscale, we are measuring just a small number of grains. The local variations are more pronounced, and we see the granularity of the films and defects in the chains. This model agrees with Josephson scanning tunneling microscope studies³¹ that showed a significant spatial variation in the energy gaps of Bi2212 when probed at the atomic scale.

We have demonstrated in this work that helium ion nanofabricated junctions can be used to conduct in-plane tunneling for probing high- $T C$ materials at different scales to compare the dependence of macroscopic and microscopic energy gap measurements in momentum space. Our measurements find the symmetry to be twice symmetric, consistent with different gap energies along a and b as also seen in the conductivity measurement of bulk crystals. Further refinements of this technique correlated with spectroscopy could provide a pathway to a predictive model of superconductivity in the cuprates.

The authors thank Bob Dynes and Kazuo Kadowaki for enlightening discussions on transport and tunneling in cuprate superconductors. This work was supported by the Air Force Office of Scientific Research under Grant No. FA9550-20-1-0144.