Experimental realisation of tunable ferroelectric/superconductor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text {B}} {\text {T}} {\text {O}}/{\text {Y}} {\text {B}}{\text {C}} {\text {O}})_{{\text {N}}}/{\text {S}}{\text {T}}{\text {O}}$$\end{document}(BTO/YBCO)N/STO 1D photonic crystals in the whole visible spectrum

Emergent technologies that make use of novel materials and quantum properties of light states are at the forefront in the race for the physical implementation, encoding and transmission of information. Photonic crystals (PCs) enter this paradigm with optical materials that allow the control of light propagation and can be used for optical communication, and photonics and electronics integration, making use of materials ranging from semiconductors, to metals, metamaterials, and topological insulators, to mention but a few. Here, we show how designer superconductor materials integrated into PCs fabrication allow for an extraordinary reduction of electromagnetic waves damping, making possible their optimal propagation and tuning through the structure, below critical superconductor temperature. We experimentally demonstrate, for the first time, a successful integration of ferroelectric and superconductor materials into a one-dimensional (1D) PC composed of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text {B}}{\text {T}}{\text {O}}/{\text {Y}}{\text {B}}{\text {C}} {\text {O}})_{{\text {N}}}/{\text {S}}{\text {T}}{\text {O}}$$\end{document}(BTO/YBCO)N/STO bilayers that work in the whole visible spectrum, and below (and above) critical superconductor temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_C=80\, {\hbox {K}}$$\end{document}TC=80K. Theoretical calculations support, for different number of bilayers N, the effectiveness of the produced 1D PCs and may pave the way for novel optoelectronics integration and information processing in the visible spectrum, while preserving their electric and optical properties.


Results and discussion
Structural properties. Figure 1a shows a schematic diagram of three 1D photonic crystals of one-, three-, and five-pair of BTO/YBCO bilayers, fabricated by DC and RF sputtering onto polished SrTiO 3 (001) substrates. Here, a and b correspond to the thicknesses of BaTiO 3 and YBa 2 Cu 3 O 7 , θ i denotes the angle with the z-axis defined in the range of 0 • ∼ ±90 • , xz is the plane of incidence, and the direction of E × B is given by the incident wave vector k, where E and B represent the electric and magnetic fields, respectively. Figure 1b displays the out-of-plane XRD θ-2θ scans for the YBCO(70 nm)/STO film, the BTO(30 nm)/YBCO(73 nm)/STO bilayer, and the BTO(30 nm)/STO film. YBCO and BTO peaks associated with the (001) direction were identified for reflections from 20 • to 80 • . The observed peaks in the individual layers are indexed in the bilayer, and indicate a textured growth of both samples. A minor Cu 2 O phase was identified in our sample, this impurity is typical for YBCO 54,55 . The following lattice parameters were obtained: a BTO = 4.035 Å , a YBCO = 3.878 Å in films, while a BTO = 4.040 Å and a YBCO = 3.867 Å for the BTO/YBCO bilayer. For a bilayer, no considerable displacement of peaks was observed compared to the YBCO and BTO films grown under identical parameters, as shown by the dashed vertical lines in the X-ray θ − 2θ scans of Fig. 1b. Hence, there is no effect due to the BTO layer on the position of the Bragg reflection peaks for the YBCO layer.
With the aim to corroborate the SC/ferroelectric PC formation, we first performed a resistivity measurement as a function of temperature for an YBCO film to confirm the superconductor state. As expected, a traditional resistance with temperature dependence was obtained, with a superconducting temperature T SC ∼ 85 K for the BTO/YBCO film. During the (BTO/YBCO) N -PC structure measurements, the YBCO layer was, at some point, exposed to laser irradiation at different wavelengths. At a first glance, this could imply the possibility of occurrence of a breakdown of the Cooper pairs during the radiation-matter interaction (e.g., in YBCO intergranular films, the radiation damage requires ∼ 1 eV/atom) [56][57][58][59] . We performed a resistance measurement for the YBCO/ STO film whilst the sample was exposed to a coherent laser radiation source, in the 500-800 nm range. For YBCO, the superconducting gap equals 30 meV and the laser radiation energy which would break down the Optical response: theory and experiment. Figure 3a shows the schematics of the experimental setup used to measure the optical response of the (BTO/YBCO) N /STO 1D PC (described in the Methods section). Figure 3b, c display the effect of the number of periods on the reflectance spectra. Continuous and dashed curves correspond to the experimental and theoretical results obtained when N is equal to 1 and 5, and the temperature is kept constant at T = 50 K , respectively. Even though measured spectra are in agreement with the theoreti-   A supercontinuum laser beam in the wavelength range between 400 and 800 nm, collimated with a Galilean telescope lenses setup, is sent to the multilayer (BTO/YBCO) N sample inside a cryostat, at a controllable temperature, toward mirrors and a focusing lens. The reflection from the sample is collected by a fiber coupler into a multimode fiber towards the spectrometer and the response is analysed in a workstation. (b), (c) Reflectance response of (BTO/YBCO) N /STO 1D PC for N = 1 , and 5, respectively. Continuous and dashed curves correspond to experimental and theoretical results at T = 50 K , respectively. www.nature.com/scientificreports/ cal predictions, the overall behaviour presents a considerable number of resonant peaks and a small variation in reflectance intensity. Based on the TEM analysis of Fig. 2, we associate these peaks with the possible nonuniformity of the thickness and the additional presence of a few YBCO grains grown along the [001] direction. Additionally, correspondence between the number of interference fringes (or bands) and the number of periods of bilayers in the structure is evidenced. These fringes are likely the result of the interference of incident light beams partially reflected and transmitted at the interfaces between layers.
To gain further insight into the optical response of our structure, we used the transfer matrix method to calculate the reflectance spectra 70,71 , and the two-fluid model 72 , to consider the contribution of the superconductor (YBCO) to the dielectric response of the PC (see the Methods section). As described ahead, this model allowed us to theoretically explain the reflectance found experimentally. In a previous work 71 , we theoretically studied the transmission of the superconductor PC as a function of the wavelength for different temperatures. We found no noticeable changes in the transmission spectra with temperature, but did find the existence of small shifts in the bands. With the aim to compare with experimental results, in Fig. 3d, we plot, in six panels, the temperature effect on the reflectance spectra measured. From panels (A), (B), and (C), where the temperature varied from 80 K, 50 K to 30 K for N = 3 , an almost negligible shift is perceived in the wavelength ranges where the transmission bands are present. Similar features were obtained in panels (D), (E) and (F), for N = 5 with T = 80 K , 50 K and 30 K, respectively. Figure 3d indicates with vertical red lines specific wavelengths ( = 543 , 720, and 760 nm for N = 3 , and = 520 , 625, and 770 nm for N = 5 ) to get a better visualisation of these findings. In addition, in Fig. 3e, we show the (BTO/YBCO) 5 /STO 1D PC optical response as a function of wavelength and temperature T, from T = 30 K to 80 K, below the critical temperature of the superconductor. The dark areas correspond to the high-reflectance ranges, while yellow areas, indicate high transmission ranges where radiation passes through the structure. We obtain a negligible shift as the temperature increases. We associate our findings with the slight decrease suffered by the superconductor dielectric constant as the wavelength increases. If this change were appreciable, the reflectance should suffer a displacement, in agreement with the electromagnetic variational principle 4 . Thus, our results demonstrate the effectiveness of the (BTO/YBCO) N /STO 1D PCs implemented as a promising choice in the design of optical transmitters/reflectors below and above critical superconductor temperature. The fact that temperature does not significantly affect the operation frequencies of the bands becomes an advantage, given that high reflectances can be achieved in that whole range of temperatures.
In order to examine in detail the band dependence on the number of periods, in Fig. 3e we plot the simulated optical response in the whole range from N = 1 to 10. As in the previous case, dark areas correspond to the highreflectance ranges, while yellow areas indicate transmission ranges where radiation passes through the structure. It is noticeable for N = 1 that reflectance decreases from 500 nm to approximately 610 nm (see Fig. 3b), which is observed in the optical response of Fig. 3f as the change from dark to yellow region. In the case N = 5 , two low-reflectance ranges are seen around 510 nm and 620 nm (Fig. 3c), which is completely in agreement with the theory. We have extended our results up to N = 10 , to show the sensitivity of the transmission/reflection bands with N: the larger N, the lower the wavelengths of the photonic bands, and their optical response experiences a switch for the EM waves propagation from forbidden to allowed frequency ranges at a given wavelength. Interestingly, such structured bands become narrower as N changes from an even to an odd number, a mechanism that could be exploited as an optical switch. Figure 4a, b plot the measured reflectance for (BTO/YBCO) 5 /STO 1D PC in the wavelength range from 500 to 700 nm at T = 50 K and incident angles of 35 • and 65 • for TE polarization. Two high reflectance regions were found around 570 nm and 650 nm at 35 • and 65 • , respectively. For better understanding of the reflectance behaviour, we have displayed in Fig. 4c, the spectra as a function of the whole range of incident angles for TE polarization. One important feature found in our results related to the reflection from a finite multilayer is its sensitive response to the light incidence angle 4 , observed in the continuous displacement of the bands to shorter wavelength as the incident angle increases. On the other hand, as the incidence angle approaches 90 • , the reflection coefficient tends to 1, a result in agreement with the fact that a wave that impinges with a right angle moves parallel to the separation surface of the two media, and therefore, its energy is not transmitted through the surface. The results for 35 • and 65 • (magenta vertical lines) are indicated in the figure, whose bands match perfectly well with measured spectra (Fig. 4a, b). Figure 4c also evidences the existence of a third transmission band for wavelengths above 700 nm. These results allow us to conclude that there exist wavelength ranges where the radiation does not pass through the PC under any incident angle, results that can be applied, for example, for the tuning of optical transmitters/reflectors fabricated to operate below critical superconductor temperature, whose response is sensitive to the light incidence angle.
For the sake of completeness, we calculate the optical response of (BTO/YBCO) 5 /STO 1D PC when the YBCO is in the non-superconducting state, above T c . In this case, the dielectric function is described by the Drude model of a metal given by Eq. (10). As is well known, for temperatures below T c there is no resistance, and for temperatures above T c there is a non-zero resistance that varies linearly with the temperature. Resistivity measurements were performed with (and without) applied laser field irradiation on the (BTO/YBCO) N 1D PCs. The main goal of this measurement was to confirm that the superconductor ( YBa 2 Cu 3 O 7 ) remains in its superconducting state under applied radiation. Even though the superconductor was radiated at frequencies above its superconductor gap ( ∼ 8 THz), the 10 mW laser power in the spectral band of 450-750 nm is not enough to destroy the superconducting state.
Accordingly, in Eq. (11), the damping γ varies linearly with temperature in accordance with ρ 0 = (3.74 × 10 −9 )T + (6.90 × 10 −7 ) for T > T c , which implies that Eq. (10) is temperature-dependent. The calculated and measured reflectance are shown in Fig. 4d, and the behaviour predicted by the Drude model is in excellent agreement with our experimental results on the reflection of electromagnetic waves at the interface between the ferroelectric and the superconductor in normal state. When the electromagnetic wave impinges on the conductor surface it induces a conduction current, which leads to a swift damping of the field inside the www.nature.com/scientificreports/ conductor. This is why metals have excellent reflecting properties (i.e., reflectance close to unity) and are broadly used in mirrors or optical reflectors. According to the above, a high reflectance would be expected in the PC now composed of the superconductor in the normal state. However, as it is observed in the Fig. 4d, e, the intensity of the reflectance increases with respect to the previous cases, but it is not total because about 60% and 40% of the light is still transmitted through the structure at certain wavelengths between 500 nm and 700 nm, at T = 80 K , and about 80% at T = 100 K , respectively. It is important to point out that reflectivity also depends on the thickness of the layers, and our findings clearly illustrate such thickness dependence 73,74 .
In order to analyse the superelectrons contribution on the optical response of the (BTO/YBCO) 5 /STO 1D PC, in Fig. 4f, we report the difference between the reflectance coefficients ( δ R) calculated from the subtraction of the reflectance spectra with and without the superelectron effect according to Eqs. (9) and (10). This result allows us to approximate the magnitude order of the contribution made by the Cooper pairs in the mixed state of the superconductor, below critical temperature, to be in the order of ∼ 10 −2 , and corroborate their significant contribution to the optical response of the superconductor. From the reflectance spectra at T = 100 K ( T > T c ), and at T = 80 K , 50 K and 30 K ( T ≤ T c ), as can be seen in Fig. 3d, panels D, E, and F, for N = 5 , we get a decreasing of the reflectance at low temperatures for wavelengths between 500-550 nm, and 600-650 nm, which implies that the main contribution to the light transmission in the structure is due to the superelectrons. This result highlights the important role played by the superconductor in the optical response of the PC. On the other hand, it is worth noting that the Drude model matches perfectly well with the experimental spectrum at 80 K, that is, the temperature around which the state transition occurs; however, and as expected, this model does not adjust the measurements above T c (e.g., at T = 100 K ). Although the Drude model is presented for temperatures above critical temperature, it is evident that for T > T c , additional contributions exist to the electronic properties, affecting the optical response.
Finally, reflectance spectra of (BTO/YBCO) N /STO heterostructures for N = 1, 3, 5 , at T = 20 K are shown in Fig. 5. The reflection spectra for N = 1 and N = 3 structures at T = 20 K clearly show a constructive interference effect between the incoming light in the YBCO and the reflected light on the YBCO/BTO interface, bearing in mind that the BTO refraction index is larger than that of the YBCO. This is clearly evidenced since the reflected spectra of the N = 3 structure shows that a maximum (minimum) takes place at each third of the wavelength of the N = 1 heterostructure. On the other hand, the reflectance spectrum for N = 5 begins to exhibit the whole reflectance behaviour of the 1D photonic crystal, as reported in 71 .  (Fig. 4a) and 65 • (Fig. 4b), respectively. www.nature.com/scientificreports/

conclusions
We have succeeded at experimentally realising ferroelectric/superconductor 1D photonic crystals as suitable engineered nanosystems for tuning and controlling electromagnetic wave propagation in a wide region of the visible spectrum. We were able to fabricate 1D photonic crystals of N = 1, 3 and 5 pairs of BTO/YBCO bilayers by DC and RF sputtering, onto polished SrTiO 3 (001) substrates, and studied the effects due to temperature and direction of the incident radiation. We have experimentally demonstrated how to tailor the number of photonic bands as a function of N, and have also been able to quantify and predict, for any N, the frequency range sensitivity and optical properties of the PCs with the direction of the incident EM waves-the larger the angle of incidence the shorter the wavelength and the bigger the width of the transmission/reflection bands. A key result from an operational point of view is that temperature does not significantly affect the frequency range of the transmission bands, which can be advantageous because this can enable either a high or low reflectance, in the whole range of studied temperatures (20-100 K). The contribution made by the Cooper pairs in the mixed state of the superconductor to the PC optical response is of the order of 10 −2 : the superelectrons are the most relevant contribution to the light transmission in the structure, at tested wavelengths between 500-550 nm, and 600-650 nm. Finally, and based on the PCs here implemented, several strategies for the development of quantum materials and possible novel optical filters and reflectors, below critical superconductor temperature and different properties of incident light, have been proposed.

Methods
Photonic crystal fabrication. The (BTO(30 nm)/YBCO(73 nm)) N=1,3,5 multilayers were grown on a (001) STO substrate by DC/RF sputtering technique in a pure oxygen atmosphere and high pressure ( ∼ 3.0 mBar), with a substrate temperature of 830 • C . Power density of 7 W/cm 2 and 12 W/cm 2 were used for YBCO and BTO targets, respectively. X-ray diffraction was used to perform structural characterisation using a Co-Kα = 1.79 Å wavelength. In addition to the local interface analysis, transmission electron microscopy (TEM) was employed. Cross-sectional lamella was prepared from the thin films deposited using a dual beam FEI Helios Nanolab 600i. Initially, the film surface was coated with a platinum layer on a sputtering to avoid charge accumulation during the process. Then, two platinum layers were applied to protect and avoid damages on the thin films. The lamella was extracted and submitted to a thinning process which ended with the use of a low energy beam to minimize amorphization. Finally, the lamella is placed onto a TEM grid. A Hitachi TEM-microscope HF3300C was operated at 300 kV to acquire the high resolution images of the cross-sectional lamella. The sample was tilted until the nearest zone axis of STO was parallel to the electron beam. Then, high resolution images were acquired at the different layers and interfaces. In addition, electron diffraction patterns were obtained to identify the crystallographic orientation of the layers with respect to the substrate. The electrical properties and the superconductor transition temperature ( T C ) were studied by using the traditional four-point technique. Resistance as a function of temperature was measured in the 20-100 K range by using silver paint and copper wires. Considering that the top layer was always the BTO layer in the (BTO/YBCO) N /STO multilayer array, we also analysed its diamagnetic properties in order to identify T c through thermal demagnetization measurements, by using a PPMS Quantum Design from 10 to 300 K.
Wide range laser reflectance measurements. A supercontinuum fiber laser (Fyla STC 1000) and a monochromator (Fyla TW) were employed to irradiate the sample in the 400-800 nm spectral range. The beam path crosses through a telescope arrangement with a magnification factor of 1 × to collimate the laser and control the beam divergence. The light is addressed with aluminum mirrors (95% of reflectance) perpendicularly towards the cryostat (Cryostat Advanced Research System) where the sample is placed under a vacuum of 10 −5 bar and a controlled temperature down to 10 K. The reflection angle is controlled with a homemade sample copper holder inside the cryostat, and set to 35 • and 65 • for taking different set of measurements. The reflecting path is collected with a collimation lens and coupled to a multimode optical quartz fiber 400 µm in diameter. The fiber is connected to a spectrometer (HD 4000, Ocean Optics) that finally displays the spectra in a workstation. www.nature.com/scientificreports/ The reference spectra for the reflectance calculations were taken at high temperatures for which the reflection of the sample is higher than all the others.
1D photonic crystal transfer matrix calculation. The studied 1D photonic superlattice has a period d, and is composed of alternating layers of a dielectric material BaTiO 3 and a superconductor YBa 2 Cu 3 O 7 , whose widths are labeled as a and b, respectively. The propagation of an in-plane linearly polarized electromagnetic field is of the form E(z, t) = E(z)e −iωtx , along the z-axis (see Fig. 1a). By using Maxwell's equation for linear and isotropic media, it is demonstrated that the amplitude of the electric field E(z) satisfies 71,75 where c is the vacuum speed of light, n(z) = √ ǫ(z) √ µ(z) and Z(z) = √ µ(z)/ √ ǫ(z) are respectively, the refraction index and the impedance of each layer material. For a photonic crystal composed of alternating layers of two different materials, Eq. (1) must be solved by assuming both, the electric field and its first derivative continuous across an interface, which means that the two-component function ψ(z) = The two-fluid model. The two-fluid model is often used to describe the behaviour of a superconductor at nonzero temperature. It consists of two distinct noninteracting fluids of electrons that carry current, where each fluid follows two parallel channels, one superconductor and one normal. Accordingly, when a material is superconducting, some of the electrons will be superconductors and some will still be normal electrons. Thus, there will be a mixture of superelectrons and normal electrons. For these reason, we can model the total conductivity as follows: for T ≤ T c , as the sum of the normal conductivity maintained by unpaired electrons, and the superconducting conductivity maintained by superelectrons; and for T > T c , by the Drude conductivity for a normal metal. More explicitly, it can be written as 72 : where ω is the EM wave frequency, µ 0 is the permeability of free space; n, q, and m are respectively the density, the charge, and the mass of the carrriers, τ denotes the scattering time of electrons. The damping frequency γ = 1 τ , f n = T T c p gives the density of normal state electrons over the total number of electrons, and L is the temperature-dependent penetration depth 72 : www.nature.com/scientificreports/ where 0 is the value of the penetration depth at zero temperature, and the exponent p corresponds to 2 and 4 for high and low temperature superconductors, respectively. The dielectric response of a given material is introduced by means of the electric permittivity. This parameter is in general a complex number, ǫ = ǫ r + iǫ i , where the imaginary part ǫ i accounts for electromagnetic losses in the material and is closely related to the current inside the material through the complex conductivity σ (ω) , such that ǫ = ǫ(ω) = ǫ ∞ + i σ (ω) ǫ 0 ω , where ǫ ∞ is the dielectric function at high frequencies and ǫ 0 the permittivity of free space 76 . By replacing Eq. (7) into ǫ(ω) , we arrive at the dielectric function of the superconductor Finally, substitution of Eq. (8) leads to the dielectric function of a metal To calculate the reflectance spectra, in our numerical simulations layer 1 corresponds to BaTiO 3 with a = 30 nm ; ǫ = 5.8 77 . As the operation temperature in the present experiment varies from 20 K to 100 K, the BaTiO 3 -dielectric constant can be considered constant in this range 78,79 . Layer 2 corresponds to YBa 2 Cu 3 O 7 , with p = 2 , T c = 80 K (the critical temperature experimentally obtained in this work), b = 73 nm , the plasma frequency ω p = 1.7 × 10 15 rad/s 80 , the damping frequency γ = 1.3 × 10 13 rad/s 80 , and the dielectric constant is modelled by Eq. (9). According to the growth direction of the bilayers (c-axis), we consider the parallel propagation to the c-axis of YBCO , i.e., the magnetic field H perpendicular to ĉ (TE case). Therefore, the penetration depth is on the a-b plane with a ⊥0 = 118.6 nm 81 . For temperatures close to the critical temperature T c , over the range 0.001 < T c −T T < 0.1 , we adopted the magnetic penetration depth L = ⊥0 [1 − (T/T c )] p , with p = − 1 3 81 .
Simultaneously, we considered the thermal expansion effect on BaTiO 3 and YBa 2 Cu 3 O 7 thicknesses. In certain temperature ranges, the thermal expansion effect adopts the law d(T) = d 0 (1 + α�T) , where α is the thermal expansion coefficient, T is the temperature deviation, and d and d 0 are the thicknesses of each layer under actual and room temperature, respectively 82 . We consider the thermal expansion coefficients to be 7.14 × 10 −6 / • C and 13.4 × 10 −6 / • C for BaTiO 3 83 and YBa 2 Cu 3 O 7 84 , respectively.
The steady-state dc conductivity ( σ 0 ) and dc resistivity ( ρ 0 ) are functions of the plasma frequency ω p and the damping γ , and they are related as follows 72