Engineering underdoped ${\mathrm{CuO}}_2$ nanoribbons in nm-thick $a$-axis ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films

In underdoped cuprate high-$T_{\mathrm{c}}$ superconductors, various local orders and symmetry-breaking states, in addition to superconductivity, reside in the ${\mathrm{CuO}}_2$ planes. The confinement of the ${\mathrm{CuO}}_2$ planes can therefore play a fundamental role in modifying the hierarchy between the various orders and their intertwining with superconductivity. Here we present the growth of $a$-axis oriented ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films, spanning the whole underdoped side of the phase diagram. In these samples, the ${\mathrm{CuO}}_2$ planes are confined by the film thickness, effectively forming unit-cell-thick nanoribbons. The unidirectional confinement at the nanoscale enhances the in-plane anisotropy of the films. By x-ray diffraction and resistance vs temperature measurements, we have discovered the suppression of the orthorhombic-to-tetragonal transition at low dopings, and a very high anisotropy of the normal state resistance in the $b\text{−}c$ plane, the latter being connected to a weak coupling between adjacent ${\mathrm{CuO}}_2$ nanoribbons. These findings show that the samples we have grown represent a novel system, different from the bulk, where future experiments can possibly shed light on the rich and mysterious physics occurring within the ${\mathrm{CuO}}_2$ planes.

Figure 1

${\mathrm{CuO}}_2$ nanoribbons from YBCO. (a) YBCO unit cell. The ${\mathrm{CuO}}_2$ planes where superconductivity, as well as various electronic local orders, reside, are highlighted in orange. (b) By growing $a$-axis oriented YBCO films, the ${\mathrm{CuO}}_2$ planes form ribbons of nanometer width, confined in one direction by the film thickness $t$.

Figure 2

Dependence of the superconducting transition of $a$-axis YBCO thin films on the oxygen annealing. (a) The resistance measured along the $c$-axis direction, $R_c$, normalized to the maximum value $R_{\max }$, is plotted vs temperature for a 300 nm thick underdoped film, achieved using an in situ annealing oxygen pressure $p_{\mathrm{ann}}=1\times {10}^{-3}$ mbar. In the inset, the derivative of the $R_c\left(T\right)$ highlights the pronounced broadening of the superconducting transition. (b) $R_c\left(T\right)$ is presented for an underdoped film, obtained by applying the same annealing pressure used for the film in panel (a), but ex situ. The homogeneity of the film is proven by a rather sharp superconducting transition, as highlighted in the inset.

Figure 3

Complete detwinning in $a$-axis oriented YBCO films. (a) Symmetrical $2\theta \text{−}\omega$ scan of a 300 nm thick underdoped film. The arrows show the positions where the ($00n$) YBCO reflections should be for a $c$-axis oriented film. The inset on the left shows the FWHM of the (300) YBCO Bragg peak, $\mathrm{\Delta }2{\theta }^{\left(300\right)}$, as a function of $p$. (b) Symmetrical $2\theta \text{−}\omega$ map of a 800 nm, slightly underdoped YBCO film. Asymmetrical $2\theta \text{−}\omega$ maps on the same sample are performed with the momentum $q$ parallel either to (c) the $c$-axis or to (d), (e) the $b$-axis direction. Panel (d) is the line scan, highlighted in panel (e) by the dashed line. (f) The untwinning degree, determined by the intensity of the measured Bragg peaks, is plotted as a function of the film thickness.

Figure 4

Locking of the ${\mathrm{CuO}}_2$ planes in $a$-axis oriented YBCO films. (a) The $c$-axis parameter, extracted from the ($\ell 00$) and ($\ell 0n$) Bragg reflections, is shown as a function of the doping $p$ for films of different thickness. For each sample, $p$ has been determined based on the $c$-axis length, and then utilizing the critical temperature $T_{\mathrm{c}}$ measured via transport (see Sec. 4) and the empirical parabolic relationship connecting doping and $T_{\mathrm{c}}$ in cuprate HTS [52, 61]. Notably, all data points for the 50 nm thickness have been collected from a single, multiply annealed thin film. (b) The $a$- and $b$-axis parameters, extracted from the ($\ell 00$) and ($\ell m0$) Bragg reflections, are plotted vs $p$ for different 300 nm thick films. (c), (d) The symmetrical $2\theta \text{−}\omega$ scans respectively of an insulating ($p\sim 0$) and of an underdoped ($p=0.14$) film are compared. The decomposition of the data into three Voigt profiles associated to the (300) PBCO, the (030) YBCO, and the (300) YBCO reflections shows first that the PBCO layer is unaffected by the annealing procedure, as the peak position is unchanged vs doping, and second, that the two YBCO peaks, related to the ${\mathrm{CuO}}_2$ planes, are distinct, even though they get closer, in the undoped sample. To facilitate the comparison, the vertical bars show the position of the two YBCO peaks in the doped sample.

Figure 5

Suppression of the orthorhombic to tetragonal transition. (a), (b) Symmetric and (c)–(f) asymmetric RSMs of two 300 nm thick $a$-axis oriented YBCO films. Panels (a), (c), (e) refer to an undoped sample, while panels (b), (d), (f) refer to a fully oxygenated sample. (a), (b) Symmetric map of the (200) reflections of the SLGO, PBCO, and YBCO. (c), (d) Asymmetric map of the (309) reflections of the SLGO, PBCO, and YBCO. (e), (f) Asymmetric map of the (330) reflections of the SLGO, PBCO, and YBCO. In panels (e) and (f), the dashed line represents the tetragonal line $a=b$. The $a, b$, and $c$ axis parameters can be determined from the RSM peaks via $a=\ell /q_{\left[100\right]}, b=m/q_{\left[010\right]}$, and $c=n/q_{\left[001\right]}$, where $\ell , m$, and $n$ are the Miller indices of the peak ($\ell mn$).

Figure 6

Scanning electron microscopy image of the structures used for the measurements of the nanoribbon resistivity. The 1 mm long and $100\mu \mathrm{m}$ wide Hall bars are oriented along either the $b$-axis or the $c$-axis direction of the YBCO film.

Figure 7

Doping dependence of nanoribbon resistivity. Panels (a)–(c) show ${\rho }_b\left(T\right)$ for various 300 nm thick films at different oxygen doping levels. The critical temperature $T_{\mathrm{c}}$ for each film is determined from the maximum of the first derivative of ${\rho }_b\left(T\right)$. $T_{\mathrm{L}}$ (violet circles), marking the crossover between the pseudogap region and the strange metal phase, is the temperature below which the resistivity ${\rho }_b\left(T\right)$ deviates by 1% from the high-temperature linear fit of the curves, performed in the interval 280 $\mathrm{K}<T<300$ K. Notably, all ${\rho }_b\left(T\right)$ datasets are extensive, featuring a sub-Kelvin temperature step size. Panel (d) presents a phase diagram constructed from the obtained values of $T_{\mathrm{c}}$ and $T_{\mathrm{L}}$, exhibiting good agreement with the superconducting (SC) and strange metal (SM) regions observed in YBCO single crystals and $c$-axis oriented films [52, 68].

Figure 8

Anisotropic transport properties of underdoped 300 nm thick ${\mathrm{CuO}}_2$ nanoribbons. Sheet resistances $R_{\square }^b\left(T\right)$ (squares) and $R_{\square }^c\left(T\right)$ (circles) of an underdoped ($p=0.09$) film. The inset, where the tails of the superconducting transition of the two measurements are presented on the same vertical scale, highlights the lower zero resistance critical temperature occurring along the $c$ axis.