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In underdoped cuprate high $T_{\mathrm{c}}$ superconductors, various localorders and symmetry breaking states, in addition to superconductivity, residein the CuO$_2$ planes. The confinement of the CuO$_2$ planes can therefore playa fundamental role in modifying the hierarchy between the various orders andtheir intertwining with superconductivity. Here we present the growth of$a$-axis oriented YBa$_2$Cu$_3$O$_{7-\delta}$ films, spanning the wholeunderdoped side of the phase diagram. In these samples, the CuO$_2$ planes areconfined by the film thickness, effectively forming unit-cell-thicknanoribbons. The unidirectional confinement at the nanoscale enhances thein-plane anisotropy of the films. By X-ray diffraction and resistance vstemperature measurements, we have discovered the suppression of theorthorhombic-to-tetragonal transition at low dopings, and a very highanisotropy of the normal state resistance in the $b$-$c$ plane, the latterbeing connected to a weak coupling between adjacent CuO$_2$ nanoribbons. Thesefindings show that the samples we have grown represent a novel system,different from the bulk, where future experiments can possibly shed light onthe rich and mysterious physics occurring within the CuO$_2$ planes.

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