A striking feature of cuprate superconductors is the ubiquity of the interplay between antiferromagnetic order, charge density waves (CDWs), and superconductivity. CDWs have clear signatures in the transport properties of YBa₂Cu₃O_6+x (YBCO). At low temperatures, the observation of low-frequency quantum oscillations, together with negative Hall and Seebeck coefficients, indicates the presence of a closed electron pocket in the reconstructed Fermi surface. The precise mechanism of the Fermi surface reconstruction by the CDW remains debated.

Here we report recent investigations into the high field transport properties of underdoped trilayer cuprate HgBa₂Ca₂Cu₃O_8+δ (Hg1223) with doping level p = 0.10–0.12 and in the composite Pr-doped YBCO system. Hg1223 exhibits exceptional sample quality, potentially surpassing even the cleanest YBCO [1]. We observe a dramatic change of the quantum oscillation spectrum as a function of temperature, supported by numerical simulations of Fermi surface reconstruction [2]. In Pr-YBCO, despite differences in disorder and doping method compared to pure YBCO, we find signatures of a Fermi surface reconstruction indicating the presence of 2D charge order [3]. This order, however, exhibits reduced competition with superconductivity.

[1] M Altangerel et al. Phys. Rev. B 112, 014522 (2025)

[2] V. Oliviero et al. npj Quant. Mat. 9, 75 (2024)

[3] C. Duffy et al, preprint on arxiv : 2512.16423 (2025)