What reconstructs the underdoped cuprate Fermi surface into small pockets
In plain words
In strong magnetic fields, underdoped YBa2Cu3O6+x shows quantum oscillations, field-periodic wiggles in resistance that reveal a small closed pocket of electrons, whereas at zero field the Fermi surface is a single large hole-like contour; some order must cut the large surface into pieces.
Precise statement
In YBa2Cu3O6+x ($p \sim 0.08\ \text{to}\ 0.15$) and HgBa2CuO4+d with superconductivity suppressed by $300\ \text{to}\ 900\,\mathrm{kG}$, quantum oscillations show a dominant frequency $F \sim 5.3\,\mathrm{MG}$ (about 2 percent of the Brillouin zone) and a negative Hall coefficient, indicating an electron pocket. Determine whether biaxial charge order with the measured $q_{\mathrm{CDW}}$ alone reconstructs the Fermi surface into this electron pocket, and where the additional hole pockets required by Luttinger counting are, or why they are absent. An answer is a reconstruction model reproducing F, its splitting and c-axis warping, the Hall sign and the carrier count, together with detection or exclusion of the predicted extra pockets.
What would settle it
Quantum-oscillation detection, or a bound on the amplitude, of the predicted hole pockets in the same field and doping range, plus angle-resolved oscillation data matching the proposed reconstruction.
Status in the literature
Reconstruction by charge order is the leading explanation of the electron pocket, but the hole pockets that such reconstructions predict have not been observed.