  Our knowledge of the ground state of underdoped hole-doped cuprates has
evolved considerably over the last few years. There is now compelling evidence
that inside the pseudogap phase, charge order breaks translational symmetry
leading to a reconstructed Fermi surface made of small pockets. Quantum
oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical
conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778]
and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys.
Rev. B 93:064513] point to a Fermi liquid regime at low temperature in the
underdoped regime. However, the observation of a quadratic temperature
dependence in the electrical resistivity at low temperatures, the hallmark of a
Fermi liquid regime, is still missing. Here, we report magnetoresistance
measurements in the magnetic-field-induced normal state of underdoped
YBa_2Cu_4O_8 which are consistent with a T^2 resistivity extending down to 1.5
K. The magnitude of the T^2 coefficient, however, is much smaller than expected
for a single pocket of the mass and size observed in quantum oscillations,
implying that the reconstructed Fermi surface must consist of at least one
additional pocket.
