Title: Scale-invariant magnetoresistance in a cuprate superconductor,
Abstract: The anomalous metallic state in high-temperature superconducting cuprates is
masked by the onset of superconductivity near a quantum critical point. Use of
high magnetic fields to suppress superconductivity has enabled a detailed study
of the ground state in these systems. Yet, the direct effect of strong magnetic
fields on the metallic behavior at low temperatures is poorly understood,
especially near critical doping, $x=0.19$. Here we report a high-field
magnetoresistance study of thin films of \LSCO cuprates in close vicinity to
critical doping, $0.161\leq x\leq0.190$. We find that the metallic state
exposed by suppressing superconductivity is characterized by a
magnetoresistance that is linear in magnetic field up to the highest measured
fields of $80$T. The slope of the linear-in-field resistivity is
temperature-independent at very high fields. It mirrors the magnitude and
doping evolution of the linear-in-temperature resistivity that has been
ascribed to Planckian dissipation near a quantum critical point. This
establishes true scale-invariant conductivity as the signature of the strange
metal state in the high-temperature superconducting cuprates.