New Mechanism of Umklapp Scattering in Cuprate High-Tc Superconductors

Cuprates display several novel symmetry-broken orders such as spin stripe, charge density wave (CDW). We propose a novel mechanism of dissipative umklapp scattering contributing to anomalous transport by fluctuating order beyond fermi surface reconstruction to electronic spectrum. Spatial-temporal fluctuating order is assumed to introduce umklapp scattering of holes, which yields a relaxation time proportional to square of order's periodicity (l_o) and a resistivity ρ=h/(π²e²n_cl_o²). This achieves a remarkable link between microscopic fluctuating orders and macroscopic transport, which yields a length mapping method (i.e. l_o∝ρ^-1/2) to derive orders' periodicity from resistivity data. The theory is validated by data of three classes of samples in LSCO, Bi-2201 and Bi-2212. We show that at underdoped regime at 'knee' temperature (of ρ vs T), l_o is indeed close to 2a₀, which is the periodicity of antiferromagnetism, while at overdoped regime l_o is near 4a₀, the CDW periodicity. In a vortex liquid, l_o is found to vary as reduced vortex distance (∝B^-1/2), and in strange metal as reduced de Broglie wave length (∝T^-1/2). These results demonstrate the universal validity of the new umklapp scattering mechanism and the length mapping method, providing a new tool to study order transitions.