Interpreting angle-dependent magnetoresistance in layered materials: Application to cuprates

The evolution of the low-temperature electronic structure of the cuprate metals from the overdoped to the underdoped side has recently been addressed through angle-dependant magnetoresistance (ADMR) experiments in ${\mathrm{La}}_{1.6\ensuremath{-}x}{\mathrm{Nd}}_0.4{\mathrm{Sr}}_x{\mathrm{CuO}}₄$. The results show a striking difference between hole dopings $p=0.24$ and $p=0.21$, which lie on either side of a putative quantum critical point at intermediate $p$. Motivated by this, we here study the theory of ADMR in correlated layered materials, paying special attention to the role of angle-dependent quasiparticle weights ${Z}_{\mathbf{k}}$. Such a ${Z}_{\mathbf{k}}$ is expected to characterize a number of popular models of the cuprate materials, particularly when underdoped. Further, in the limit of weak interlayer hopping the quasiparticle weight will affect the $c$-axis transport measured in ADMR experiments. We show that proper inclusion of the quasiparticle weight does not support an interpretation of the data in terms of a $(\ensuremath{\pi},\ensuremath{\pi})$ spin density wave ordered state, in agreement with the lack of direct evidence for such order. We show that a simple model of Fermi surface reconfiguring across a van Hove point captures many of the striking differences seen between $p=0.21$ and $p=0.24$. We comment on why such a model may be appropriate for interpreting the ADMR data, despite having a large Fermi surface at $p=0.21$, seemingly in contradiction with other evidence for a small Fermi surface at that doping level.