We propose the possible detection of broken mirror symmetries in correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the shearconductivity $Gamma_{xx,xy}$, defined as the linear change of th
e longitudinal conductivity $sigma_{xx}$ due to a shear strain $epsilon_{xy}$. This quantity can only be non-vanishing when in-plane mirror symmetries are broken and we discuss how candidate states in the cuprate pseudogap regime (e.g. various loop current or charge orders) may exhibit a finite shearconductivity. We also provide a realistic experimental protocol for detecting such a response.
Motivated by recent observations of charge order in the pseudogap regime of hole-doped cuprates, we show that {it crisscrossed} stripe order can be stabilized by coherent, momentum-dependent interlayer tunneling, which is known to be present in sever
al cuprate materials. We further describe how subtle variations in the couplings between layers can lead to a variety of stripe ordering arrangements, and discuss the implications of our results for recent experiments in underdoped cuprates.
