Shearconductivity as evidence for broken mirror symmetries

We propose the possible detection of broken mirror symmetries in highly correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the shearconductance $\Gamma_{xx,xy}=\partial \sigma_{xx}/ \partial \epsilon_{xy}$, the linear change of the longitudinal conductivity $\sigma_{xx}$ due to a shear strain $\epsilon_{xy}$. This quantity can only be non-vanishing if the in-plane mirror symmetries are broken and we show that a square lattice with checkerboard charge and bond density wave shows a finite shearconductivity. This implies that a measurement of $\Gamma_{xx,xy}$ opens the possibility to verify broken mirror symmetry in the pseudogap regime of high-$T_c$ superconductors. Experimental setups to detect shearconductance are presented.