Symmetric, off-diagonal, resistance from rotational symmetry breaking in graphene-WSe${}_2$ heterostructure: prediction for a large magic angle in a Moire system

We show that any two-dimensional system with a non-zero $\mathit{\text{symmetric}}$ off-diagonal component of the resistance matrix, $R_{xy}=R_{yx}\mathrm{\ne }0$, must have the in-plane rotational symmetry broken down to $C_2$. Such a resistance response is Ohmic, and is different from the Hall response which is the $\mathit{\text{anti-symmetric}}$ part of the resistance tensor, $R_{xy}=-R_{yx}$, is rotationally symmetric in the 2D plane, and requires broken time-reversal symmetry. We show how a minute amount of strain due to lattice mismatch - less than $1\mathrm{\%}$ - can produce a vastly exaggerated symmetric off-diagonal response - $\frac{R_{xy}}{R_{xx}}\sim 20\mathrm{\%}$ - because of the momentum matching constraints in a Moire system. Our results help explain an important new transport experiment on graphene-WSe${}_2$ heterostructures, as well as are relevant for other experimental systems with rotational symmetry breaking, such as nematic systems and Kagome charge density waves. Additionally, our work predicts an example of a `magic’ angle, $\theta \sim {27}^0$, in a Moire system which is a significant fraction of $\pi$. Our prediction that the anomalous resistance anisotropy occurs at a large value of magic angle, in contrast to known examples of magic angle transport anomalies that are small fractions of $\pi$, can be experimentally tested in graphene-WSe${}_2$ heterostructures.