Large anisotropic magnetoresistance in $\alpha$-MnTe induced by strain

$\alpha\textrm{-MnTe}$ is a p-type semiconducting altermagnet with a N\'eel temperature near $300\thinspace\textrm{K}$. Due to the altermagnetic nature, $\mathcal{PT}$ symmetry is broken, and Kramers degeneracy is lifted in the valence band maxima along the $\Gamma\textrm{-K}$ line and the A point. However, the energy difference is found to be small, and any small shift in the spectrum can dramatically change the linear-response transport properties. Here we show that a strain modulating the [0001] axis of the unit cell by $\sim\pm0.5\%$ can significantly change the transport signature by switching the thermal window between the two regions of the valence band. When the $\Gamma\textrm{-K}$ line is dominating, the planar Hall effect and the anisotropic magnetoresistance can be enhanced by an order of magnitude, with the maximum up to $\sim70\%$.