Long-Ranged Order and Flow Alignment in Sheared <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math> ‐atic Liquid Crystals

We formulate a hydrodynamic theory of $p$-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic $p$-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of $p$-atic phases, allows us to unveil several unknown aspects of flowing $p$-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.