Quantum Hall charge density waves under anisotropy: from first-order to continuoustransitions

We investigate the quantum Hall charge density wave states in theN= 2 Landau level undermass anisotropy. In the absence of anisotropy, there are two first-order phase transitions betweenthe Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy,our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripephase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystalsthat may be observed experimentally is unveiled after the bubble phase gets out. Upon increase ofthe anisotropy, the energy of the phases at the transitions becomes progressively smooth as a functionof the filling. We conclude that all first-order phase transitions are replaced by continuous phasetransitions, providing a possible realisation of continuous quantum crystalline phase transitions.