Possible continuous transition from fractional quantum Hall to stripe phase at $\nu_e=7/3$

We study the phase diagram of $\nu_e=7/3$ state in the $N=1$ Landau level in the presence of band mass anisotropy. Using density matrix renormalization group on an infinite cylinder geometry, we find a continuous transition from the topologically ordered Laughlin fractional quantum Hall state to a stripe phase with a period of approximately five and a half magnetic lengths. The transition is driven by the condensation of the magnetoroton mode which becomes gapless at the critical point. We interpret the transition within the composite-boson theory as the onset of stripe order in a superfluid background, resulting from the roton mode going soft.