# Is the Laughlin wave function with $m > 3$ less important than the $m =3$ one?

It is known that the $m= 3$ Laughlin wave function is a very accurate approximation of the realistic ground state.

Is it the case that as $m$ increases, the Laughlin wave function as an approximation becomes less accurate and thus it becomes less relevant?

Experiments observe quantized Hall plateaus corresponding to Laughlin-type states at $\nu = \tfrac{1}{3}$ and $\tfrac{1}{5}$, and the Laughlin wavefunction is a good description for both (though it may be a bit less accurate for the latter). However, the story is different for $m > 5$, $\nu = \tfrac{1}{7}, \tfrac{1}{9}, \cdots$. Plateaus either aren't observed at these small filling fractions, or they're absorbed into the neighboring IQHE plateau. For clean systems, it is believed that the electrons form a Wigner crystal, breaking translation symmetry, rather than a liquid state. So the Laughlin wavefunction is no longer an accurate description, even qualitatively.
• For $\nu = 1/7$, the magnetic field would be very high. Is it achievable experimentally? Sep 26, 2016 at 2:17
• Yes, it is a high but achievable field, see for example Phys. Rev. Lett. 61, 881 and the theoretical followup Phys. Rev. B 48, 11473 . Note the physics should be similar at filling $\nu = 1 + 1/m$, which is a lower field.