between incompressible liquids and compressible states with charge density wave ordering. In $n\geq 2$ Landau levels, mass anisotropy selects and enhances stripe ordering with compatible wave vectors at partial 1/3 and 1/2 fillings.'
author:
- 'Bo Yang$^1$, Z. Papić$^2$, E. H. Rezayi$^3$, R. N. Bhatt$^{2}$, and F. D. M. Haldane$^1$'
title: Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
---

Introduction {#sec_introduction}
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Two-dimensional electron systems (2DES) placed in a high magnetic field exhibit a wide variety of strongly correlated phases, which have been the subject of numerous theoretical and experimental investigations since the first observation of fractionally quantized Hall conductivity [@tsg]. Examples of such phases of matter are the Laughlin states [@laughlin], describing partial fillings $\nu=1/3,1/5$ of the lowest ($n=0$) Landau level (LL), as well as their generalizations to other odd-denominator fillings in the framework of hierarchy [@prange] and composite fermion theory [@jainbook]. These phases are topologically ordered and possess quasiparticle excitations with fractional statistics. At half filling of the first excited, $n=1$ LL, an even more exotic paired state, the Moore-Read Pfaffian [@mr], might be realized, which possesses non-Abelian excitations – the Majorana fermions [@mr; @readgreen].

Besides the incompressible liquids, some fillings $\nu$ also 