Comment on 'Evidence for Anisotropic State of Two-Dimensional Electrons in High Landau Levels

In a recent letter M. Lilly et al have shown that a highly anisotropic state can arise in certain 2D electron systems. (This effect has also now been seen by another group). Most of the samples studied are square. In these samples, the restances in the two perpendicular directions are found to have a ration R sub (yy)/R sub (xx) that may be as much as 60 or even larger at low temperature and at certain magnetic fields. In the same work, Hall bar measurements were also performed which can be thought of, at least conceptually, as being measurements on rectangular samples (with side lengths L sub x and L sub y). In such measurements R sub (yy) is measured in a sample with L sub y > L sub x and R sub (xx) in a sample where L sub x > L sub y. In the Hall bar experiments it is found that the anisotropy ration is much smaller - with R sub (yy)/R sub (xx) ~ 5. In this comment, we resolve this discrepancy by noting that the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in the resistance measurements on square samples due to simple geometric effects. We note, however, that the origin of this underlying resistivity anisotropy remains unknown, and is not addressed here.