Nonuniversal behavior of finite quantum Hall systems as a result of weak macroscopic inhomogeneities.

We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights {sigma}{sub {ital xx}}{sup max} compared to the universal values previously predicted for infinite homogeneous samples. This effect is expected to occur for the conductivity peaks measured in standard experimental geometries such as the Hall bar and the Corbino disk. At the lowest temperatures, the decrease in {sigma}{sub {ital xx}}{sup max}({ital T}) is found to saturate at values proportional to the difference between the adjacent plateaus in {sigma}{sub {ital xy}}, with a prefactor that depends on the particular realization of disorder in the sample. We argue that this provides a possible explanation of the {open_quote}{open_quote}nonuniversal scaling{close_quote}{close_quote} of {sigma}{sub {ital xx}}{sup max} observed in a number of experiments. We also predict an enhancement of the {open_quote}{open_quote}nonlocal{close_quote}{close_quote} resistance due to the macroscopic inhomogeneities. We argue that, in the Hall bar with a sharp edge, the enhanced {open_quote}{open_quote}nonlocal{close_quote}{close_quote} resistance and the size corrections to the {open_quote}{open_quote}local{close_quote}{close_quote} resistance {ital R}{sub {ital xx}} are directly related. Using this relation, we suggest a method by which the finite-size corrections may be eliminated from {ital R}{sub {ital xx}} and {italmore » R}{sub {ital xy}} in this case. {copyright} {ital 1996 The American Physical Society.}« less