Screened quantum Hall edge strips

Self-consistent electrostatics allows a partially filled edge Landau level to screen strongly and flatten its effective energy. Such compressible regions alternate with incompressible strips whose chemical potential lies in a gap and across which the potential changes. An externally prescribed unscreened smooth edge misses this redistribution. Temperature, disorder and interactions beyond the electrostatic approximation can change the strip profile.

An incompressible quantum Hall edge strip is an edge region where the local chemical potential lies in a gap between available electron states. Small potential changes then alter the local electron density only weakly, so that region cannot screen an external field as effectively as a neighboring compressible quantum Hall edge strip.

In the self-consistent electrostatic picture, incompressible regions alternate with compressible ones as the confining potential varies toward an edge. Much of the potential change can occur across the incompressible regions. Their widths depend on the gap and density profile; a prescribed unscreened edge potential misses the redistribution that produces the strips.^[ref]

A compressible quantum Hall edge strip is an edge region where a Landau level is partly occupied and nearby states permit the local electron density to adjust. This adjustment screens the confining field and tends to flatten the effective energy of that level near the chemical potential.

It contrasts with an incompressible quantum Hall edge strip, where a gap suppresses the corresponding density response. Their alternating arrangement is a self-consistent property of electrons and the confining electrostatics, rather than simply a drawing of unperturbed levels through a fixed potential. Finite temperature, disorder and interactions can modify the ideal strip structure.^[ref]