Critical level statistics of a quantum Hall system with Dirichlet boundary conditions

• Published in: Annalen der Physik Vol. 7; no. 5-6; pp. 457 - 461
• Main Authors: Potempa, H., Schweitzer, L.
• Format: Journal Article
• Language: English
• Published: Leipzig WILEY-VCH Verlag 01.11.1998; WILEY‐VCH Verlag
• Subjects: Boundary conditions; Critical spacing distribution; Level statistics; QHE
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/(SICI)1521-3889(199811)7:5/6<457::AID-ANDP457>3.0.CO;2-Q

We investigate numerically the influence of Dirichlet boundary conditions on the nearest neighbor level spacing distribution P(s) of a two‐dimensional disordered tightbinding model in the presence of a strong perpendicular magnetic field. From the calculation of the second moment of P(s) it is shown that for Dirichlet boundary conditions, due to the presence of edge states, the position of the critical energy shifts with increasing system size to the location of the critical energy for periodic boundary conditions. An extrapolation to infinite system size results in different critical (scale independent) P(s) distributions for periodic and Dirichlet boundary conditions.