A variational approach to dislocation problems for periodic Schrödinger operators
- Hempel, Rainer
- Kohlmann, Martin
DOIAbstract
AbstractAs a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential V=V(x,y) on R2 with period lattice Z2 by setting Wt(x,y)=V(x+t,y) for x<0 and Wt(x,y)=V(x,y) for x⩾0, for t∈[0,1]. For Lipschitz-continuous V it is shown that the Schrödinger operators Ht=−Δ+Wt have spectrum (surface states) in the spectral gaps of H0, for suitable t∈(0,1). We also discuss the density of these surface states as compared to the density of the bulk. Our approach is variational and it is first applied to the well-known dislocation problem (Korotyaev (2000, 2005) [15,16]) on the real line. We then proceed to the dislocation problem for an infinite strip and for the plane....
Add to ORKG