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A Study of Relativistic Interface States
Author(s) -
Roy C. L.,
Roy G.
Publication year - 1984
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221210230
Subject(s) - eigenvalues and eigenvectors , momentum (technical analysis) , interface (matter) , energy–momentum relation , dirac equation , wave function , dirac (video compression format) , physics , quantum mechanics , gibbs isotherm , finance , neutrino , surface tension , economics
Abstract A relativistic study is made of the interface states in a solid which is reduced to a one‐dimensional system. The electronic states of such a model are governed by a two‐component Dirac equation. The interface connects two semi‐infinite solids represented by two semi‐infinite chains of δ‐function potential wells with a certain strength for either solid. In solving the Dirac equation for this model one is led to the energy—momentum relation of the system, that is to the band structure associated with non‐localised states and to isolated energy eigenvalues referring to interface states with certain complex momentum wave vectors. To eliminate isolated energy eigenvalues associated with states which increase exponentially towards the bulk on either side of the interface, existence conditions are derived which guarantee that only eigenvalues referring to interface states are selected. The influence of relativistic effects on the spectrum of interface states is demonstrated by choosing various sets of values for the parameters characterising the two solids. For the same purpose these interface state energies are recalculated for an approximately relativistic case using an approach by Steslicka and Davison, and for the strictly non‐relativistic case.