GAUGE PROPERTIES OF K-CENTER-DOT-P HAMILTONIANS FOR CRYSTALS WITH LINEAR TOPOLOGICAL DEFECTS

A general expression for the k . p Hamiltonian in crystals with linear topological defects such as dislocations, disclinations, and dispirat ions has been found. It has been shown to contain gauge potential term s corresponding to a non-Abelian gauge group, E(3), which is the prope r Euclidean group. The gauge field is confined within the cores of top ological defects and influences the carriers in the bulk of the crysta l through the gauge potential which extends beyond it. A general expre ssion for the gauge potential A(r) is presented, For a crystal that co ntains only dislocations the gauge group E(3) degenerates into T(3), t he Abelian subgroup of translations. The corresponding gauge potential becomes (A) over cap(r) = i beta(T)(r)((p) over cap/HBAR-k alpha), wh ere k(alpha) is the electron wave vector related to the point in the B rillouin zone for which the k . p Hamiltonian is written, (p) over cap is the momentum-operator matrix in the basis of Bloch functions corre sponding to k(alpha), and beta(r) is the distortion tenser.