Yt. Rebane, GAUGE PROPERTIES OF K-CENTER-DOT-P HAMILTONIANS FOR CRYSTALS WITH LINEAR TOPOLOGICAL DEFECTS, Physical review. B, Condensed matter, 52(3), 1995, pp. 1590-1595
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.