Scattering of electrons due to screw dislocations

The phase dismatching effect on the scattering due to screw dislocations is reformulated to take the discreteness of lattice sites into account. Thet-matrix for an electron scattered from the statep top′ is $$begin{gathered} tleft( {p,p'} right) = ip_z Texp left{ {ileft( {p - p'} right) cdot m_A } right}exp left{ {ileft( {p - p'} right) cdot left( {i + j} right)/2} right} hfill cdot frac{{left[ {exp left( { - ip_y } right) - exp left( {ip'_y } right)} right] + left( {upsilon _y /upsilon _x } right)left[ {exp left( {ip_x } right) - exp left( { - ip'_x } right)} right]}}{{1 - exp left[ {ileft{ {left( {p_x - p'_x } right) + left( {upsilon _y /upsilon _x } right)left( {p_y - p'_y } right)} right}} right]}} hfill end{gathered}$$ for 0≦v _y ≦v _x ≦1 and |p _y |, |p′ _y |?1. Here,v is the group velocity of the incident electron andm _A is the position of the dislocation axis. All vector notations represent vectors in two-dimensional space, the unit vectors of which are represented byi andj. Expressions for |p _y |, |p′ _y |?π and other values ofv are obtained through simple modifications. As an application, the resistivity due to screw dislocations is discussed qualitatively.