Abstract
Crystal dislocations govern the plastic mechanical properties of materials but also affect the electrical and optical properties. However, a fundamental and quantitative quantum field theory of a dislocation has remained undiscovered for decades. Here we present an exactly-solvable one-dimensional quantum field theory of a dislocation, for both edge and screw dislocations in an isotropic medium, by introducing a new quasiparticle which we have called the ‘dislon’. The electron-dislocation relaxation time can then be studied directly from the electron self-energy calculation, which is reducible to classical results. In addition, we predict that the electron energy will experience an oscillation pattern near a dislocation. Compared with the electron density’s Friedel oscillation, such an oscillation is intrinsically different since it exists even with only single electron is present. With our approach, the effect of dislocations on materials’ non-mechanical properties can be studied at a full quantum field theoretical level.
Highlights
Crystal dislocations are a basic type of one-dimensional topological defects in crystalline materials [1]
We find that in an isotropic medium, the exact Hamiltonian for both the edge and screw dislocations can be written as a new type of harmonic-oscillator-like Bosonic excitation along the dislocation line, the name ‘dislon’
We have developed a fully-quantized theory of crystal dislocations in order to describe the effect of a dislocation on the electronic properties of materials at a many-body level
Summary
Crystal dislocations are a basic type of one-dimensional topological defects in crystalline materials [1]. ∮ satisfies the dislocation’s topological constraint du = -b, where b is the Burgers vector, L is a closed L contour enclosing the dislocation line (denoted as D in figure 1(a)), and u is the lattice displacement vector, i.e. the atomic position deviation occurs after the crystal is dislocated, and du is the differential displacement along the contour L. Using this approach, the scattering between an electron and the 3D displacement field induced by.
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