Download presentation

Presentation is loading. Please wait.

Published byGilbert Minter Modified over 3 years ago

1
Topology of Complex Energy Bands in the Resonant Scattering Problem An exercise in complex variable theory applied to condensed matter physics

2
Resonant Scattering If a defect tends to form a bound state at energy E b, then propagating states close to this energy are very strongly scattered e.g. GaAs with a small concentration of N replacing some As atoms EbEb Modified Band Structure

3
Momentum States Current-carrying states scattering by defects momentum is not exactly conserved momentum states are not exact energy eigenstates best approximation to an eigenstate with momentum k : Lifetime = Energy of momentum state k is shifted by scattering from E k to z = E - iγ

4
Self-consistent Greens Function Defect Greens function : Momentum Greens function : Defect energy broadening: Solve Self- consistently 4 Greens Function: G(z) diverges at excitation energies ΔE is complex

5
The Poles of Momentum Greens Function The poles Greens function The poles of G kk occur at : Band energies z are then defined by: 5 Defines continuous curves z(ε) in the complex plane Project: investigate the topology of these curves

6
Project Challenges Understanding Green's functions in this context Understanding complex analytic function theory associated with the Green's function Developing a numerical approach to solve the complex energy equation (programming & solution) Interpreting the complex bands to give physical quantities: density of states, group velocity, etc.

Similar presentations

OK

How does diffusion affect radiative efficiency measurements? Caroline Vaughan and Tim Gfroerer, Davidson College, Davidson, NC Mark Wanlass, National Renewable.

How does diffusion affect radiative efficiency measurements? Caroline Vaughan and Tim Gfroerer, Davidson College, Davidson, NC Mark Wanlass, National Renewable.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on electrical circuit breaker Ppt on dairy farm management Ppt on power system protection Ppt on nepali culture show Ppt on viruses and anti viruses history Ppt on power line communication standard Ppt on operating system by galvin Ppt on 4-stroke petrol engines Ppt on conservation of environmental degradation Ppt on formation of company