Special features of "peierls"
You may also want to look at the full parameter list of all the buttons and sliders, or at one of the general help files, Sliders, or
Graphs.
- THE ENERGY BAND
- The dispersion relation used by "peierls", the same as by "ziman", is
E(k) = (h-bar^2)/(2*m){(k_x)^2[1 - (1/2)(k_x*a/pi)^2] + A*(k_y)^2[1 -
(1/2)(k_y*a/pi)^2]},
with numerical values based on a lattice constant a=2 Angstroms.
- A is the anisotropy parameter. It gives the ratio of the xx- to the yy-components of the effective mass at k = 0.
- Specific energy contours may be shown by selecting the corresponding Fermi energy
- KEY EQUIVALENTS
- run/stop: spacebar
- initialize: i-key
- HOLE REPRESENTATION
- The show hole toggle opens the left-hand display, a hole representation of same band as seen on the right. Each unoccupied state in the right-hand display at position k is displayed on the left by showing the state -k as occupied (a white dot) by a hole. See Kittel's discussion of holes for the rationale.
- The shift origin toggle shifts quadrants of the Brillouin zone by appropriate reciprocal lattice vectors to bring the occupied hole states together near the upper right-hand corner of the zone.. Then the origin of the display is shifted to bring the center the hole distribution to the center of the panel.
- In both the left and right displays, the edges of the Brillouin zone are the blue lines.
- COLORED DOTS
-
Though of dubious significance, the equilibrium average wave vector of the electron (or hole) distribution is shown in red, and the current average value in green. (For the holes, these are shown only with the shift origin toggle on.)
- NUMBER OF ELECTRONS
- The "peierls" scattering algorithm does not strictly conserve electron number: it can destroy an electron by scattering before it is sure that it can find a permitted state into which to scatter it. The problem is most obvious for a choice of Fermi energy which is very close in energy to the highest filled state. With the electric field at 0.1x10^6 V/m, compare the electron number variation in preset 2 with the Fermi energy at the two values 2.36 eV and 2.25 eV, both of which correspond initially to 44 electrons, Appendix B of Chapter 10 of Simulations for Solid State Physics gives best choices for the Fermi energy for the 14x14 grid of initial states.