Parameter definitions for "peierls"
It's probably useful to look first at the special features page. You may also want to look at one of the general help files, Sliders, or
Graphs.
Inputs
- SLIDERS
- E_x: x-component of applied DC electric field, in units of 10^6 Volts/meter
- E_y: y-component of applied DC electric field, in units of 10^6 Volts/meter
- B_z: magnitude of magnetic field, in tesla. Field is perpendicular to the plane of the screen (the z-direction).
- tau: scattering time parameter. Roughly the scattering time, but see Chapter 10 of Simulations for Solid State Physics for details. (Restricted to positive values.)
- Fermi energy: Fermi energy, in electron volts, of the electrons. The red trace in the displays is the Fermi surface (line in two dimensions). (Restricted to positive values.)
- anisotropy: introduces anisotropy into the dispersion relation . See .special features for definition of E(k) and the anisotropy. (Restricted to positive values.)
- speed: adjusts the animation speed. (Restricted to positive values.)
- TOGGLES
- show holes: opens and closes the left-hand display, the hole representation of the partially filled band.
- shift origin: shifts three of the quadrants of the Brillouin zone to join together at the upper right
corner of the original zone, and then shifts the display to center that corner point in the panel. The blue lines remain the boundaries of the original first zone.
- show graph: opens and closes the graph displaying average carrier velocities.
- run/stop: starts and stops the animation: key equivalent is the spacebar.
- BUTTONS
- initialize: initializes the program to the ground state configuration: key equivalent is the i-key.
- presets: Takes you to a tear-off menu with which you may select the presets. For more details, see the preset item in the miscellaneous help file.
- configure: allows variation of the less frequently changed parameters:
- k-space grid: controls the spacing of initial k-states which are distributed on a uniform (k-space grid) by (k-space grid) grid in the Brillouin zone. (Use the largest value your patience will bear!) (Restricted to positive integers.)
- worm length: specifies the number of successive positions of the electrons which are left in the display to suggest directions and magnitudes of the velocities. (Restricted to positive integers.)
- graph update increments: changes the number of animation display steps between successive updating of the graphical results. (Restricted to positive integers.)
- revert: updates the listed configure parameters to the current values (which may have been changed by a preset command).
- close: closes the configure window.
- help: Opens the help system which you have already found!
- quit: Terminates "peierls".
Outputs
- DISPLAYS
- right side: first Brillouin zone in reciprocal space showing the trajectories of a set of band electrons in response to applied DC fields. The average electron wave vector for the equilibrium state is given by the red dot, and for the current configuration by the green dot,
- left side: hole representation of the same set of electrons. The left display is derived from the right by placing a hole as a white dot in the state -k whenever the state k in the right=hand display is empty. (See Kittel's discussion of holes for the rationale for the minus sign!) If the shift origin toggle is on, the average hole wave vector for the equilibrium state is given by the red dot, and for the current configuration by the green dot,
- graph: gives the average x- (blue) and y- (red) components of the electron (or hole) velocity as a function of time. The graphs are for electrons if show holes is off, and for holes if show holes is on.
- READOUTS
- time: a clock reading time, in picoseconds, since the last initialize.
- number of electrons: gives the number of electrons for various choices of Fermi energy. The scattering algorithm used by "peierls" does not strictly conserve the number of electrons so don't be surprised by small changes in this number during a run.
- cursor positions: the coordinate pairs beneath the two displays give the positions of the cursors in units of inverse Angstroms. Since the lattice constant in "peierls" is arbitrarily chosen to be 2 A, the zone boundaries are at (pi/a) = 1.57 1/A.