Solid State Physics Fermi Surface Exercise

Login, web interface and logout

Use user-id st## and password as given in class
ssh -Y st##@eulers.phys.cmu.edu
test xclock
Note graphics is rather slow over wireless networks w2web -p 240##
http://eulers.phys.cmu.edu:240##
when done: pkill w2web -u st##
logout


Assignment


See User guide for help as needed. Items in bold are to be handed in. Double arrows >> are menus on web server.

Read chapter 15 of Ashcroft and Mermin, especially the section on Noble metals (e.g. copper) and trivalent metals (e.g. aluminum).

Electronic structure of copper (Cu)

Create session : enter Cu
New directory: click "create/change" to create and change to new directory; click "Select current directory"; click "click to restart"
Keep defaults (complex calculation, no inversion)


Execution/StructGen >> generate template for 1 atom. Why 1 atom, not 4 for FCC?
Lattice FCC (space group 225 Fm-3m)
lattice constant a=b=c=3.61 Angstrom, angles 90 degrees
1 Cu atom at x=y=z=0
Save structure; Set automatically RMT; adjust RMT 0% (do it);
Save structure; Save and clean up;
View structure using xcrysden, modify # units drawn to 2x2x2 and rotate to obsrve symmetries and latice planes. Find a nice view and print figure to save as png file

Execution >> initialize calc; Fast mode accept defaults
Run batch initialization; View STDOUT look at output and find "init_lapw finished ok"
Execution >> run SCF; accept defaults; start SCF cycle
View the output STDOUT (optionally, Utils >> show dayfile); reload in reverse order click every few seconds to watch progress
briefly describe roles of LAPW0/1/2/CORE/MIXER
Check charge and energy convergence; How many SCF cycles were performed and how long did each cycle take?
Utils : save_lapw


Tasks >> E. Dens.
Look at the scf1 and scf2 files.
How many electrons are there? What is the Fermi energy? What are the energy ranges of the core levels, and the valence/conduction band? Hint: core levels are low energy and very narrow. Valence band is broad and occupied.
Set Emin to a value between core and valence levels in order to eliminate the core charge desity. The default of -1.0 should be OK; Run x lapw2;
Calculate and visualize electron density with XCrysden. Choose a 2D plane of high symmetry passing through atoms. See Section 3.11.1 of the user guide for detailed help.
Some hints: show a 2x2x2 supercell. Expand plane to whole structure. Choose a small density range (say 0-1) or else a log scale. Try rainbow colors. Shrink the atomic diameters to avoid hiding the region near the atoms.
Save 2D figure of electron density as rho.png.

Tasks >> DOS
Edit Cu.in1 to increase Emin (to above core levels, units are Ry)
Double the k-mesh and run x lapw1 then x qtl and xlapw2 -qtl for partial charges
What are these k-points (e.g. what do they have to do with the wavefunctions?) and why is such a large number of k-points needed?
Configure input file for TETRA. Plot the partial density of states for s, p and d levels. Download and print to turn in a PostScript file with the total DOS, and the s, p, and d partial DOS.

Tasks >> Bandstructure
create klist from xcrysden (needs X11 graphics) along path shown in Ashcroft and Mermin Fig. 15.4
Then select "from xcrysden" and click create Cu.klist_band
Alternatively (easier), select "fcc" and click create Cu.klist_band
Run x lapw1 -band; Insert EF into Cu.insp; x spaghetti; plot bandstructure ; print figure

Draw Fermi surface
In a terminal windows connected to eulers, change directory to Cu session cd /home/st##/WIEN2k/Cu. Enter xcrysden --wien_fermisurface . (don't forget the "." and notice the double "--"). Generate a k-mesh of 10000 k-points
Calculate eigenvalues x lapw1; Calculae Fermi energy x lapw2 -fermi; Render Fermi Surface
A window will open showing energy bands. You should see band #9 crossing EF. Select band 9 and render. print a figure of Fermi surface.
Experiment with views including toggling of restriction to Brillouin zone. Discuss your findings and compare with discussion of noble metals in Ashcroft and Mermin.

Repeat entire calculation for Al
How many electrons and valence electrons does Al have, and how do these compare to Cu?
Create session Al; create structure (FCC a=4.05 Angstrom); initialize and run SCF; view band structure along fcc k-point path; print figure and compare with free electron model and with band structure for Cu.
In terminal window run xcrysden to render Fermi surface; You should use a high number of k-points (say, 100000) to get good resultion of fine details; Select the bands that cross EF (should be 5 and 6 What's wrong with 1-3?)
View the individual bands within and outside the first Brillouin zone; view the merged bands;
Print figure of merged bands inside Brillouin zone. View band 5 in reciprocal unit cell - What color corresponds to the high energy side of the Fermi surface? Which band (5 or 6) is a "hole" surface?