Items in bold are to be handed in. Note that the commands listed shown on the web page (e.g. x lapw1) can be run directly from the command line from the appropriate directory, without using the web browser interface. See User guide for help as needed.
Read the paper Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface by Zhang et al.
Create Session : enter Bi2Se3
New directory: click create/change to create new directory click Select current directory; click "click to restart"
Keep defaults (complex calculation, no inversion)
Execution/StructGen >> generate template for 3 atoms
Lattice spacegroup 166_R-3m, a=b=4.1355, c=28.615 (Angstrom), gamma=120
Se 0 0 0
Bi 0.4006 0.4006 0.4006
Se 0.2109 0.2109 0.2109
Save Structure; Set automatically RMT; Reduce by 0% (do it)
Save Structure; Save file and clean up
How many atoms of each type are in the hexagonal unit cell and in the rhombohedral primitive cell?
How many electrons?
Execution >> view structure (opens xcrysden)
Modify # units drawn (2x2x1) and rotate to nice view. Print Crystal 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
Utils >> show dayfile; reload in reverse order click every few minutes
While you wait 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 name noLS
Tasks >> E. Dens.
Look at the scf1 and scf2 files.
What is the Fermi energy? What is the band gap?
What are the energy ranges of the core levels, the valence band and the conduction band? Hint: core levels are low energy and very narrow. Valence band is broad and occupied. Conduction band is empty.
Run x lapw2; Calculate and visualize electron density with XCrysden. Choose a 2D plane containing a Bi atom and both types of Se. A good choice is a plane containing the c-axis. See Section 3.11.1 of the user guide for detailed help.
Some hints: show a 2x2x1 supercell. Expand plane to whole structure. Choose a small density range. Try rainbow colors. Shrink the atomic diameters.
Save 2D figure of electron density as rho.png.
Tasks >> DOS
Edit Bi2Se3.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 Bi and Se s and p levels. Download and print to turn in a PostScript file with the total DOS, and the local p dos on each atom type
Tasks >> Band structure
Use xcrysden to create klist. Note: if you have not gotten X11 to work, you can simply copy my list. In your login window navigate to your WIEN2k/Bi2Se3 directory and enter cp ~widom/tmp/xcrysden.klist . (don't forget the final ".")
What points in the Brillouin zone are time reversal invariant, and why?
Select path GZFGL (see paper) with 80 points along path. Save klist file with name xcrysden.klist.
select "from xcrysden"; click create Bi2Se3.klist_band; select "copy it"
x lapw1 -band; x lapw2 -band -qtl
Edit insp file for band character plot : Insert EF; select energy range +-2.0 eV; choose line switch 2
Set jatom 1, 2 or 3; set jtype 4 for pz character; size 0.6; Save and continue
x spaghetti; plot bandstructure; download and print. Repeat for jatom 1, 2 and 3.
Feel free to look at other band characters. See headder of your *.qtl file for list of jtypes (e.g. jtype=5 gives px+py)
New session >> Bi2Se3-LS
Briefly describe what spin orbit coupling is. Does it break time reversal invariance?
Execution >> run SCF : Repeat self-consistent calculation including spin-orbit coupling.
Edit *.inso file : replace NX with 0 and delete following line
Compare the timing including spin-orbit
Utils >> save_lapw yesLS
Plot band structure with band character weighting for Se (pz)
Compare to case without spin-orbit and discuss.