Hi centaur,
Thank you a lot for your explanation. I did the correction Mahmoud suggested
and I can get numerical results for all k in the Brillouin zone now. But
plotting the eigenvales doesn't give the correct band structure (at least that
one depicted in the textbook at page 72 for instance). The first 3 bands I get
are similar, but the forth one is different. I used a 128 grid resolution and
here's what I got:
init-params: initializing eigensolver data
Computing 8 bands with 1.000000e-07 tolerance.
Working in 2 dimensions.
Grid size is 128 x 128 x 1.
Solving for 8 bands at a time.
Creating Maxwell data...
Allocating fields...
Mesh size is 3.
Lattice vectors:
(1, 0, 0)
(0, 1, 0)
(0, 0, 1)
Cell volume = 1
Reciprocal lattice vectors (/ 2 pi):
(1, -0, 0)
(-0, 1, -0)
(0, -0, 1)
Geometric objects:
block, center = (0,0,0)
size (1,1,0)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon = 8.9
block, center = (0,0,0)
size (0.9175,0.9175,0)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon = 1
Geometric object tree has depth 4 and 19 object nodes (vs. 2 actual objects)
Initializing dielectric function...
16 k-points:
(0,0,0)
(0.1,0,0)
(0.2,0,0)
(0.3,0,0)
(0.4,0,0)
(0.5,0,0)
(0.5,0.1,0)
(0.5,0.2,0)
(0.5,0.3,0)
(0.5,0.4,0)
(0.5,0.5,0)
(0.4,0.4,0)
(0.3,0.3,0)
(0.2,0.2,0)
(0.1,0.1,0)
(0,0,0)
Solving for band polarization: tm.
Initializing fields to random numbers...
elapsed time for initialization: 0 seconds.
epsilon: 1-8.9, mean 2.22403, harm. mean 1.16912, 16.449% > 1, 15.4941% "fill"
matrixio: cannot output "epsilon" (compiled without HDF)
Outputting epsilon...
solve_kpoint (0,0,0):
tmfreqs:, k index, k1, k2, k3, kmag/2pi, tm band 1, tm band 2, tm band 3, tm
band 4, tm band 5, tm band 6, tm band 7, tm band 8
Solving for bands 2 to 8...
Finished solving for bands 2 to 8 after 24 iterations.
tmfreqs:, 1, 0, 0, 0, 0, 0, 0.55462, 0.584893, 0.647329, 0.647329, 0.916036,
0.975607, 1.02498
elapsed time for k point: 3 seconds.
solve_kpoint (0.1,0,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 11 iterations.
tmfreqs:, 2, 0.1, 0, 0, 0.1, 0.0669224, 0.540818, 0.576425, 0.648193, 0.668831,
0.906108, 0.966719, 1.01149
elapsed time for k point: 1 seconds.
solve_kpoint (0.2,0,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 6 iterations.
tmfreqs:, 3, 0.2, 0, 0, 0.2, 0.133004, 0.500709, 0.576419, 0.650482, 0.706253,
0.883264, 0.941601, 1.00332
elapsed time for k point: 1 seconds.
solve_kpoint (0.3,0,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 7 iterations.
tmfreqs:, 4, 0.3, 0, 0, 0.3, 0.197058, 0.451673, 0.581184, 0.653367, 0.74477,
0.858876, 0.909578, 1.00078
elapsed time for k point: 1 seconds.
solve_kpoint (0.4,0,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 6 iterations.
tmfreqs:, 5, 0.4, 0, 0, 0.4, 0.256026, 0.401307, 0.585904, 0.655749, 0.780163,
0.840954, 0.877558, 0.999922
elapsed time for k point: 0 seconds.
solve_kpoint (0.5,0,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 5 iterations.
tmfreqs:, 6, 0.5, 0, 0, 0.5, 0.290329, 0.369845, 0.587855, 0.656671, 0.799715,
0.83437, 0.859091, 0.999707
elapsed time for k point: 1 seconds.
solve_kpoint (0.5,0.1,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 7 iterations.
tmfreqs:, 7, 0.5, 0.1, 0, 0.509902, 0.295654, 0.375827, 0.568536, 0.67548,
0.800089, 0.81972, 0.859164, 0.980526
elapsed time for k point: 1 seconds.
solve_kpoint (0.5,0.2,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 6 iterations.
tmfreqs:, 8, 0.5, 0.2, 0, 0.538516, 0.3108, 0.392257, 0.533092, 0.709383,
0.78517, 0.801307, 0.859364, 0.947961
elapsed time for k point: 1 seconds.
solve_kpoint (0.5,0.3,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 6 iterations.
tmfreqs:, 9, 0.5, 0.3, 0, 0.583095, 0.333404, 0.414639, 0.495614, 0.743953,
0.745908, 0.804065, 0.859616, 0.913533
elapsed time for k point: 1 seconds.
solve_kpoint (0.5,0.4,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 5 iterations.
tmfreqs:, 10, 0.5, 0.4, 0, 0.640312, 0.358894, 0.435299, 0.461556, 0.714307,
0.771476, 0.811843, 0.859821, 0.880291
elapsed time for k point: 0 seconds.
solve_kpoint (0.5,0.5,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 5 iterations.
tmfreqs:, 11, 0.5, 0.5, 0, 0.707107, 0.373594, 0.444088, 0.444088, 0.7018,
0.781038, 0.823407, 0.859899, 0.859899
elapsed time for k point: 1 seconds.
solve_kpoint (0.4,0.4,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 5 iterations.
tmfreqs:, 12, 0.4, 0.4, 0, 0.565685, 0.341631, 0.45163, 0.456954, 0.725973,
0.766027, 0.79736, 0.87409, 0.885092
elapsed time for k point: 1 seconds.
solve_kpoint (0.3,0.3,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 6 iterations.
tmfreqs:, 13, 0.3, 0.3, 0, 0.424264, 0.271729, 0.472824, 0.483875, 0.735067,
0.757502, 0.782055, 0.902434, 0.922019
elapsed time for k point: 0 seconds.
solve_kpoint (0.2,0.2,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 7 iterations.
tmfreqs:, 14, 0.2, 0.2, 0, 0.282843, 0.186379, 0.503616, 0.519534, 0.699542,
0.715404, 0.844811, 0.933312, 0.959658
elapsed time for k point: 1 seconds.
solve_kpoint (0.1,0.1,0):
Solving for bands 1 to 8...
Finished solving for bands 1 to 8 after 9 iterations.
tmfreqs:, 15, 0.1, 0.1, 0, 0.141421, 0.0944507, 0.536736, 0.55934, 0.665262,
0.673318, 0.895697, 0.961462, 0.996788
elapsed time for k point: 1 seconds.
solve_kpoint (0,0,0):
Solving for bands 2 to 8...
Finished solving for bands 2 to 8 after 14 iterations.
tmfreqs:, 16, 0, 0, 0, 0, 0, 0.55462, 0.584893, 0.647329, 0.647329, 0.916036,
0.975607, 1.02498
elapsed time for k point: 2 seconds.
Band 1 range: 0.0 at #(0 0 0) to 0.373593761541658 at #(0.5 0.5 0)
Band 2 range: 0.369845219009963 at #(0.5 0 0) to 0.554619673821229 at #(0 0 0)
Band 3 range: 0.44408758157381 at #(0.5 0.5 0) to 0.587854966282244 at #(0.5 0
0)
Band 4 range: 0.647329007716348 at #(0 0 0) to 0.743953468761287 at #(0.5 0.3 0)
Band 5 range: 0.647329011025346 at #(0 0 0) to 0.80008895291846 at #(0.5 0.1 0)
Band 6 range: 0.7820547571181 at #(0.3 0.3 0) to 0.916036167003583 at #(0 0 0)
Band 7 range: 0.859091237355604 at #(0.5 0 0) to 0.975607478161245 at #(0 0 0)
Band 8 range: 0.859899019931888 at #(0.5 0.5 0) to 1.02498251525285 at #(0 0 0)
Gap from band 3 (0.587854966282244) to band 4 (0.647329007716348),
9.62998916535034%
total elapsed time for run: 16 seconds.
done.
Some deprecated features have been used. Set the environment
variable GUILE_WARN_DEPRECATED to "detailed" and rerun the
program to get more information. Set it to "no" to suppress
this message.
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