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Commit 2ef5f643 authored by Anton Akhmerov's avatar Anton Akhmerov
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use inline code execution

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.gitlab-ci.yml
+ 1
− 4
View file @ 2ef5f643
......@@ -24,11 +24,8 @@ build and upload the contents:
script:
# Compile lectures
- python code/band_structures.py
- python code/bands_2d.py
- python code/misc.py
- python code/semiconductors.py
- python code/heat_capacity.py
- python execute.py
- mkdocs build
- "rsync -rv site/* solidstate@tnw-tn1.tudelft.net:"
only:
......
code/band_structures.py deleted 100644 → 0
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− 227
View file @ a9ea54e8
import os
import numpy as np
import matplotlib
import mpl_toolkits
matplotlib.use('agg')
from matplotlib import pyplot
import common
from common import draw_classic_axes
pi = np.pi
def fermi_dirac():
fig = pyplot.figure()
ax = fig.add_subplot(1,1,1)
xvals = np.linspace(0, 2, 200)
mu = .75
beta = 20
ax.plot(xvals, xvals < mu, ls='dashed', label='$T=0$')
ax.plot(xvals, 1/(np.exp(beta * (xvals-mu)) + 1),
ls='solid', label='$T>0$')
ax.set_xlabel(r'$\varepsilon$')
ax.set_ylabel(r'$f(\varepsilon, T)$')
ax.set_yticks([0, 1])
ax.set_yticklabels(['$0$', '$1$'])
ax.set_xticks([mu])
ax.set_xticklabels([r'$\mu$'])
ax.set_ylim(-.1, 1.1)
ax.legend()
draw_classic_axes(ax)
pyplot.tight_layout()
fig.savefig('fermi_dirac.svg')
def phonons_1d():
k = np.linspace(-2*pi, 6*pi, 500)
fig, ax = pyplot.subplots()
pyplot.plot(k, np.abs(np.sin(k/2)))
ax.set_ylim(bottom=0, top=1.2)
ax.set_xlabel('$ka$')
ax.set_ylabel(r'$\omega$')
pyplot.xticks(list(2*pi*np.arange(-1, 4)) + [-pi, pi],
[r'$-2\pi$', '$0$', r'$2\pi$', r'$4\pi$', r'$6\pi$',
r'$-\pi$', r'$\pi$'])
pyplot.yticks([1], [r'$2\sqrt{\frac{\kappa}{m}}$'])
pyplot.vlines([-pi, pi], 0, 1.1, linestyles='dashed')
pyplot.hlines([1], .1*pi, 1.3*pi, linestyles='dashed')
draw_classic_axes(ax)
ax.annotate(s='', xy=(-pi, -.15), xytext=(pi, -.15),
arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
ax.text(0, -.25, '1st Brillouin zone', ha='center')
ax.set_ylim(bottom=-.7)
pyplot.savefig('phonons3.svg')
def aliasing():
x = np.linspace(-.2, 2.8, 500)
fig, ax = pyplot.subplots()
ax.plot(x, np.cos(pi*(x - .3)), label=r'$k=\pi/a$')
ax.plot(x, np.cos(3*pi*(x - .3)), label=r'$k=3\pi/a$')
ax.plot(x, np.cos(5*pi*(x - .3)), label=r'$k=5\pi/a$')
sites = np.arange(3) + .3
ax.scatter(sites, np.cos(pi*(sites - .3)), c='k', s=64, zorder=5)
ax.set_xlabel('$x$')
ax.set_ylabel('$u_n$')
ax.set_xlim((-.1, 3.2))
ax.set_ylim((-1.3, 1.3))
ax.legend(loc='lower right')
draw_classic_axes(ax)
ax.annotate(s='', xy=(.3, -1.1), xytext=(1.3, -1.1),
arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
ax.text(.3 + .5, -1.25, '$a$', ha='center')
pyplot.savefig('phonons4.svg')
def tight_binding_1d():
pyplot.figure()
k = np.linspace(-pi, pi, 300)
pyplot.plot(k, -np.cos(k))
pyplot.xlabel('$ka$'); pyplot.ylabel('$E$')
pyplot.xticks([-pi, 0, pi], [r'$-\pi$', 0, r'$\pi$'])
pyplot.yticks([-1, 0, 1], ['$E_0+2t$', '$E_0$', '$E_0-2t$'])
pyplot.savefig('tight_binding_1d.svg')
def meff_1d_tb():
pyplot.figure(figsize=(8, 5))
k = np.linspace(-pi, pi, 300)
meff = 1/np.cos(k)
color = list(matplotlib.rcParams['axes.prop_cycle'])[0]['color']
pyplot.plot(k[meff > 0], meff[meff > 0], c=color)
pyplot.plot(k[meff < 0], meff[meff < 0], c=color)
pyplot.ylim(-5, 5)
pyplot.xlabel('$ka$'); pyplot.ylabel('$m_{eff}$')
pyplot.xticks([-pi, 0, pi], [r'$-\pi$', 0, r'$\pi$']);
pyplot.savefig('meff_1d_tb.svg')
def dispersion_2m(k, kappa=1, M=1.4, m=1, acoustic=True):
Mm = M*m
m_harm = (M + m) / Mm
root = kappa * np.sqrt(m_harm**2 - 4*np.sin(k/2)**2 / Mm)
if acoustic:
root *= -1
return np.sqrt(kappa*m_harm + root)
def phonons_1d_2masses():
# TODO: Add panels with eigenvectors
k = np.linspace(-2*pi, 6*pi, 300)
fig, ax = pyplot.subplots()
ax.plot(k, dispersion_2m(k, acoustic=False), label='optical')
ax.plot(k, dispersion_2m(k), label='acoustic')
ax.set_xlabel('$ka$')
ax.set_ylabel(r'$\omega$')
pyplot.xticks([-pi, 0, pi], [r'$-\pi$', '$0$', r'$\pi$'])
pyplot.yticks([], [])
pyplot.vlines([-pi, pi], 0, 2.2, linestyles='dashed')
pyplot.legend()
pyplot.xlim(-1.75*pi, 3.5*pi)
pyplot.ylim(bottom=0)
draw_classic_axes(ax, xlabeloffset=.2)
pyplot.savefig('phonons6.svg')
def DOS_2masses():
matplotlib.rcParams['font.size'] = 24
k = np.linspace(-.25*pi, 1.5*pi, 300)
k_dos = np.linspace(0, pi, 20)
fig, (ax, ax2) = pyplot.subplots(ncols=2, sharey=True, figsize=(10, 5))
ax.plot(k, dispersion_2m(k, acoustic=False), label='optical')
ax.plot(k, dispersion_2m(k), label='acoustic')
ax.vlines(k_dos, 0, dispersion_2m(k_dos, acoustic=False),
colors=(0.5, 0.5, 0.5, 0.5))
ax.hlines(
np.hstack((dispersion_2m(k_dos, acoustic=False), dispersion_2m(k_dos))),
np.hstack((k_dos, k_dos)),
1.8*pi,
colors=(0.5, 0.5, 0.5, 0.5)
)
ax.set_xlabel('$ka$')
ax.set_ylabel(r'$\omega$')
ax.set_xticks([0, pi])
ax.set_xticklabels(['$0$', r'$\pi$'])
ax.set_yticks([], [])
ax.set_xlim(-pi/4, 2*pi)
ax.set_ylim((0, dispersion_2m(0, acoustic=False) + .2))
draw_classic_axes(ax, xlabeloffset=.2)
k = np.linspace(0, pi, 1000)
omegas = np.hstack((
dispersion_2m(k, acoustic=False), dispersion_2m(k)
))
ax2.hist(omegas, orientation='horizontal', bins=75)
ax2.set_xlabel(r'$g(\omega)$')
ax2.set_ylabel(r'$\omega$')
# Truncate the singularity in the DOS
max_x = ax2.get_xlim()[1]
ax2.set_xlim((0, max_x/2))
draw_classic_axes(ax2, xlabeloffset=.1)
matplotlib.rcParams['font.size'] = 16
pyplot.savefig('phonons8.svg')
def consistency_1_2_masses():
k = np.linspace(0, 2*pi, 300)
k_dos = np.linspace(0, pi, 20)
fig, ax = pyplot.subplots()
ax.plot(k, dispersion_2m(k, acoustic=False), label='optical')
ax.plot(k, dispersion_2m(k), label='acoustic')
omega_max = dispersion_2m(0, acoustic=False)
ax.plot(k, omega_max * np.sin(k/4), label='equal masses')
ax.set_xlabel('$ka$')
ax.set_ylabel(r'$\omega$')
ax.set_xticks([0, pi, 2*pi])
ax.set_xticklabels(['$0$', r'$\pi/2a$', r'$\pi/a$'])
ax.set_yticks([], [])
ax.set_xlim(-pi/8, 2*pi+.4)
ax.set_ylim((0, dispersion_2m(0, acoustic=False) + .2))
ax.legend(loc='lower right')
pyplot.vlines([pi, 2*pi], 0, 2.2, linestyles='dashed')
draw_classic_axes(ax, xlabeloffset=.2)
pyplot.savefig('phonons7.svg')
def DOS_finite_phonon_chain(n, output_name):
rhs = 2 * np.eye(n) - np.eye(n, k=1) - np.eye(n, k=-1)
rhs[0, 0] -= 1
rhs[-1, -1] -= 1
pyplot.figure()
pyplot.hist(np.sqrt(np.abs(np.linalg.eigvalsh(rhs))), bins=30)
pyplot.xlabel("$\omega$")
pyplot.ylabel("Number of levels")
pyplot.savefig(output_name)
def DOS_finite_electron_chain(n, output_name):
rhs = - np.eye(n, k=1) - np.eye(n, k=-1)
pyplot.figure()
pyplot.hist(np.linalg.eigvalsh(rhs), bins=30)
pyplot.xlabel("$E$")
pyplot.ylabel("Number of levels")
pyplot.savefig(output_name)
def main():
os.chdir('docs/figures')
fermi_dirac()
phonons_1d()
phonons_1d_2masses()
consistency_1_2_masses()
DOS_2masses()
aliasing()
meff_1d_tb()
tight_binding_1d()
DOS_finite_phonon_chain(3, '3_phonons.svg')
DOS_finite_phonon_chain(300, '300_phonons.svg')
DOS_finite_electron_chain(3, '3_electrons.svg')
DOS_finite_electron_chain(300, '300_electrons.svg')
if __name__ == "__main__":
main()
code/common.py
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import os
import numpy as np
from IPython import get_ipython
import matplotlib
import mpl_toolkits
matplotlib.rcParams['text.usetex'] = True
matplotlib.rcParams['figure.figsize'] = (8, 5)
matplotlib.rcParams['font.size'] = 16
matplotlib.rcParams['savefig.transparent'] = True
def configure_plotting():
# Configure matplotlib
ip = get_ipython()
ip.config['InlineBackend']['figure_format'] = 'svg'
# Fix for https://stackoverflow.com/a/36021869/2217463
ip.config['InlineBackend']['rc'] = {}
ip.enable_matplotlib(gui='inline')
matplotlib.rcParams['text.usetex'] = False
matplotlib.rcParams['figure.figsize'] = (10, 7)
matplotlib.rcParams['font.size'] = 16
def draw_classic_axes(ax, x=0, y=0, xlabeloffset=.1, ylabeloffset=.07):
ax.set_axis_off()
x0, x1 = ax.get_xlim()
y0, y1 = ax.get_ylim()
ax.annotate(ax.get_xlabel(), xytext=(x1, y), xy=(x0, y),
arrowprops=dict(arrowstyle="<-"), va='center')
ax.annotate(ax.get_ylabel(), xytext=(x, y1), xy=(x, y0),
arrowprops=dict(arrowstyle="<-"), ha='center')
ax.annotate(
ax.get_xlabel(), xytext=(x1, y), xy=(x0, y),
arrowprops=dict(arrowstyle="<-"), va='center'
)
ax.annotate(
ax.get_ylabel(), xytext=(x, y1), xy=(x, y0),
arrowprops=dict(arrowstyle="<-"), ha='center'
)
for pos, label in zip(ax.get_xticks(), ax.get_xticklabels()):
ax.text(pos, y - xlabeloffset, label.get_text(),
ha='center', va='bottom')
......
code/heat_capacity.py deleted 100644 → 0
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import os
import matplotlib
matplotlib.use('agg')
from matplotlib import pyplot
import numpy as np
from scipy.optimize import curve_fit
from scipy.integrate import quad
import common
from common import draw_classic_axes
# Data from Einstein's paper
T = [222.4, 262.4, 283.7, 306.4, 331.3, 358.5, 413.0, 479.2, 520.0, 879.7, 1079.7, 1258.0],
c = [0.384, 0.578, 0.683, 0.798, 0.928, 1.069, 1.343, 1.656, 1.833, 2.671, 2.720, 2.781]
def plot_n_e():
fig, (ax, ax2) = pyplot.subplots(ncols=2, figsize=(10, 5))
omega = np.linspace(0.1, 2)
ax.plot(omega, 1/(np.exp(omega) - 1))
ax.set_ylim(0, top=3)
ax.set_xlim(left=0)
ax.set_xlabel(r'$\hbar \omega$')
ax.set_xticks([0, 1])
ax.set_xticklabels(['$0$', '$k_B T$'])
ax.set_ylabel('$n$')
ax.set_yticks([1, 2])
ax.set_yticklabels(['$1$', '$2$'])
draw_classic_axes(ax, xlabeloffset=.2)
T = np.linspace(0.01, 2)
ax2.plot(T, 1/2 + 1/(np.exp(1/T)-1))
ax2.set_ylim(bottom=0)
ax2.set_xlabel('$k_B T$')
ax2.set_xticks([0, 1])
ax2.set_xticklabels(['$0$', r'$\hbar \omega$'])
ax2.set_ylabel(r"$\bar\varepsilon$")
ax2.set_yticks([1/2])
ax2.set_yticklabels([r'$\hbar\omega/2$'])
draw_classic_axes(ax2, xlabeloffset=.15)
fig.savefig('bose_einstein.svg')
def c_einstein(T, T_E=1):
x = T_E / T
return 3 * x**2 * np.exp(x) / (np.exp(x) - 1)**2
def integrand(y):
return y**4 * np.exp(y) / (np.exp(y) - 1)**2
@np.vectorize
def c_debye(T, T_D=1):
x = T / T_D
return 9 * x**3 * quad(integrand, 0, 1/x)[0]
def plot_einstein():
T = np.linspace(0.01, 1.5, 500)
fig, ax = pyplot.subplots()
ax.plot(T, c_einstein(T)/3)
ax.fill_between(T, c_einstein(T)/3, 1, alpha=0.5)
ax.set_ylim(bottom=0, top=1.2)
ax.set_xlabel('$T$')
ax.set_ylabel(r'$\omega$')
ax.set_xticks([1])
ax.set_xticklabels([r'$\hbar \omega/k_B$'])
ax.set_yticks([1])
ax.set_yticklabels(['$k_B$'])
pyplot.hlines([1], 0, 1.5, linestyles='dashed')
draw_classic_axes(ax)
pyplot.savefig('zeropoint.svg')
def plot_debye():
T = np.linspace(0.01, 1.5, 500)
fig, ax = pyplot.subplots()
ax.plot(T, c_einstein(T), label="Einstein model")
ax.plot(T, c_debye(T), label="Debye model")
ax.set_ylim(bottom=0, top=3.4)
ax.set_xlabel('$T$')
ax.set_ylabel(r'$\omega$')
ax.set_xticks([1])
ax.set_xticklabels([r'$\Theta_D$'])
ax.set_yticks([3])
ax.set_yticklabels(['$3Nk_B$'])
ax.legend(loc='lower right')
pyplot.hlines([3], 0, 1.5, linestyles='dashed')
draw_classic_axes(ax, xlabeloffset=0.3)
pyplot.savefig('debye.svg')
def main():
os.chdir('docs/figures')
plot_n_e()
plot_einstein()
plot_debye()
if __name__ == "__main__":
main()
code/misc.py deleted 100644 → 0
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import os
import matplotlib
matplotlib.use('agg')
from matplotlib import pyplot
import numpy as np
from scipy.optimize import curve_fit
from scipy.integrate import quad
import common
from common import draw_classic_axes
def plot_curie():
B = np.linspace(-2, 2, 1000)
fig, ax = pyplot.subplots()
sqrt_plus = lambda x: np.sqrt(x * (x >= 0))
ax.plot(B, np.tanh(B * 3), label="low $T$")
ax.plot(B, np.tanh(B), label="high $T$")
ax.legend()
ax.set_ylabel("$M$")
ax.set_xlabel("$B$")
draw_classic_axes(ax, xlabeloffset=.2)
fig.savefig('curie.svg')
def plot_free_electron_DOS():
E = np.linspace(0, 2, 500)
fig, ax = pyplot.subplots()
ax.plot(E, np.sqrt(E))
ax.set_ylabel(r"$g(\varepsilon)$")
ax.set_xlabel(r"$\varepsilon$")
draw_classic_axes(ax, xlabeloffset=.2)
fig.savefig('sqrt.svg')
def plot_finite_T_FEM():
E = np.linspace(0, 2, 500)
fig, ax = pyplot.subplots()
ax.plot(E, np.sqrt(E), linestyle='dashed')
ax.text(1.7, 1.4, r'$g(\varepsilon)\propto \sqrt{\varepsilon}$', ha='center')
ax.fill_between(E, np.sqrt(E) * (E < 1), alpha=.3)
n = np.sqrt(E) / (1 + np.exp(20*(E-1)))
ax.plot(E, n)
ax.fill_between(E, n, alpha=.5)
w = .17
ax.annotate(s='', xy=(1, 1), xytext=(1-w, 1),
arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
ax.text(1-w/2, 1.1, r'$\sim k_BT$', ha='center')
ax.plot([1-w, 1+w], [1, 0], c='k', linestyle='dashed')
ax.annotate(s='', xy=(1, 0), xytext=(1, 1),
arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
ax.text(1.2, .7, r'$g(\varepsilon_F)$', ha='center')
ax.set_xticks([1])
ax.set_xticklabels([r'$\varepsilon_F$'])
ax.set_ylabel(r"$g(\varepsilon)$")
ax.set_xlabel(r"$\varepsilon$")
draw_classic_axes(ax, xlabeloffset=.2)
fig.savefig('FD_DOS.svg')
def main():
os.chdir('docs/figures')
plot_curie()
plot_free_electron_DOS()
plot_finite_T_FEM()
if __name__ == "__main__":
main()
code/semiconductors.py deleted 100644 → 0
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import os
import matplotlib
matplotlib.use('agg')
from matplotlib import pyplot
import numpy as np
from scipy.optimize import curve_fit
from scipy.integrate import quad
import common
from common import draw_classic_axes
E_V, E_C, E_F = -1.2, 1.8, .4
E_D, E_A = E_C - .7, E_V + .5
m_h, m_e = 1, .5
sqrt_plus = lambda x: np.sqrt(x * (x >= 0))
def plot_dos():
E = np.linspace(-3, 3, 1000)
fig, ax = pyplot.subplots()
n_F = 1/(np.exp(2*(E - E_F)) + 1)
g_e = m_e * sqrt_plus(E - E_C)
g_h = m_h * sqrt_plus(E_V - E)
ax.plot(E, g_h, label="$g_e$")
ax.plot(E, g_e, label="$g_h$")
ax.plot(E, 10 * g_h * (1-n_F), label="$n_h$")
ax.plot(E, 10 * g_e * n_F, label="$n_e$")
ax.plot(E, n_F, label="$n_F$", linestyle='dashed')
ax.set_ylim(top=1.5)
ax.set_xlabel('$E$')
ax.set_ylabel('$g$')
ax.set_xticks([E_V, E_C, E_F])
ax.set_xticklabels(['$E_V$', '$E_C$', '$E_F$'])
ax.legend()
draw_classic_axes(ax, xlabeloffset=.2)
fig.savefig('intrinsic_DOS.svg')
def plot_doping():
E = np.linspace(-3, 3, 1000)
fig, ax = pyplot.subplots()
n_F = 1/(np.exp(2*(E - E_F)) + 1)
g_e = m_e * sqrt_plus(E - E_C)
g_h = m_h * sqrt_plus(E_V - E)
ax.plot(E, g_h, label="$g_e$")
ax.plot(E, g_e, label="$g_h$")
sigma = 0.01
g_D = np.exp(-(E_D - E)**2 / sigma**2)
g_A = .7 * np.exp(-(E_A - E)**2 / sigma**2)
ax.plot(E, g_D, label='$g_D$')
ax.plot(E, g_A, label='$g_A$')
ax.legend()
ax.set_xticks([E_V, E_C, E_A, E_D])
ax.set_xticklabels(['$E_V$', '$E_C$', '$E_A$', '$E_D$'])
draw_classic_axes(ax, xlabeloffset=.2)
fig.savefig('doping.svg')
def main():
os.chdir('docs/figures')
plot_dos()
plot_doping()
if __name__ == "__main__":
main()
docs/mathjaxhelper.js deleted 100644 → 0
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MathJax.Hub.Config({
config: ["MMLorHTML.js"],
jax: ["input/TeX", "output/HTML-CSS", "output/NativeMML"],
extensions: ["MathMenu.js", "MathZoom.js"]
});
execute.py 0 → 100644
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from pathlib import Path
import shutil
import nbconvert
import notedown
from traitlets.config import Config
reader = notedown.MarkdownReader()
src = Path('src')
target = Path('docs')
shutil.rmtree(target, ignore_errors=True)
target.mkdir(exist_ok=True)
shutil.copytree(src / 'figures', target / 'figures')
exporter = nbconvert.MarkdownExporter(
config=Config(dict(
MarkdownExporter=dict(
preprocessors=[
nbconvert.preprocessors.ExecutePreprocessor,
nbconvert.preprocessors.ExtractOutputPreprocessor,
],
exclude_input=True
)
))
)
writer = nbconvert.writers.FilesWriter(build_directory=str(target))
for source_file in src.glob('*.md'):
fname = source_file.name[:-len('.md')]
notebook = reader.reads(source_file.read_text())
output, resources = exporter.from_notebook_node(
notebook,
resources={
'unique_key': fname,
'output_files_dir': 'figures',
'metadata': {'path': str(Path('.') / 'code')}
}
)
writer.write(output, resources, fname)
mkdocs.yml
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......@@ -13,7 +13,8 @@ pages:
- Crystal structure and diffraction: 'lecture_5.md'
- Tight binding and nearly free electrons: 'lecture_6.md'
- Semiconductors: 'lecture_7.md'
- Magnetism: 'lecture_8.md'
- Attic:
- Magnetism: 'lecture_8.md'
theme:
name: material
......@@ -22,7 +23,6 @@ theme:
primary: 'white'
accent: 'indigo'
markdown_extensions:
- mdx_math:
enable_dollar_delimiter: True
......@@ -33,6 +33,5 @@ markdown_extensions:
extra_javascript:
- 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/MathJax.js?config=TeX-AMS_HTML'
- 'mathjaxhelper.js'
copyright: "Copyright © 2017-2018 Delft University of Technology, CC-BY-SA-NC 4.0."
docs/figures/DOS.svg → src/figures/DOS.svg
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docs/figures/DOS_periodic.svg → src/figures/DOS_periodic.svg
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docs/figures/RKKY.svg → src/figures/RKKY.svg
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docs/figures/adsorption.svg → src/figures/adsorption.svg
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docs/figures/bonding.svg → src/figures/bonding.svg
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