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Commit 34101aa4 authored by Anton Akhmerov's avatar Anton Akhmerov
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migrade 2 mass dos to code

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code/band_structures.py
+ 66
− 36
View file @ 34101aa4
......@@ -6,26 +6,11 @@ import mpl_toolkits
matplotlib.use('agg')
from matplotlib import pyplot
matplotlib.rcParams['text.usetex'] = True
matplotlib.rcParams['figure.figsize'] = (8, 5)
matplotlib.rcParams['font.size'] = 16
matplotlib.rcParams['savefig.transparent'] = True
import common
from common import draw_classic_axes
pi = np.pi
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')
for pos, label in zip(ax.get_xticks(), ax.get_xticklabels()):
ax.text(pos, y - xlabeloffset, label.get_text(),
ha='center', va='bottom')
for pos, label in zip(ax.get_yticks(), ax.get_yticklabels()):
ax.text(x - ylabeloffset, pos, label.get_text(),
ha='right', va='center')
def fermi_dirac():
fig = pyplot.figure()
......@@ -47,13 +32,14 @@ def fermi_dirac():
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'$\omega$')
......@@ -101,23 +87,66 @@ def dispersion_2m(k, kappa=1, M=1.4, m=1, acoustic=True):
if acoustic:
root *= -1
return np.sqrt(kappa*m_harm + root)
def phonons_1d_2masses():
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')
# 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 DOS_finite_phonon_chain(n, output_name):
rhs = 2 * np.eye(n) - np.eye(n, k=1) - np.eye(n, k=-1)
......@@ -144,6 +173,7 @@ def main():
fermi_dirac()
phonons_1d()
phonons_1d_2masses()
DOS_2masses()
meff_1d_tb()
tight_binding_1d()
DOS_finite_phonon_chain(3, '3_phonons.svg')
......
code/common.py 0 → 100644
+ 26
− 0
View file @ 34101aa4
import os
import numpy as np
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 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')
for pos, label in zip(ax.get_xticks(), ax.get_xticklabels()):
ax.text(pos, y - xlabeloffset, label.get_text(),
ha='center', va='bottom')
for pos, label in zip(ax.get_yticks(), ax.get_yticklabels()):
ax.text(x - ylabeloffset, pos, label.get_text(),
ha='right', va='center')
docs/figures/phonons8.svg deleted 100644 → 0
+ 0
− 441
View file @ 9eed2f75
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