From 34101aa48cf3003984cd803b84b0648ad2766240 Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Tue, 24 Apr 2018 10:33:46 +0200
Subject: [PATCH] migrade 2 mass dos to code
---
code/band_structures.py | 102 +++++----
code/common.py | 26 +++
docs/figures/phonons8.svg | 441 --------------------------------------
3 files changed, 92 insertions(+), 477 deletions(-)
create mode 100644 code/common.py
delete mode 100644 docs/figures/phonons8.svg
diff --git a/code/band_structures.py b/code/band_structures.py
index 54f9ec8e..47e0c489 100644
--- a/code/band_structures.py
+++ b/code/band_structures.py
@@ -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')
diff --git a/code/common.py b/code/common.py
new file mode 100644
index 00000000..dc0e58de
--- /dev/null
+++ b/code/common.py
@@ -0,0 +1,26 @@
+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')
+
diff --git a/docs/figures/phonons8.svg b/docs/figures/phonons8.svg
deleted file mode 100644
index 663c74c4..00000000
--- a/docs/figures/phonons8.svg
+++ /dev/null
@@ -1,441 +0,0 @@
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