MoS2 monolayer schematic view of valleys band structure.

MoS2-schematic-band.py

#!/usr/bin/env python3

from enum import Enum, unique
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse

mpl.rcParams["font.sans-serif"] = "monospace"
mpl.rcParams["text.usetex"] = True
mpl.rcParams["text.latex.preamble"] = " ".join([
    r"\usepackage{physics}",
    ])

KWIDTH = 0.7
KX = np.linspace(-KWIDTH, +KWIDTH, 51)

@unique
class Spin(Enum):
    Up = 1
    Down = -1

@unique
class CircularPolarization(Enum):
    Left = 1
    Right = -1

def single_band(ax, a=1.0, x0=0.0, y0=0.0, spin=Spin.Up):
    y = a * (KX ** 2) + y0
    x = KX + x0
    color = "r" if spin == Spin.Up else "b"
    if spin == Spin.Up:
        color = "r"
        text = r"${\ket{\uparrow}}$"
    else:
        color = "b"
        text = r"$\ket{\downarrow}$"

    ax.plot(x, y, color=color, lw=1.5)
    ax.text(x[-1]+0.13, y[-1], text, va="center", ha="center", color=color)
    return (x, y)

def arrow_with_circular_polarization(ax, p1=(0.0, 0.0), p2=(0.0, 1.0), polarization=CircularPolarization.Left):
    mid = ((p2[0] + p1[0])/2.0, (p2[1] + p1[1])/2.0)
    ax.annotate("", p1, p2, zorder=4.0,
                arrowprops=dict(
                    arrowstyle="<->",
                    shrinkA=0.0,
                    shrinkB=0.0,
                    linestyle="--"))

    if polarization == CircularPolarization.Left:
        color = "tab:orange"
        posData = (mid[0] + 0.125, mid[1] + 0.01)
        posText = (mid[0] + 0.125, mid[1] + 0.00)
        polText = r"$\sigma^+$"
    else:
        color = "tab:green"
        posData = (mid[0] - 0.125, mid[1] + 0.01)
        posText = (mid[0] - 0.125, mid[1] + 0.00)
        polText = r"$\sigma^-$"

    ellipse = Ellipse(xy=mid, width=0.25, height=0.1, edgecolor=color, fc="None", lw=1.0)
    ax.add_patch(ellipse)
    ax.annotate("", posData, posText, zorder=5.0,
                va="center", ha="center",
                arrowprops=dict(arrowstyle="->,head_length=0.2",
                                shrinkA=0.0,
                                shrinkB=0.0,
                                color=color,
                                lw=0.7))
    ax.text(mid[0] + 0.25, mid[1]+0.00, polText, color=color, ha="center", va="center")
    pass


if '__main__' == __name__:
    fig, ax = plt.subplots(figsize=(4, 3))

    K0 = 1.0
    gap = 0.4
    # CBM, K+u & K-d
    single_band(ax, a=1.25, x0= K0, y0=gap, spin=Spin.Up)
    single_band(ax, a=1.25, x0=-K0, y0=gap, spin=Spin.Down)

    # CB, K+d & K-u
    single_band(ax, a=1.0, x0= K0, y0=gap+0.015, spin=Spin.Down)
    single_band(ax, a=1.0, x0=-K0, y0=gap+0.015, spin=Spin.Up)

    # VBM, K+u & K-d
    single_band(ax, a=-1.0, x0= K0, y0=0, spin=Spin.Up)
    xkp, ykp = single_band(ax, a=-1.0, x0=-K0, spin=Spin.Down, y0=0)

    # VB, K+d & K-u
    single_band(ax, a=-1.25, x0= K0, y0=-0.05, spin=Spin.Down)
    xkm, ykm = single_band(ax, a=-1.25, x0=-K0, y0=-0.05, spin=Spin.Up)

    # arrow with circular polarization
    arrow_with_circular_polarization(ax, ( K0, 0.0), ( K0, gap), CircularPolarization.Left)
    arrow_with_circular_polarization(ax, (-K0, 0.0), (-K0, gap), CircularPolarization.Right)

    # labeling K+ and K- valley
    ax.text( K0, ykp.min() - 0.1, r"K$^+$", ha="center", va="center", weight="bold")
    ax.text(-K0, ykp.min() - 0.1, r"K$^-$", ha="center", va="center", weight="bold")

    # Fermi level
    ax.axhline(y=0.02, ls="--", lw=0.3, color="k")
    ax.text(-K0-KWIDTH, 0.03, r"E\textsubscript{F}", color="k", ha="center", va="bottom")

    ax.axis('off')
    fig.tight_layout(pad=0.5)
    fig.savefig("schematic_band.png", dpi=400)
    fig.savefig("schematic_band.pdf", dpi=400)
    fig.savefig("schematic_band.svg", dpi=400)