def plotHalfBands(tmd, nOrb, Ny, SAVE):
abs_t0, e1, e2, t0, t1, t2,\
t11, t12, t22, E0, E1, E2, E3, E4, E5, E6\
= setParams(tmd)
nks = 512
ks = np.linspace(-np.pi, np.pi, nks)
ksF = np.concatenate( ( np.linspace(0, - np.pi / 2, int(nks / 4) ) ,\
np.linspace(-np.pi / 2 , np.pi / 2, int(nks / 2) ),\
np.linspace(np.pi / 2, 0, int(nks / 4) )) )
ksAF = np.linspace(-np.pi / 2, np.pi / 2, nks)
bandEnF = np.zeros((nks, Ny * nOrb))
bandEnAF = np.zeros((nks, 2 * Ny * nOrb))
for en, k in enumerate(ks):
bandEnF[en,:] = la.eigvalsh(\
HribbonKSpace(k, nOrb, Ny, e1, e2, t0, t1, t2, t11, t12, t22)\
) * abs_t0
for en, k in enumerate(ksAF):
bandEnAF[en,:] = la.eigvalsh(\
HribbonKSpace2sublat(k, nOrb, Ny, E0, E1, E2, E3, E4)\
) * abs_t0
fig = plt.figure(1, figsize=(8, 6))
ax = fig.add_subplot(1, 1, 1)
ax.plot(ksF, bandEnF, c = "darkblue", linestyle = '--', label =\
'Normal unit cell - ' + r'$\frac{1}{2}$' + 'FBZ')
ax.plot(ksAF, bandEnAF, c = "darkred", linestyle = '-', linewidth = 0.58, label =\
'Doubled unit cell - ' + 'FBZ')
ax.set_xlabel(r'$k$')
ax.set_ylabel(r'$\varepsilon_k \, [eV]$')
ax.set_xticks([-np.pi / 2, -np.pi / 3, 0, np.pi / 3, np.pi / 2])
ax.set_xticklabels(
[r"$-\pi/2$", r"$-\pi/3$", r"$0$", r"$\pi/3$", r"$\pi/2$"])
ax.legend(bbox_to_anchor=(1, 1))
if SAVE == True:
plt.savefig("../plots/lib_test/" + "free-bands-doubled-unit-cell.png",
dpi=300,
bbox_inches='tight')
plt.figure(2)
plt.plot(np.sort(bandEnF.flatten()), np.linspace(0, 2, num=nks * Ny * nOrb),\
c = 'darkblue', marker = 'o', markersize = 0.1, markeredgewidth = 6,\
linewidth = 0., label = 'Normal unit cell', linestyle = '--')
plt.plot(np.sort(bandEnAF.flatten()), np.linspace(0, 2, num=2 * nks * Ny * nOrb ),\
c = 'darkred', marker = '^', markersize = 0.01, markeredgewidth = 2,\
linewidth = 0., label = 'Double unit cell', linestyle = '--')
plt.plot([-0.7, 3.6], [2 / 3, 2 / 3],
c='seagreen',
linewidth=1,
label=r'Charge neutrality')
plt.xlim(-0.7, 3.6)
plt.xlabel(r'$\varepsilon_F [eV]$')
plt.ylabel(r'$\left\langle n \right\rangle$')
plt.legend(bbox_to_anchor=(1, 1))
if SAVE == True:
plt.savefig("../plots/lib_test/" + "filling-doubled-unit-cell.png",
dpi=300,
bbox_inches='tight')
def plot_matToDiagonalize(nOrb, Ny, k, SAVE):
tmd = 'MoS2'
abs_t0, e1, e2, t0, t1, t2,\
t11, t12, t22, E0, E1, E2, E3, E4, E5, E6\
= setParams(tmd)
mat = HribbonKSpace2sublat(k, nOrb, Ny, E0, E1, E2, E3, E4)
plt.figure(1, figsize=(9, 9))
plt.imshow(np.absolute(mat), interpolation='nearest')
plt.title(r'$\mathbf{H}(k)$')
plt.xlabel(r'$(\alpha, n, o)$')
plt.ylabel(r'$(\beta, n\prime, o\prime)$')
if SAVE == True:
plt.savefig("../plots/lib_test/" +
"matrix-to-diagonalize-double-unit-cell.png",
dpi=300)
def plotBands(nOrb, Ny, SAVE):
# Number of k-points taken when computing the band structure
nks = 1024
ks = np.linspace(-np.pi, np.pi, nks)
bandEn = np.zeros((nks, Ny * nOrb))
fig = plt.figure(figsize=(9, 8))
fig.subplots_adjust(hspace=0.05, wspace=0.02)
nCols = 2
tmds = ['MoS2', 'WS2', 'MoSe2', 'WSe2', 'MoTe2', 'WTe2']
tmdLatex = [
r'$MoS_2$', r'$WS_2$', r'$MoSe_2$', r'$WSe_2$', r'$MoTe_2$', r'$WTe_2$'
]
for idx, tmd in enumerate(tmds):
abs_t0, e1, e2, t0, t1, t2, t11, t12, t22, \
E0, E1, E2, E3, E4, E5, E6 = setParams(tmd)
for en, k in enumerate(ks):
bandEn[en, :] = la.eigvalsh(
HribbonKSpace(k, nOrb, Ny, e1, e2, t0, t1, t2, t11, t12,
t22)) * abs_t0
ax = fig.add_subplot(len(tmds) / nCols, nCols, idx + 1)
ax.plot(ks, bandEn, c = 'Darkblue',\
label= tmdLatex[idx], linewidth = 0.3, markersize = 0.05, marker = 'o',\
markeredgewidth = 0.5)
lgd = ax.legend(fontsize=16, loc=1)
if (idx + 1) > len(tmds) - nCols:
ax.set_xlabel(r'$k \, a$', fontsize=20)
if (idx + nCols) % nCols == 0:
ax.set_ylabel(r'$\varepsilon_{k} [eV]$',\
fontsize = 20, labelpad = 10)
else:
ax.set_yticklabels([])
if idx > 3:
ax.set_xticks([-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi])
ax.set_xticklabels(
[r"$-\pi$", r"$-\pi/2$", r"$0$", r"$\pi/2$", r'$\pi$'])
else:
ax.set_xticklabels([])
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(12)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(12)
ax.set_ylim(-1.2, 5.5)
if SAVE == True:
plt.savefig("../plots/lib_test/" + "bandStructures.png", dpi=600)
def plotFreeBands(tmd, nOrb, Ny, SAVE):
abs_t0, e1, e2, t0, t1, t2,\
t11, t12, t22, E0, E1, E2, E3, E4, E5, E6\
= setParams(tmd)
nks = 512
ksAF = np.linspace(-np.pi / 2, np.pi / 2, nks)
bandEnAF = np.zeros((nks, 2 * Ny * nOrb))
for en, k in enumerate(ksAF):
bandEnAF[en,:] = la.eigvalsh(\
HribbonKSpace2sublat(k, nOrb, Ny, E0, E1, E2, E3, E4)\
) * abs_t0
fig = plt.figure(1, figsize=(7, 6))
ax = fig.add_subplot(1, 1, 1)
ax.plot(ksAF, bandEnAF, c="darkblue", linestyle='-', linewidth=1)
# ax.axvline(np.pi / 4, linewidth = 0.8)
# ax.axhline(0.95, linewidth = 0.8)
# ax.plot(ksAF, bandEnAF[:,:2*Ny-2], c = "darkblue", linestyle = '-', linewidth = 0.58, label =\
# 'Doubled unit cell - ' + 'FBZ', alpha = 0.1)
# ax.plot(ksAF, bandEnAF[:,2*Ny-2:2*Ny+1], c = "darkblue", linestyle = '-', linewidth = 0.58, label =\
# 'Doubled unit cell - ' + 'FBZ')
# ax.plot(ksAF, bandEnAF[:,2*Ny+1:2*Ny+25], c = "darkblue", linestyle = '-', linewidth = 0.58, label =\
# 'Doubled unit cell - ' + 'FBZ')
# ax.plot(ksAF, bandEnAF[:,2*Ny+25:6*Ny], c = "darkblue", linestyle = '-', linewidth = 0.58, label =\
# 'Doubled unit cell - ' + 'FBZ', alpha = 0.1)
ax.set_xlabel(r'$k \, a$', fontsize=20)
ax.set_ylabel(r'$\varepsilon_{k, \sigma} \,\, [eV]$',\
fontsize = 20, labelpad = 10)
ax.set_xticks([-np.pi / 2, - np.pi / 4, 0,\
np.pi / 4, np.pi / 2])
ax.set_xticklabels([r"$-\pi/2$", r"$-\pi/4$",\
r"$0$" , r"$\pi/4$", r"$\pi/2$"], fontsize = 12)
fig.tight_layout()
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(12)
if SAVE == True:
plt.savefig("../plots/lib_test/" + "free-bands-halved.png",
dpi=600,
bbox_inches='tight')
def plotFillings(nOrb, Nx, Ny, SAVE):
'''
Plots the filling as a function of the Fermi energy for TMD nanoribbons with different
transition metal and chalcogens.
'''
fig = plt.figure(figsize=(16, 8))
fig.subplots_adjust(hspace=0.1, wspace=0.15)
nCols = 3
tmds = ['MoS2', 'WS2', 'MoSe2', 'WSe2', 'MoTe2', 'WTe2']
tmdLatex = [
r'$MoS_2$', r'$WS_2$', r'$MoSe_2$', r'$WSe_2$', r'$MoTe_2$', r'$WTe_2$'
]
for idx, tmd in enumerate(tmds):
abs_t0, e1, e2, t0, t1, t2, t11, t12, t22, \
E0, E1, E2, E3, E4, E5, E6 = setParams(tmd)
ens = la.eigvalsh(
HribbonRealSpace(nOrb, Nx, Ny, E0, E1, E2, E3, E4, E5, E6))
ax = fig.add_subplot(len(tmds) / nCols, nCols, idx + 1)
# The factor of 2 below is due to spin degeneracy of the bands
ax.plot(ens * abs_t0, np.arange(ens.size) / ens.size * 2,\
label= str(Nx) + r'$\times$' + str(Ny) + ' ' +\
tmdLatex[idx], linewidth = 0.7, markersize = 1,\
markeredgewidth = 6, color = 'r')
if (idx + 1) > len(tmds) - nCols:
ax.set_xlabel(r'$\varepsilon_F [eV]$')
if (idx + nCols) % nCols == 0:
ax.set_ylabel(r'$\left\langle n \right\rangle$')
else:
ax.set_yticklabels([])
ax.set_xlim(-1, 4)
ax.plot([-1, 3.5], [2 / 3, 2 / 3], linewidth = 1,\
c = 'green', linestyle = '--', label = 'Charge neutrality')
lgd = ax.legend(fontsize='large')
if SAVE == True:
plt.savefig("../plots/lib_test/" + "filling.png", dpi=200)
nOrb = 3 # Number of k-points Nk = 512 # Dimensions of the ribbon Ny = int(sys.argv[1]) # Model parameters t = 1 U = int(sys.argv[2]) # Choose TMD tmd = 'MoS2' abs_t0, e1, e2, t0, t1, t2, t11, t12, t22, \ E0, E1, E2, E3, E4, E5, E6 = setParams(tmd) # For a hole-doped system (0 means no holes) nHole = 0 # Self-explanatory anneal_or_not = False osc = False # Inverse temperature and annealing parameters invTemp = 'infty' betaStart = 0.1 betaSpeed = 1.25 betaThreshold = 20 # Solver parameters