def plot_p(self):
uvb = UpperValenceBand(self.dichalcogenide)
sc = Induced(self.dichalcogenide)
dk = sc.Δk(0)
p = Optical(self.dichalcogenide).p_circular
psc = lambda a, xi: p(xi + uvb.μ, 1, a)
fn_m = lambda xi: psc(-1, xi)
fn_p = lambda xi: psc(1, xi)
xi = numpy.linspace(-0.01, 0, self.opts['n'])
err = numpy.geterr()
numpy.seterr(invalid='ignore')
line = next(self.lines)
self.plot[0].plot(xi,
numpy.vectorize(fn_p)(xi),
line,
color='black',
linewidth=2)
self.plot[1].plot(xi,
numpy.vectorize(fn_m)(xi),
line,
color='black',
linewidth=2)
numpy.seterr(**err)
self.plot[1].set_xlabel(
'$E - \\mu$ $\\left(\\mathregular{eV} \\right)$')
return self
def plot_bands(self):
"""Plot energy bands."""
e = Energy(self.dichalcogenide).e
mu = self.opts['mu_scale'] * UpperValenceBand(self.dichalcogenide).μ
lk = Induced(self.dichalcogenide).λk
k0, dk = self.opts['k0'], self.opts['dk']
p = (-1, 1)
for x in itertools.product(p, p, p):
n = self.opts['n']
k = numpy.linspace(x[1] * (k0 - dk), x[1] * (k0 + dk), n)
if x[0] == -1 and x[1] == x[2]:
fn = lambda k, s=x: mu + lk(e(k - s[1] * k0, *s))
self.plot.plot(k, numpy.vectorize(fn)(k), color='black')
if x[0] == -1:
pass
else:
fn = lambda k, s=x: e(k - s[1] * k0, *s)
self.plot.plot(k, numpy.vectorize(fn)(k), color='black')
self.plot.annotate('BCS Condensate', (0, -1.0),
horizontalalignment='center',
verticalalignment='center')
return self
def plot_chemical_potential(self):
"""Add chemical potential."""
t = self.opts['t']
uvb = UpperValenceBand(self.dichalcogenide)
self.plot.axhline(uvb.μ, linestyle='--', color='black')
self.plot.annotate('$\\mu$', (-1, uvb.μ + t))
return self
def plot_pairs(self):
e = Energy(self.dichalcogenide).e
mu = self.opts['mu_scale'] * UpperValenceBand(self.dichalcogenide).μ
lk = Induced(self.dichalcogenide).λk
k0, dk = self.opts['k0'], self.opts['dk']
k1 = 1.5 * dk
self.plot.plot(k1,
e(k1 - k0, 1, 1, 1),
marker='o',
color='black',
markersize=10)
self.plot.plot(-k1,
mu + lk(e(k1 - k0, -1, 1, 1)),
marker='o',
color='black',
markersize=10)
return self
class Induced(Superconductor):
"""Induced superconductor.
Inherits from :class:`.Superconductor`.
"""
def __init__(self, model):
super().__init__(model)
self._energy = UpperValenceBand(self.model)
@property
def Δc(self):
"""Conduction band coupling constant.
:return: :math:`Δ_c`
:rtype: float
"""
return self.model.system_parameter('Δc')
@property
def Δv(self):
"""Valance band coupling constant.
:return: :math:`Δ_v`
:rtype: float
"""
return self.model.system_parameter('Δv')
@property
def Δk(self):
"""The superconducting parameter :math:`Δ_\\mathbf{k}`
as a function of the energy :math:`E`.
:return: :math:`Δ(E)`
:rtype: func
"""
Δc, Δv = self.Δc, self.Δv
cos = self._energy.trig('cos θ')
return lambda e: (1 / 2) * ((Δc + Δv) + (Δc - Δv) * cos(e))
class Induced(Superconductor):
"""Induced superconductor.
Inherits from :class:`.Superconductor`.
"""
def __init__(self, model):
super().__init__(model)
self._energy = UpperValenceBand(self.model)
@property
def Δc(self):
"""Conduction band coupling constant.
:return: :math:`Δ_c`
:rtype: float
"""
return self.model.system_parameter('Δc')
@property
def Δv(self):
"""Valance band coupling constant.
:return: :math:`Δ_v`
:rtype: float
"""
return self.model.system_parameter('Δv')
@property
def Δk(self):
"""The superconducting parameter :math:`Δ_\\mathbf{k}`
as a function of the energy :math:`E`.
:return: :math:`Δ(E)`
:rtype: func
"""
Δc, Δv = self.Δc, self.Δv
cos = self._energy.trig('cos θ')
return lambda e: (1 / 2) * ((Δc + Δv) + (Δc - Δv) * cos(e))
def plot_p_sc(self):
uvb = UpperValenceBand(self.dichalcogenide)
sc = Induced(self.dichalcogenide)
xi = sc.ξ
dk = sc.Δk(0)
sc_trig = sc.trig('sin^2 β')
p = Optical(self.dichalcogenide).p_circular
psc = lambda a, lk: sc_trig(dk, lk) * p(xi(dk, lk) + uvb.μ, 1, a)
fn_m = lambda lk: psc(-1, lk)
fn_p = lambda lk: psc(1, lk)
lk = numpy.linspace(*sc.λk_bounds(dk), self.opts['n'])
x = lk / dk
err = numpy.geterr()
numpy.seterr(invalid='ignore')
line = next(self.lines)
self.plot[0].plot(x,
numpy.vectorize(fn_p)(x * dk),
line,
color='black',
linewidth=2)
self.plot[1].plot(x,
numpy.vectorize(fn_m)(x * dk),
line,
color='black',
linewidth=2)
numpy.seterr(**err)
self.plot[1].set_xlabel(
'$\\lambda_{\\mathbf{k}} / \\Delta_{\\mathbf{k}}$')
return self
def __init__(self, model, energy=None):
self.model = model
if not energy: self._energy = UpperValenceBand(self.model)
def __init__(self, model):
super().__init__(model)
self._energy = UpperValenceBand(self.model)
def __init__(self, model):
super().__init__(model)
self._energy = UpperValenceBand(self.model)