1###############################################################################
2# This file assumes "effective atomic units". Let us recall what this means.
3# We start with the usual atomic units:
4#
5# hbar = e^2 = m_e = 1
6#
7# The unit of length, Bohr, is given by
8#
9# a_0 = (hbar^2 / (e^2 * m_e)) * 4*pi*epsilon_0,
10#
11# where epsilon_0 = 1 / (4*pi), so that in fact 4*pi*epsilon_0 = 1.
12# The unit of energy is
13#
14# Ha = e^2 / a_0 = (e^4 * m_e) / (hbar^2 * 4*pi*epsilon_0)
15#
16# In effective atomic units:
17#
18#  hbar = e^2/epsilon = m = 1
19#
20# In this relations, epsilon is
21# adimensional and is not equal to one, and m = m_e * m^*, being m^*
22# the "effective mass" in atomic units, also an adimensional factor.
23# The unit of length is given by
24#
25#    a_0^* = (hbar^2 / (e^2 * m)) * 4*pi*epsilon*epsilon_0
26#          = a_0 * (epsilon/m^*)
27#
28# And the unit of energy is given by:
29#
30#    Ha^* = e^2 / (a_0^* * epsilon) = Ha * (m^* / epsilon^2)
31#
32# For the material in [M. Governale, Phys. Rev. Lett. 89, 206802 (2002)].
33#
34# m^* = 0.022
35# epsilon = 14.6
36#
37# The confining potential is 5 meV, corresponding to 0.00018374663 Ha, and
38# therefore, 0.00018374663 * (e^2/m^*) Ha^* = 1.78033780231 Ha^*
39#
40#
41#
42# Even though we do not use magnetic fields, here, it is worth recalling
43# the conversions here.
44#
45# 1 Tesla corresponds to 10^4 Gauss, i.e.:
46#
47#   1 Tesla =>  10^4 g^(1/2) cm^(-1/2) s^(-1)
48#
49# I do not write the sign "equal", because both sides of the equation do
50# not have the same dimensions. Since we have fractional exponents, it is
51# more convenient to work with squared relations:
52#
53#   1 Tesla^2 => 10^8 g / (cm * s^2)
54#
55# In atomic units:
56#
57#   1 Tesla^2 => 3.3989315000000 * 10^(-7) Ha / a0^3
58#
59# This can also be written as:
60#
61#   1 Tesla => 5.8300355916580818 * 10(-4) sqrt(Ha / a0^3) =
62#              5.8300355916580818 * 10(-4) a.u.(B)
63#
64# The sqrt(Ha/a0^3) is the atomic unit of magnetic induction. This can
65# be rewritten as:
66#
67#   1 a.u.(B) => T / 1715.25539471980586102447
68#
69# Now we can get the effective unit of magnetic induction, as:
70#
71#   1 eff.a.u.(B) = sqrt(Ha^*/(a0^*)^3) =
72#                   sqrt(Ha * (m^* / epsilon^2) / (a_0 * (epsilon/m^*))^3) =
73#                   sqrt(Ha/a_0^3) * sqrt( (m^*/epsilon^2) / (epsilon/m^*)^3 ) =
74#                   a.u.(B) * ((m^*)^2 / epsilon^(5/2))
75#
76###############################################################################
77
78
79CalculationMode = gs
80FromScratch = yes
81Dimensions = 2
82
83ExperimentalFeatures = yes
84
85# omega should be 5 meV. In effective atomic units:
86omega = 1.78033780231
87
88%Species
89"qd" | species_user_defined | potential_formula | "0.5*omega^2*r^2" | valence | 8
90%
91
92%Coordinates
93"qd" | 0 | 0 | 0
94%
95
96BoxShape = sphere
97Radius = 6
98Spacing = 0.15
99
100SpinComponents = spinors
101
102TheoryLevel = independent_particles
103
104EigenSolver = cg
105EigenSolverTolerance = 1e-6
106EigenSolverMaxIter = 25
107
108Output = wfs
109OutputFormat = axis_x
110
111mu=0.7896
112meff = 1.0
113lambda=mu*sqrt(omega/meff)
114RashbaSpinOrbitCoupling = lambda
115
116
117
118
119