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