diff --git a/doc/user_guide/berry.tex b/doc/user_guide/berry.tex index 3b0e271ff..e761a2a9a 100644 --- a/doc/user_guide/berry.tex +++ b/doc/user_guide/berry.tex @@ -335,10 +335,10 @@ \section{{\tt berry\_task=sc}: shift current} The shift-current contribution to the second-order response is characterized by a frequency-dependent third-rank tensor~\cite{sipe-prb00} -\begin{equation} +\begin{equation}\label{eq:shiftcurrent} \begin{split} \sigma^{abc}(0;\omega,-\omega)=&-\frac{i\pi e^3}{4\hbar^2 \Omega_c N_k} -\sum_{\bm{k}} \sum_{n,m}f_{nm} +\sum_{\bm{k}} \sum_{n,m}(f_{n\bm{k}}-f_{m\bm{k}}) \times \left(r^b_{ mn}(\bm{k})r^{c;a}_{nm}(\bm{k}) + r^c_{mn}(\bm{k})r^{b;a}_{ nm}(\bm{k})\right)\\ &\times \left[\delta(\omega_{mn\bm{k}}-\omega)+\delta(\omega_{nm\bm{k}}-\omega)\right], @@ -346,7 +346,7 @@ \section{{\tt berry\_task=sc}: shift current} \end{equation} where $a,b,c$ are spatial indexes and $\omega_{mn\bm{k}}=(\epsilon_{n\bm{k}}-\epsilon_{m\bm{k}})/\hbar$. -The above expression involves +The expression in Eq.~\ref{eq:shiftcurrent} involves the dipole matrix element \begin{equation} \label{eq:r} @@ -364,8 +364,19 @@ \section{{\tt berry\_task=sc}: shift current} above expression is technically challenging due to the presence of an extra $k$-space derivative. The implementation in {\tt wannier90} follows the scheme proposed in Ref.~\cite{ibanez-azpiroz_ab_2018}, -please cite this reference when publishing shift-current results using this method. +following the spirit of the Wannier-interpolation +method for calculating the AHC~\cite{wang-prb06} by reformulating $k\cdot p$ +perturbation theory within the subspace of wannierized bands. +This strategy inherits the practical advantages of the sum-over-states +approach, but without introducing the truncation errors usually associated with this procedure~\cite{sipe-prb00}. + +As in the case of the optical conductivity, a broadened delta function can be +applied in Eq.~\ref{eq:shiftcurrent} by means of the parameter +$\eta$ (see Eq.~\ref{eq:lorentzian}) using the keyword +{\tt[kubo\_]smr\_fixed\_en\_width}, and adaptive smearing can +be employed using the keyword {\tt [kubo\_]adpt\_smr}. +Please cite Ref.~\cite{ibanez-azpiroz_ab_2018} when publishing shift-current results using this method. \section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients} \label{sec:kdotp} @@ -437,13 +448,11 @@ \section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients} Collecting terms in \eq{pert-exp} up to second order in $k$ we get \beq\label{eq:Htilde} -\begin{split} -& \tilde{H}_{mm'}(\bm{k}) = -\overline{H}_{mm'} + \sum_{a} \left(\overline{H}_{a}\right)_{mm'}k_{a}\\ -& + \dfrac{1}{2}\sum_{a,b}\left[ + \tilde{H}_{mm'}(\bm{k}) = +\overline{H}_{mm'} + \sum_{a} \left(\overline{H}_{a}\right)_{mm'}k_{a} + + \dfrac{1}{2}\sum_{a,b}\left[ \left(\overline{H}_{ab}\right)_{mm'} + \left({T}_{ab}\right)_{mm'} \right]k_{a}k_{b}+ \mathcal{O}(k^{3}), -\end{split} \eeq where $m,m'\in A$ and we have defined the virtual-transition matrix \beq\label{eq:Tab} @@ -462,7 +471,11 @@ \section{{\tt berry\_task=kdotp}: $k\cdot p$ coefficients} The implementation in {\tt wannier90} follows the scheme proposed in Ref.~\cite{ibanez-azpiroz-ArXiv2019}, -please cite this reference when publishing $k\cdot p$ results using this method. +and outputs $\overline{H}_{mm'}$ in {\tt seedname-kdotp\_0.dat}, +$\left(\overline{H}_{a}\right)_{mm'}$ in {\tt seedname-kdotp\_1.dat}, and +$\left[\left(\overline{H}_{ab}\right)_{mm'} + \left({T}_{ab}\right)_{mm'}\right]/2$ in {\tt seedname-kdotp\_2.dat}. + +Please cite Ref.~\cite{ibanez-azpiroz-ArXiv2019} when publishing $k\cdot p$ results using this method. \section{Needed matrix elements} diff --git a/examples/README b/examples/README index 63c5e2df1..5e3dff480 100644 --- a/examples/README +++ b/examples/README @@ -72,3 +72,7 @@ example29: Platinum - Berry curvature-like term and spin Hall conductivity example30: Gallium Arsenide - ac spin Hall conductivity example31: Platinum - Selected columns of density matrix algorithm for spinor wavefunctions + +example32: Tungsten - SCDM parameters from projectability + +example33: BC2N - Expansion coefficients for kdotp bands diff --git a/examples/example33/bc2n.nscf b/examples/example33/bc2n.nscf new file mode 100644 index 000000000..15d4d8b59 --- /dev/null +++ b/examples/example33/bc2n.nscf @@ -0,0 +1,141 @@ + &control + verbosity = 'high' + calculation = 'nscf' + wf_collect = .true. + restart_mode = 'from_scratch' + prefix = 'bc2n' + pseudo_dir = '../../pseudo/' + outdir = './' +/ +&system + ibrav=0, + celldm(1) = 1.8897261245650618 + nat= 4, + ntyp= 3, + ecutwfc=70, + degauss=0.05, + occupations="smearing", smearing="mp", + nbnd = 40 + / +&electrons + mixing_beta = 0.1 + conv_thr = 1.0d-7 + electron_maxstep = 1000 +/ +&IONS +/ +ATOMIC_SPECIES +B 74.000 B.pbe-n-kjpaw_psl.0.1.UPF +C 16.000 C.pbe-n-kjpaw_psl.0.1.UPF +N 18.000 N.pbe-n-kjpaw_psl.0.1.UPF +CELL_PARAMETERS + 2.466 0.000000000 0.000000000 + 0.000000000 20.0 0.000000000 + 0.000000000 0.000000000 4.323 +ATOMIC_POSITIONS alat +B 1.2330000 0.0000000 1.1830592 +C 1.2330000 0.0000000 2.6963492 +C 0.0000000 0.0000000 3.3885933 +N 0.0000000 0.0000000 4.7677273 +K_POINTS {crystal} +100 +0.0 0.0 0.0 1.0 +0.0 0.0 0.1 1.0 +0.0 0.0 0.2 1.0 +0.0 0.0 0.3 1.0 +0.0 0.0 0.4 1.0 +0.0 0.0 0.5 1.0 +0.0 0.0 0.6 1.0 +0.0 0.0 0.7 1.0 +0.0 0.0 0.8 1.0 +0.0 0.0 0.9 1.0 +0.1 0.0 0.0 1.0 +0.1 0.0 0.1 1.0 +0.1 0.0 0.2 1.0 +0.1 0.0 0.3 1.0 +0.1 0.0 0.4 1.0 +0.1 0.0 0.5 1.0 +0.1 0.0 0.6 1.0 +0.1 0.0 0.7 1.0 +0.1 0.0 0.8 1.0 +0.1 0.0 0.9 1.0 +0.2 0.0 0.0 1.0 +0.2 0.0 0.1 1.0 +0.2 0.0 0.2 1.0 +0.2 0.0 0.3 1.0 +0.2 0.0 0.4 1.0 +0.2 0.0 0.5 1.0 +0.2 0.0 0.6 1.0 +0.2 0.0 0.7 1.0 +0.2 0.0 0.8 1.0 +0.2 0.0 0.9 1.0 +0.3 0.0 0.0 1.0 +0.3 0.0 0.1 1.0 +0.3 0.0 0.2 1.0 +0.3 0.0 0.3 1.0 +0.3 0.0 0.4 1.0 +0.3 0.0 0.5 1.0 +0.3 0.0 0.6 1.0 +0.3 0.0 0.7 1.0 +0.3 0.0 0.8 1.0 +0.3 0.0 0.9 1.0 +0.4 0.0 0.0 1.0 +0.4 0.0 0.1 1.0 +0.4 0.0 0.2 1.0 +0.4 0.0 0.3 1.0 +0.4 0.0 0.4 1.0 +0.4 0.0 0.5 1.0 +0.4 0.0 0.6 1.0 +0.4 0.0 0.7 1.0 +0.4 0.0 0.8 1.0 +0.4 0.0 0.9 1.0 +0.5 0.0 0.0 1.0 +0.5 0.0 0.1 1.0 +0.5 0.0 0.2 1.0 +0.5 0.0 0.3 1.0 +0.5 0.0 0.4 1.0 +0.5 0.0 0.5 1.0 +0.5 0.0 0.6 1.0 +0.5 0.0 0.7 1.0 +0.5 0.0 0.8 1.0 +0.5 0.0 0.9 1.0 +0.6 0.0 0.0 1.0 +0.6 0.0 0.1 1.0 +0.6 0.0 0.2 1.0 +0.6 0.0 0.3 1.0 +0.6 0.0 0.4 1.0 +0.6 0.0 0.5 1.0 +0.6 0.0 0.6 1.0 +0.6 0.0 0.7 1.0 +0.6 0.0 0.8 1.0 +0.6 0.0 0.9 1.0 +0.7 0.0 0.0 1.0 +0.7 0.0 0.1 1.0 +0.7 0.0 0.2 1.0 +0.7 0.0 0.3 1.0 +0.7 0.0 0.4 1.0 +0.7 0.0 0.5 1.0 +0.7 0.0 0.6 1.0 +0.7 0.0 0.7 1.0 +0.7 0.0 0.8 1.0 +0.7 0.0 0.9 1.0 +0.8 0.0 0.0 1.0 +0.8 0.0 0.1 1.0 +0.8 0.0 0.2 1.0 +0.8 0.0 0.3 1.0 +0.8 0.0 0.4 1.0 +0.8 0.0 0.5 1.0 +0.8 0.0 0.6 1.0 +0.8 0.0 0.7 1.0 +0.8 0.0 0.8 1.0 +0.8 0.0 0.9 1.0 +0.9 0.0 0.0 1.0 +0.9 0.0 0.1 1.0 +0.9 0.0 0.2 1.0 +0.9 0.0 0.3 1.0 +0.9 0.0 0.4 1.0 +0.9 0.0 0.5 1.0 +0.9 0.0 0.6 1.0 +0.9 0.0 0.7 1.0 +0.9 0.0 0.8 1.0 +0.9 0.0 0.9 1.0 diff --git a/examples/example33/bc2n.pw2wan b/examples/example33/bc2n.pw2wan new file mode 100644 index 000000000..20efa1802 --- /dev/null +++ b/examples/example33/bc2n.pw2wan @@ -0,0 +1,7 @@ +&inputpp + outdir = './' + prefix = 'bc2n' + seedname = 'bc2n' + write_mmn = .true. + write_amn = .true. +/ diff --git a/examples/example33/bc2n.scf b/examples/example33/bc2n.scf new file mode 100644 index 000000000..2dab86f10 --- /dev/null +++ b/examples/example33/bc2n.scf @@ -0,0 +1,40 @@ + &control + verbosity = 'high' + calculation = 'scf' + wf_collect = .true. + restart_mode = 'from_scratch' + prefix = 'bc2n' + pseudo_dir = '../../pseudo/' + outdir = './' +/ +&system + ibrav=0, + celldm(1) = 1.8897261245650618 + nat= 4, + ntyp= 3, + ecutwfc=70, + degauss=0.05, + occupations="smearing", smearing="mp", + / +&electrons + mixing_beta = 0.1 + conv_thr = 1.0d-7 + electron_maxstep = 1000 +/ +&IONS +/ +ATOMIC_SPECIES +B 74.000 B.pbe-n-kjpaw_psl.0.1.UPF +C 16.000 C.pbe-n-kjpaw_psl.0.1.UPF +N 18.000 N.pbe-n-kjpaw_psl.0.1.UPF +CELL_PARAMETERS + 2.466 0.000000000 0.000000000 + 0.000000000 20.0 0.000000000 + 0.000000000 0.000000000 4.323 +ATOMIC_POSITIONS alat +B 1.2330000 0.0000000 1.1830592 +C 1.2330000 0.0000000 2.6963492 +C 0.0000000 0.0000000 3.3885933 +N 0.0000000 0.0000000 4.7677273 +K_POINTS automatic +10 1 10 0 0 0 diff --git a/examples/example33/bc2n.win b/examples/example33/bc2n.win new file mode 100644 index 000000000..4e0c5f129 --- /dev/null +++ b/examples/example33/bc2n.win @@ -0,0 +1,173 @@ + +num_bands = 29 +num_wann = 4 + +num_iter = 10000 +num_print_cycles = 40 + +dis_froz_max = 0.95d0 +dis_froz_min = -5.28d0 +dis_num_iter = 10200 +dis_mix_ratio = 1.d0 + +dis_conv_tol = 1E-9 + +search_shells = 30 + +#restart = plot + +bands_plot : true +bands_num_points : 151 +bands_plot_format : gnuplot + +exclude_bands : 1, 31-40 + +################ +### POSTW90 #### +berry = true +berry_task = kdotp + + +kdotp_kpoint = 0.5000 0.0000 0.5000 +kdotp_num_bands = 2 +kdotp_bands = 2,3 +berry_kmesh = 1 1 1 +fermi_energy = 54.10400040 +################ + + + +begin unit_cell_cart + 2.466 0.000000000 0.000000000 + 0.000000000 20.00 0.000000000 + 0.000000000 0.000000000 4.323 +end unit_cell_cart + + +begin atoms_cart +B 1.2330000 0.0000000 1.1830592 +C 1.2330000 0.0000000 2.6963492 +C 0.0000000 0.0000000 3.3885933 +N 0.0000000 0.0000000 4.7677273 +end atoms_cart + +mp_grid = 10 1 10 + + +#reciprocal lattice units +begin kpoint_path +S 0.50000 0.00000 0.50000 X 0.50000 0.00000 0.00000 +end kpoint_path + + +Begin Projections +C:py +B:py +N:py +end projections + + + + +begin kpoints +0.0 0.0 0.0 +0.0 0.0 0.1 +0.0 0.0 0.2 +0.0 0.0 0.3 +0.0 0.0 0.4 +0.0 0.0 0.5 +0.0 0.0 0.6 +0.0 0.0 0.7 +0.0 0.0 0.8 +0.0 0.0 0.9 +0.1 0.0 0.0 +0.1 0.0 0.1 +0.1 0.0 0.2 +0.1 0.0 0.3 +0.1 0.0 0.4 +0.1 0.0 0.5 +0.1 0.0 0.6 +0.1 0.0 0.7 +0.1 0.0 0.8 +0.1 0.0 0.9 +0.2 0.0 0.0 +0.2 0.0 0.1 +0.2 0.0 0.2 +0.2 0.0 0.3 +0.2 0.0 0.4 +0.2 0.0 0.5 +0.2 0.0 0.6 +0.2 0.0 0.7 +0.2 0.0 0.8 +0.2 0.0 0.9 +0.3 0.0 0.0 +0.3 0.0 0.1 +0.3 0.0 0.2 +0.3 0.0 0.3 +0.3 0.0 0.4 +0.3 0.0 0.5 +0.3 0.0 0.6 +0.3 0.0 0.7 +0.3 0.0 0.8 +0.3 0.0 0.9 +0.4 0.0 0.0 +0.4 0.0 0.1 +0.4 0.0 0.2 +0.4 0.0 0.3 +0.4 0.0 0.4 +0.4 0.0 0.5 +0.4 0.0 0.6 +0.4 0.0 0.7 +0.4 0.0 0.8 +0.4 0.0 0.9 +0.5 0.0 0.0 +0.5 0.0 0.1 +0.5 0.0 0.2 +0.5 0.0 0.3 +0.5 0.0 0.4 +0.5 0.0 0.5 +0.5 0.0 0.6 +0.5 0.0 0.7 +0.5 0.0 0.8 +0.5 0.0 0.9 +0.6 0.0 0.0 +0.6 0.0 0.1 +0.6 0.0 0.2 +0.6 0.0 0.3 +0.6 0.0 0.4 +0.6 0.0 0.5 +0.6 0.0 0.6 +0.6 0.0 0.7 +0.6 0.0 0.8 +0.6 0.0 0.9 +0.7 0.0 0.0 +0.7 0.0 0.1 +0.7 0.0 0.2 +0.7 0.0 0.3 +0.7 0.0 0.4 +0.7 0.0 0.5 +0.7 0.0 0.6 +0.7 0.0 0.7 +0.7 0.0 0.8 +0.7 0.0 0.9 +0.8 0.0 0.0 +0.8 0.0 0.1 +0.8 0.0 0.2 +0.8 0.0 0.3 +0.8 0.0 0.4 +0.8 0.0 0.5 +0.8 0.0 0.6 +0.8 0.0 0.7 +0.8 0.0 0.8 +0.8 0.0 0.9 +0.9 0.0 0.0 +0.9 0.0 0.1 +0.9 0.0 0.2 +0.9 0.0 0.3 +0.9 0.0 0.4 +0.9 0.0 0.5 +0.9 0.0 0.6 +0.9 0.0 0.7 +0.9 0.0 0.8 +0.9 0.0 0.9 +end kpoints diff --git a/examples/example33/kdotp_plot.py b/examples/example33/kdotp_plot.py new file mode 100644 index 000000000..2b57f0294 --- /dev/null +++ b/examples/example33/kdotp_plot.py @@ -0,0 +1,230 @@ +import numpy as N +import sys as SYS +import os as OS + +import matplotlib +import matplotlib.pyplot as plt + +from matplotlib.font_manager import FontProperties + +from matplotlib import rc +rc('text', usetex=True) + +font = FontProperties() +font.set_size(20) + +#------------------------------------------------------ +# Extract W90 bands data +#------------------------------------------------------ + +W_band_dir = './' +W_band_file = 'bc2n_band.dat' + +eF=-1.6103 + +data = N.loadtxt(W_band_dir+W_band_file) + +list_xW = data[:,0] +bandsW = data[:,1:].transpose()-eF + + +#---------------------------------------------------------- +# plot +#---------------------------------------------------------- + +fig = plt.figure(figsize=(10,7)) + +axplot = fig.add_subplot(111) + +for band in bandsW: + axplot.plot(list_xW,band,linestyle='',label='ab initio (W90)', color='k',marker='o',markersize=2) + + + +###################################### +###################################### +####### extract k.p coefficients #### + +seed = 'bc2n' + +filename_0 = seed + '-kdotp_0.dat' +filename_1 = seed + '-kdotp_1.dat' +filename_2 = seed + '-kdotp_2.dat' + +# arrays containing pauli matrix coefficients proportional to +# kx, ky, kx**2, ky**2 and kx*ky, 5 entries in total +a1 = [0] * 5 +a2 = [0] * 5 +a3 = [0] * 6 # contains extra term independent of k +a0 = [0] * 5 + +# assign spatial directions +# indexes: 0=x, 1=y, 2=z +index_x = 2 +index_y = 0 + + +#### 0th order #### +data = N.loadtxt(filename_0) +re = data[:,0] +im = data[:,1] + +# Az +a3[0] = 0.5*N.real(re[0]-re[3]) +offset = re[0] - a3[0] + + +#### 1st order #### +data = N.loadtxt(filename_1) +re = data[:,0] +im = data[:,1] +full = re + im*1.j + +# Az +# index_i*4 chooses the matrix chunk corresponding to the proper direction (the 4 factor comes from 2x2 bands), +# +1 gets the band-off-diagonal entry +a3[1] = 0.5*(full[index_x*4]-full[index_x*4+3]).real +a3[2] = 0.5*(full[index_y*4]-full[index_y*4+3]).real + +# Ax +# index_i*4 chooses the matrix chunk corresponding to the proper direction (the 4 factor comes from 2x2 bands), +# +1 gets the band-off-diagonal entry +a1[0] = (full[index_x*4+1]).real +a1[1] = -(full[index_y*4+1]).imag + +# Ay +# index_i*4 chooses the matrix chunk corresponding to the proper direction (the 4 factor comes from 2x2 bands), +# +1 gets the band-off-diagonal entry +a2[0] = -(full[index_x*4+1]).imag +a2[1] = (full[index_y*4+1]).real + +# A0 +# index_i*4 chooses the matrix chunk corresponding to the proper direction (the 4 factor comes from 2x2 bands), +# +1 gets the band-off-diagonal entry +a0[0] = 0.5*(full[index_x*4]+full[index_x*4+3]).real +a0[1] = 0.5*(full[index_y*4]+full[index_y*4+3]).real + + + +#### 2nd order #### +data = N.loadtxt(filename_2) +re = data[:,0] +im = data[:,1] +full = re + im*1.j + +# a1 +# first index jumps 12=3*4 (3 for spatial indexes, 4=2x2 for bands) +# second index only jumps 4=2x2 for bands +# +1 gets the band-off-diagonal term +a1[2] = full[index_x*(12+4)+1].real +a1[3] = -full[index_y*(12+4)+1].imag +a1[4] = full[index_x*12+index_y*4+1].real + full[index_y*12+index_x*4+1].real + +# a2 +# first index jumps 12=3*4 (3 for spatial indexes, 4=2x2 for bands) +# second index only jumps 4=2x2 for bands +# +1 gets the band-off-diagonal term +a2[2] = -full[index_x*(12+4)+1].imag +a2[3] = full[index_y*(12+4)+1].real +a2[4] = -full[index_x*12+index_y*4+1].imag - full[index_y*12+index_x*4+1].imag + +# a3 +# first index jumps 12=3*4 (3 for spatial indexes, 4=2x2 for bands) +# second index only jumps 4=2x2 for bands +# +0 and +3 get the 11 and 22 band-diagonal terms +a3[3] = N.real(0.5*(full[index_x*(12+4)] - full[index_x*(12+4)+3])) +a3[4] = N.real(0.5*(full[index_y*(12+4)] - full[index_y*(12+4)+3])) +a3[5] = 0.5*N.real( (full[index_x*12+index_y*4]+full[index_y*12+index_x*4] ) - (full[index_x*12+index_y*4+3] + full[index_y*12+index_x*4+3] ) ) + +# a0 +a0[2] = N.real(0.5*(full[index_x*(12+4)] + full[index_x*(12+4)+3])) +a0[3] = N.real(0.5*(full[index_y*(12+4)] + full[index_y*(12+4)+3])) +a0[4] = 0.5*N.real( (full[index_x*12+index_y*4]+full[index_y*12+index_x*4] ) + (full[index_x*12+index_y*4+3] + full[index_y*12+index_x*4+3] ) ) + + +# set up k.p band dispersion +# energy is in eV +# linear coefficients are in units of eV*Ang +# quadratic coefficients are in units of eV*Ang**2 +a0_angs = 1.0 +bxfac = -0.5*0.231321 +byfac = 0.0 +bfac = N.sqrt( (bxfac)**(2) + (byfac)**(2) ) +cos_xangle = bxfac/bfac +sin_yangle = byfac/bfac +kfac = bfac*2*N.pi/a0_angs + +# define quantities to be plotted +kk_list = [] +band_1 = [] +band_2 = [] +band_1lin = [] +band_2lin = [] + +# k along x +num_k = 200 +for ii in range(0,num_k+1): + + kk = kfac*float(ii)/float(num_k) + kkx = cos_xangle*kk + kky = sin_yangle*kk + + # coefficients with quadratic dispersion + a1_coeff = (a1[0])*(kkx) + (a1[1])*(kky) + (a1[2])*(kkx**(2)) + (a1[3])*(kky**(2)) + (a1[4])*(kky*kkx) + a2_coeff = (a2[0])*(kkx) + (a2[1])*(kky) + (a2[2])*(kkx**(2)) + (a2[3])*(kky**(2)) + (a2[4])*(kky*kkx) + a3_coeff = a3[0] + (a3[1])*(kkx) + (a3[2])*(kky) + (a3[3])*(kkx**(2)) + (a3[4])*(kky**(2)) + (a3[5])*(kky*kkx) + a0_coeff = a0[0]*(kkx) + a0[1]*(kky) + a0[2]*(kkx)**(2) + a0[3]*(kky)**(2) + (a0[4])*(kky*kkx) + + eps = N.sqrt((N.abs(a1_coeff-a2_coeff*(1.j)))**(2) + (N.abs(a3_coeff))**(2)) + + kk_list.append(kk) + band_1.append(a0_coeff+eps+offset-eF) + band_2.append(a0_coeff-eps+offset-eF) + + # coefficients with linear dispersion + a1_coeff = (a1[0])*(kkx) + (a1[1])*(kky) + a2_coeff = (a2[0])*(kkx) + (a2[1])*(kky) + a3_coeff = a3[0] + (a3[1])*(kkx) + (a3[2])*(kky) + a0_coeff = a0[0]*(kkx) + a0[1]*(kky) + + eps = N.sqrt((N.abs(a1_coeff-a2_coeff*(1.j)))**(2) + (N.abs(a3_coeff))**(2)) + + band_1lin.append(a0_coeff+eps+offset-eF) + band_2lin.append(a0_coeff-eps+offset-eF) + + + +axplot.plot(kk_list,band_1lin,color='b',linestyle='--',label='linear $k\cdot p$') +axplot.plot(kk_list,band_2lin,color='b',linestyle='--') + +axplot.plot(kk_list,band_1,color='r',linestyle='-',label='quadratic $k\cdot p$') +axplot.plot(kk_list,band_2,color='r',linestyle='-') + + + +###################################### +###################################### +## set up figure + +axplot.set_xlim([list_xW[0],list_xW[-1]]) + +xtick_positions = [0.0,list_xW[len(list_xW)-1]] +xtick_labels = ['$\mathrm{S}$','$\mathrm{X}$'] + +axplot.set_xticks(xtick_positions) +axplot.set_xticklabels(xtick_labels,fontproperties=font) + +for y_tick in axplot.yaxis.get_major_ticks(): + y_tick.label1.set_fontsize(20) + +# Set the yticks properties +axplot.set_ylabel('$E-E_{F}$ $\mathrm{(eV)}$',fontproperties=font) + + +axplot.axhline(0, color='k',linestyle='-',lw=0.25) +axplot.legend(loc=0,fancybox=True,shadow=True,prop=font) + +fig.tight_layout() + +plt.savefig('kdotp_bands_SX.pdf') +plt.show() diff --git a/pseudo/B.pbe-n-kjpaw_psl.0.1.UPF b/pseudo/B.pbe-n-kjpaw_psl.0.1.UPF new file mode 100644 index 000000000..8baa6fb42 --- /dev/null +++ b/pseudo/B.pbe-n-kjpaw_psl.0.1.UPF @@ -0,0 +1,9212 @@ + + + Generated using "atomic" code by A. Dal Corso v.5.0.2 svn rev. 9415 + Author: ADC + Generation date: 11Sep2012 + Pseudopotential type: PAW + Element: B + Functional: SLA PW PBX PBC + + Suggested minimum cutoff for wavefunctions: 43. Ry + Suggested minimum cutoff for charge density: 170. Ry + The Pseudo was generated with a Scalar-Relativistic Calculation + L component and cutoff radius for Local Potential: 2 1.2000 + + Valence configuration: + nl pn l occ Rcut Rcut US E pseu + 2S 1 0 2.00 1.300 1.400 -0.694058 + 2P 2 1 1.00 1.200 1.400 -0.265108 + Generation configuration: + 2S 1 0 2.00 1.300 1.400 -0.694053 + 2S 1 0 0.00 1.300 1.400 0.050000 + 2P 2 1 1.00 1.200 1.400 -0.265108 + 2P 2 1 0.00 0.800 1.400 1.500000 + 3D 3 2 -2.00 1.200 1.200 0.150000 + + Pseudization used: troullier-martins + + &input + title='B', + zed=5.0, + rel=1, + config='1s2.0 2s2.0 2p1.0 3d-2.0', + iswitch=3, + dft='PBE' + / + &inputp + lpaw=.true., + pseudotype=3, + file_pseudopw='B.pbe-n-kjpaw_psl.0.1.UPF', + author='ADC', + lloc=2, + which_augfun ='BESSEL', + rmatch_augfun=1.30, + nlcc=.true., + tm=.true. + / +5 +2S 1 0 2.00 0.00 1.30 1.40 0.0 +2S 1 0 0.00 0.05 1.30 1.40 0.0 +2P 2 1 1.00 0.00 1.20 1.40 0.0 +2P 2 1 0.00 1.50 0.80 1.40 0.0 +3D 3 2 -2.00 0.15 1.20 1.20 0.0 + + + + + + + + + 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Dal Corso v.5.0.2 svn rev. 9415 + Author: Lorenzo Paulatto + Generation date: 11Sep2012 + Pseudopotential type: PAW + Element: C + Functional: SLA PW PBX PBC + + Suggested minimum cutoff for wavefunctions: 37. Ry + Suggested minimum cutoff for charge density: 147. Ry + The Pseudo was generated with a Scalar-Relativistic Calculation + L component and cutoff radius for Local Potential: 2 1.1000 + + Valence configuration: + nl pn l occ Rcut Rcut US E pseu + 2S 1 0 2.00 1.000 1.300 -1.010676 + 2P 2 1 2.00 1.000 1.450 -0.388489 + Generation configuration: + 2S 1 0 2.00 1.000 1.300 -1.010668 + 2S 1 0 0.00 1.000 1.300 0.050000 + 2P 2 1 2.00 1.000 1.450 -0.388486 + 2P 2 1 0.00 1.000 1.450 0.050000 + 3D 3 2 -2.00 1.100 1.100 0.100000 + + Pseudization used: troullier-martins + + &input + title='C', + zed=6, + rel=1, + config='[He] 2s2 2p2 3d-2', + iswitch=3, + dft='PBE' + / + &inputp + lpaw=.true., + pseudotype=3, + file_pseudopw='C.pbe-n-kjpaw_psl.0.1.UPF', + author='Lorenzo Paulatto', + lloc=2, + which_augfun ='BESSEL', + rmatch_augfun=1.1, + nlcc=.true., + new_core_ps=.true., + rcore=0.8, + tm=.true. + / +5 +2S 1 0 2.00 0.00 1.00 1.30 0.0 +2S 1 0 0.00 0.05 1.00 1.30 0.0 +2P 2 1 2.00 0.00 1.00 1.45 0.0 +2P 2 1 0.00 0.05 1.00 1.45 0.0 +3D 3 2 -2.00 0.10 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-8.075794025691484E-002 +-7.975474901134030E-002 + + + diff --git a/pseudo/N.pbe-n-kjpaw_psl.0.1.UPF b/pseudo/N.pbe-n-kjpaw_psl.0.1.UPF new file mode 100644 index 000000000..0aea09a8b --- /dev/null +++ b/pseudo/N.pbe-n-kjpaw_psl.0.1.UPF @@ -0,0 +1,9452 @@ + + + Generated using "atomic" code by A. Dal Corso v.5.0.2 svn rev. 9415 + Author: Lorenzo Paulatto, modified by ADC + Generation date: 11Sep2012 + Pseudopotential type: PAW + Element: N + Functional: SLA PW PBX PBC + + Suggested minimum cutoff for wavefunctions: 39. Ry + Suggested minimum cutoff for charge density: 264. Ry + The Pseudo was generated with a Scalar-Relativistic Calculation + L component and cutoff radius for Local Potential: 2 1.1000 + + Valence configuration: + nl pn l occ Rcut Rcut US E pseu + 2S 1 0 2.00 1.000 1.300 -1.365820 + 2P 2 1 3.00 1.000 1.450 -0.521109 + Generation configuration: + 2S 1 0 2.00 1.000 1.300 -1.365812 + 2S 1 0 0.00 1.000 1.300 0.050000 + 2P 2 1 3.00 1.000 1.450 -0.521105 + 2P 2 1 0.00 1.000 1.450 0.050000 + 3D 3 2 -2.00 1.100 1.100 0.150000 + + Pseudization used: troullier-martins + + &input + title='N', + zed=7., + rel=1, + config='[He] 2s2 2p3 3d-2', + iswitch=3, + dft='PBE' + / + &inputp + lpaw = .true., + pseudotype=3, + file_pseudopw='N.pbe-n-kjpaw_psl.0.1.UPF', + author='Lorenzo Paulatto, modified by ADC', + which_augfun='PSQ', + rmatch_augfun=1.0, + lloc=2, + nlcc=.true., + new_core_ps=.true., + rcore=0.8, + tm=.true. + / +5 +2S 1 0 2.00 0.00 1.00 1.30 0.0 +2S 1 0 0.00 0.05 1.00 1.30 0.0 +2P 2 1 3.00 0.00 1.00 1.45 0.0 +2P 2 1 0.00 0.05 1.00 1.45 0.0 +3D 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