mirror of
https://github.com/triqs/dft_tools
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128 lines
4.0 KiB
Python
128 lines
4.0 KiB
Python
from numpy import array, zeros
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import math
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from pytriqs.lattice.tight_binding import *
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# Define the Bravais Lattice : a square lattice in 2d
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BL_1 = BravaisLattice(units = [(1,0,0) , (0,1,0) ], orbital_positions= {"": (0,0,0)} )
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BL_2 = BravaisLattice(units = [(1,1,0) , (-1,1,0) ], orbital_positions= {"A": (0,0,0), "B": (.5,.5,0)} )
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BL_4 = BravaisLattice(units = [(2,0,0) , (0,2,0) ], orbital_positions= {"A": (0,0,0), "B": (0,.5,0), "C": (.5,0,0), "D": (.5,.5,0)} )
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# Hopping dictionaries
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t = .25; tp = -.1;
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hop_1= { (1,0) : [[ t]], (-1,0) : [[ t]], (0,1) : [[ t]], (0,-1) : [[ t]],
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(1,1) : [[ tp]], (-1,-1): [[ tp]], (1,-1) : [[ tp]], (-1,1) : [[ tp]]
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}
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hop_2= { (0,0) :[[0.,t],
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[t,0.]],
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(1,0) : [[ tp, 0],
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[ t ,tp]],
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(-1,0) : [[ tp, t],
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[ 0 ,tp]],
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(0,1) :[[ tp, 0],
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[ t, tp]],
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(0,-1) :[[ tp, t],
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[ 0 ,tp]],
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(1,1) : [[ 0, 0],
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[ t,0]],
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(-1,-1) :[[ 0, t],
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[ 0,0]],
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(-1,1) : [[ 0, 0],
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[ 0,0]],
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(1,-1) : [[ 0, 0],
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[ 0,0]]
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}
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hop_4= { (0,0) :[[0.,t, tp,t],
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[t,0., t,tp],
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[tp,t,0,t],
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[t,tp,t,0]],
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(1,0) : [[0.,0, 0,0],
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[t,0.,0,tp],
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[tp,0,0,t],
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[0,0,0,0]],
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(-1,0) : [[0.,t, tp,0],
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[0,0.,0,0],
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[0,0,0,0],
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[0,tp,t,0]],
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(0,1) : [[0.,0, 0,0],
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[0,0.,0,0],
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[tp,t,0,0],
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[t,tp,0,0]],
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(0,-1) :[[0.,0, tp,t],
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[0,0.,t,tp],
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[0,0,0,0],
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[0,0,0,0]],
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(1,1) : [[0.,0, 0,0],
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[0,0.,0,0],
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[tp,0,0,0],
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[0,0,0,0]],
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(-1,-1) : [[0.,0, tp,0],
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[0,0.,0,0],
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[0,0,0,0],
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[0,0,0,0]],
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(-1,1) : [[0.,0, 0,0],
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[0,0.,0,0],
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[0,0,0,0],
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[0,tp,0,0]],
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(1,-1) :[[0.,0, 0,0],
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[0,0.,0,tp],
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[0,0,0,0],
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[0,0,0,0]],
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}
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TB_1 = TightBinding(BL_1, hop_1)
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TB_2 = TightBinding(BL_2, hop_2)
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TB_4 = TightBinding(BL_4, hop_4)
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# High-symmetry points
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Gamma = array([0. ,0. ]);
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PiPi = array([math.pi ,math.pi ])*1/(2*math.pi);
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Pi0 = array([math.pi ,0 ])*1/(2*math.pi);
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PihPih = array([math.pi/2 ,math.pi/2])*1/(2*math.pi)
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TwoPi0 = array([2*math.pi ,0 ])*1/(2*math.pi);
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TwoPiTwoPi= array([math.pi*2 ,math.pi*2])*1/(2*math.pi)
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n_pts=50
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# Paths along high-symmetry directions
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path_1=[Gamma,Pi0,PiPi,Gamma]
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path_2=[Gamma,PiPi,TwoPi0,Gamma] #equivalent to path_1 in coordinates of 2at/ucell basis
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path_4=[Gamma,TwoPi0,TwoPiTwoPi,Gamma] #equivalent to path_1 in coordinates of 4at/ucell basis
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def energies_on_path(path, TB, n_pts, n_orb=1):
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E=zeros((n_orb,n_pts*(len(path)-1)))
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for i in range(len(path)-1,0,-1):
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energies = energies_on_bz_path (TB, path[i-1], path[i], n_pts)
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for orb in range(n_orb): E[orb,(i-1)*n_pts:(i)*n_pts]=energies[orb,:]
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print "index of point #"+str(i-1)+" = "+str((i-1)*n_pts)
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return E
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E_1= energies_on_path(path_1,TB_1,n_pts,1)
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E_2= energies_on_path(path_2,TB_2,n_pts,2)
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E_4= energies_on_path(path_4,TB_4,n_pts,4)
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from matplotlib import pylab as plt
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plt.plot(E_1[0], '--k', linewidth=4, label = "1 at/unit cell")
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plt.plot(E_2[0],'-.g', linewidth=4, label = "2 ats/unit cell")
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plt.plot(E_2[1],'-.g', linewidth=4)
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plt.plot(E_4[0],'-r', label = "4 ats/unit cell")
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plt.plot(E_4[1],'-r')
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plt.plot(E_4[2],'-r')
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plt.plot(E_4[3],'-r')
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plt.grid()
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plt.legend()
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plt.axes().set_xticks([0,50,100,150])
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plt.axes().set_xticklabels([r'$\Gamma_1$',r'$M_1$',r'$X_1$',r'$\Gamma_1$'])
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plt.ylabel(r"$\epsilon$")
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