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import numpy as np
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from math import *
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import cmath
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import functools
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import guan
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# Installation: pip install --upgrade guan
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def main():
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M = 0
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t1 = 1
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phi= pi/2
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t2 = 0.03
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tc = 0.31
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bilayer_bands(M, t1, t2, phi, tc)
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chern_number(M, t1, t2, phi)
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def hamiltonian_of_Haldane(k1, k2, M, t1, t2, phi, a=1/sqrt(3)):
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h0 = np.zeros((2, 2), dtype=complex)
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h1 = np.zeros((2, 2), dtype=complex)
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h2 = np.zeros((2, 2), dtype=complex)
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h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
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h1[0, 1] = h1[0, 1].conj()
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h2[0, 0] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
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h2[1, 1] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
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matrix = h0 + h1 + h2 + h2.transpose().conj()
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return matrix
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def hamiltonian_of_modified_Haldane(k1, k2, M, t1, t2, phi, a=1/sqrt(3)):
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h0 = np.zeros((2, 2), dtype=complex)
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h1 = np.zeros((2, 2), dtype=complex)
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h2 = np.zeros((2, 2), dtype=complex)
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k1 = -k1 # kx # Note that to get the unit cell the bilayer honeycomb lattice containing all possible layer hoppings, here one layer (HM layer or mHM layer） needs to be applied with its counterpart of mirror symmetry along x direction.
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h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
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h1[0, 1] = h1[1, 0].conj()
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h2[0, 0] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
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h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
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matrix = h0 + h1 + h2 + h2.transpose().conj()
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return matrix
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def hamiltonian_of_bilayer(k1, k2, M, t1, t2, phi, tc):
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hamiltonian1 = hamiltonian_of_Haldane(k1, k2, M, t1, t2, phi, a=1/sqrt(3))
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hamiltonian2 = hamiltonian_of_modified_Haldane(k1, k2, M, t1, t2, phi, a=1/sqrt(3))
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hamiltonian = np.zeros((4, 4), dtype=complex)
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hamiltonian[0:2, 0:2] = hamiltonian1
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hamiltonian[2:4, 2:4] = hamiltonian2
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# AB stacking
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hamiltonian[1, 2] = tc # B on HM， A on mHM
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hamiltonian[2, 1] = tc
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# BA stacking
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# hamiltonian[0, 3] = tc # A on HM， B on mHM
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# hamiltonian[3, 0] = tc
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# AA stacking
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# hamiltonian[0, 2] = tc
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# hamiltonian[2, 0] = tc
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# hamiltonian[1, 3] = tc
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# hamiltonian[3, 1] = tc
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return hamiltonian
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def bilayer_bands(M, t1, t2, phi, tc):
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k1_array = np.linspace(0, 4*pi, 3000)
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k2 = 0
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hamiltonian = functools.partial(hamiltonian_of_bilayer, k2=k2, M=M, t1=t1, t2=t2, phi=phi, tc=tc)
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eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k1_array, hamiltonian)
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plt, fig, ax = guan.import_plt_and_start_fig_ax(labelsize=25)
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guan.plot_without_starting_fig_ax(plt, fig, ax, k1_array, eigenvalue_array[:, 0], linewidth=2)
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guan.plot_without_starting_fig_ax(plt, fig, ax, k1_array, eigenvalue_array[:, 1], linewidth=2)
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guan.plot_without_starting_fig_ax(plt, fig, ax, k1_array, eigenvalue_array[:, 2], linewidth=2, color='k')
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guan.plot_without_starting_fig_ax(plt, fig, ax, k1_array, eigenvalue_array[:, 3], linewidth=2, color='k')
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guan.plot_without_starting_fig_ax(plt, fig, ax, [], [], fontsize=30, y_max=1.5, y_min=-1.5, xlabel='$\mathrm{k_x}$', ylabel='$\mathrm{E}$')
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plt.show()
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def chern_number(M, t1, t2, phi):
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tc_array = np.arange(0.05, 0.8, 0.05)
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chern_number_array = []
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for tc in tc_array:
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print(tc)
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hamiltonian = functools.partial(hamiltonian_of_bilayer, M=M, t1=t1, t2=t2, phi=phi, tc=tc)
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chern_number = guan.calculate_chern_number_for_honeycomb_lattice(hamiltonian, a=1/sqrt(3), precision=500, print_show=0)
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print(chern_number, '\n')
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chern_number_array.append(chern_number[0:2])
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guan.plot(tc_array, np.real(chern_number_array), xlabel='$\mathrm{t_c}$', ylabel='$\mathrm{C}$', style='o-')
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if __name__ == '__main__':
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main()
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@ -0,0 +1,220 @@
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import numpy as np
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import functools
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from math import *
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import cmath
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import guan
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# Installation: pip install --upgrade guan
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def main():
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N = 15
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M = 0
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t1 = 1
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phi= pi/2
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t2= 0.03
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tc = 0.8
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layer_num = 2
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bands_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num)
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conductance_of_bilayer_model_with_disorder_array(N, M, t1, t2, phi, tc, layer_num)
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# Haldane model
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def hamiltonian_of_Haldane_model(k, N, M, t1, t2, phi, sign):
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h00 = h00_of_Haldane_model(N, M, t1, t2, phi, sign)
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h01 = h01_of_Haldane_model(N, M, t1, t2, phi, sign)
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hamiltonian = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
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return hamiltonian
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def h00_of_Haldane_model(N, M, t1, t2, phi, sign):
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h00 = np.zeros((4*N, 4*N), dtype=complex)
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for i0 in range(N):
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h00[i0*4+0, i0*4+0] = M
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h00[i0*4+1, i0*4+1] = -M
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h00[i0*4+2, i0*4+2] = M
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h00[i0*4+3, i0*4+3] = -M
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h00[i0*4+0, i0*4+1] = t1
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h00[i0*4+1, i0*4+0] = t1
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h00[i0*4+1, i0*4+2] = t1
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h00[i0*4+2, i0*4+1] = t1
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h00[i0*4+2, i0*4+3] = t1
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h00[i0*4+3, i0*4+2] = t1
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h00[i0*4+0, i0*4+2] = t2*cmath.exp(1j*phi*sign)
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h00[i0*4+2, i0*4+0] = h00[i0*4+0, i0*4+2].conj()
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h00[i0*4+1, i0*4+3] = t2*cmath.exp(1j*phi*sign)
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h00[i0*4+3, i0*4+1] = h00[i0*4+1, i0*4+3].conj()
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for i0 in range(N-1):
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h00[i0*4+3, (i0+1)*4+0] = t1
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h00[(i0+1)*4+0, i0*4+3] = t1
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h00[i0*4+2, (i0+1)*4+0] = t2*cmath.exp(-1j*phi*sign)
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h00[(i0+1)*4+0, i0*4+2] = h00[i0*4+2, (i0+1)*4+0].conj()
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h00[i0*4+3, (i0+1)*4+1] = t2*cmath.exp(-1j*phi*sign)
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h00[(i0+1)*4+1, i0*4+3] = h00[i0*4+3, (i0+1)*4+1].conj()
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return h00
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def h01_of_Haldane_model(N, M, t1, t2, phi, sign):
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h01 = np.zeros((4*N, 4*N), dtype=complex)
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for i0 in range(N):
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h01[i0*4+1, i0*4+0] = t1
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h01[i0*4+2, i0*4+3] = t1
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h01[i0*4+0, i0*4+0] = t2*cmath.exp(-1j*phi*sign)
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h01[i0*4+1, i0*4+1] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+2, i0*4+2] = t2*cmath.exp(-1j*phi*sign)
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h01[i0*4+3, i0*4+3] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+1, i0*4+3] = t2*cmath.exp(-1j*phi*sign)
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h01[i0*4+2, i0*4+0] = t2*cmath.exp(1j*phi*sign)
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if i0 != 0:
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h01[i0*4+1, (i0-1)*4+3] = t2*cmath.exp(-1j*phi*sign)
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for i0 in range(N-1):
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h01[i0*4+2, (i0+1)*4+0] = t2*cmath.exp(1j*phi*sign)
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return h01
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# modified_Haldane_model
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def hamiltonian_of_modified_Haldane_model(k, N, M, t1, t2, phi, sign):
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h00 = h00_of_modified_Haldane_model(N, M, t1, t2, phi, sign)
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h01 = h01_of_modified_Haldane_model(N, M, t1, t2, phi, sign)
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hamiltonian = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
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return hamiltonian
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def h00_of_modified_Haldane_model(N, M, t1, t2, phi, sign):
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h00 = np.zeros((4*N, 4*N), dtype=complex)
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for i0 in range(N):
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h00[i0*4+0, i0*4+0] = M
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h00[i0*4+1, i0*4+1] = -M
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h00[i0*4+2, i0*4+2] = M
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h00[i0*4+3, i0*4+3] = -M
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h00[i0*4+0, i0*4+1] = t1
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h00[i0*4+1, i0*4+0] = t1
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h00[i0*4+1, i0*4+2] = t1
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h00[i0*4+2, i0*4+1] = t1
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h00[i0*4+2, i0*4+3] = t1
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h00[i0*4+3, i0*4+2] = t1
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h00[i0*4+0, i0*4+2] = t2*cmath.exp(-1j*phi*sign)
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h00[i0*4+2, i0*4+0] = h00[i0*4+0, i0*4+2].conj()
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h00[i0*4+1, i0*4+3] = t2*cmath.exp(1j*phi*sign)
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h00[i0*4+3, i0*4+1] = h00[i0*4+1, i0*4+3].conj()
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for i0 in range(N-1):
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h00[i0*4+3, (i0+1)*4+0] = t1
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h00[(i0+1)*4+0, i0*4+3] = t1
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h00[i0*4+2, (i0+1)*4+0] = t2*cmath.exp(1j*phi*sign)
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h00[(i0+1)*4+0, i0*4+2] = h00[i0*4+2, (i0+1)*4+0].conj()
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h00[i0*4+3, (i0+1)*4+1] = t2*cmath.exp(-1j*phi*sign)
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h00[(i0+1)*4+1, i0*4+3] = h00[i0*4+3, (i0+1)*4+1].conj()
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return h00
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def h01_of_modified_Haldane_model(N, M, t1, t2, phi, sign):
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h01 = np.zeros((4*N, 4*N), dtype=complex)
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for i0 in range(N):
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h01[i0*4+1, i0*4+0] = t1
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h01[i0*4+2, i0*4+3] = t1
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h01[i0*4+0, i0*4+0] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+1, i0*4+1] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+2, i0*4+2] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+3, i0*4+3] = t2*cmath.exp(1j*phi*sign)
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h01[i0*4+1, i0*4+3] = t2*cmath.exp(-1j*phi*sign)
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h01[i0*4+2, i0*4+0] = t2*cmath.exp(-1j*phi*sign)
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if i0 != 0:
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h01[i0*4+1, (i0-1)*4+3] = t2*cmath.exp(-1j*phi*sign)
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for i0 in range(N-1):
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h01[i0*4+2, (i0+1)*4+0] = t2*cmath.exp(-1j*phi*sign)
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return h01
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# bilayer model
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def hamiltonian_of_bilayer_model(k, N, M, t1, t2, phi, tc, layer_num):
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modified_Haldane_model = hamiltonian_of_modified_Haldane_model(k=k, N=N, M=M, t1=t1, t2=t2, phi=phi, sign=1)
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Haldane_model = hamiltonian_of_Haldane_model(k=k, N=N, M=M, t1=t1, t2=t2, phi=phi, sign=1)
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hamiltonian = np.zeros((4*N*layer_num, 4*N*layer_num), dtype=complex)
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for layer in range(layer_num):
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if np.mod(layer,2) == 0:
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hamiltonian[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = modified_Haldane_model
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if np.mod(layer,2) == 1:
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hamiltonian[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = Haldane_model
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for layer in range(layer_num-1):
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for i0 in range(N):
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# AB stacking
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hamiltonian[layer*4*N+i0*4+0, (layer+1)*4*N+i0*4+1] = tc
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hamiltonian[(layer+1)*4*N+i0*4+1, layer*4*N+i0*4+0] = tc
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hamiltonian[layer*4*N+i0*4+2, (layer+1)*4*N+i0*4+3] = tc
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hamiltonian[(layer+1)*4*N+i0*4+3, layer*4*N+i0*4+2] = tc
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# # # BA stacking
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# hamiltonian[layer*4*N+i0*4+1, (layer+1)*4*N+i0*4+0] = tc
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# hamiltonian[(layer+1)*4*N+i0*4+0, layer*4*N+i0*4+1] = tc
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# hamiltonian[layer*4*N+i0*4+3, (layer+1)*4*N+i0*4+2] = tc
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# hamiltonian[(layer+1)*4*N+i0*4+2, layer*4*N+i0*4+3] = tc
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# # AA stacking
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# hamiltonian[layer*4*N+i0*4+0, (layer+1)*4*N+i0*4+0] = tc
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# hamiltonian[(layer+1)*4*N+i0*4+0, layer*4*N+i0*4+0] = tc
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# hamiltonian[layer*4*N+i0*4+1, (layer+1)*4*N+i0*4+1] = tc
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# hamiltonian[(layer+1)*4*N+i0*4+1, layer*4*N+i0*4+1] = tc
|
||||||
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# hamiltonian[layer*4*N+i0*4+2, (layer+1)*4*N+i0*4+2] = tc
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||||||
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# hamiltonian[(layer+1)*4*N+i0*4+2, layer*4*N+i0*4+2] = tc
|
||||||
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# hamiltonian[layer*4*N+i0*4+3, (layer+1)*4*N+i0*4+3] = tc
|
||||||
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# hamiltonian[(layer+1)*4*N+i0*4+3, layer*4*N+i0*4+3] = tc
|
||||||
|
return hamiltonian
|
||||||
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|
||||||
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def h00_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num):
|
||||||
|
h00_modified = h00_of_modified_Haldane_model(N, M, t1, t2, phi, sign=1)
|
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|
h00_Haldane = h00_of_Haldane_model(N, M, t1, t2, phi, sign=1)
|
||||||
|
h00 = np.zeros((4*N*layer_num, 4*N*layer_num), dtype=complex)
|
||||||
|
for layer in range(layer_num):
|
||||||
|
if np.mod(layer,2) == 0:
|
||||||
|
h00[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = h00_modified
|
||||||
|
if np.mod(layer,2) == 1:
|
||||||
|
h00[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = h00_Haldane
|
||||||
|
for layer in range(layer_num-1):
|
||||||
|
for i0 in range(N):
|
||||||
|
# AB stacking
|
||||||
|
h00[layer*4*N+i0*4+0, (layer+1)*4*N+i0*4+1] = tc
|
||||||
|
h00[(layer+1)*4*N+i0*4+1, layer*4*N+i0*4+0] = tc
|
||||||
|
h00[layer*4*N+i0*4+2, (layer+1)*4*N+i0*4+3] = tc
|
||||||
|
h00[(layer+1)*4*N+i0*4+3, layer*4*N+i0*4+2] = tc
|
||||||
|
|
||||||
|
# # BA stacking
|
||||||
|
# h00[layer*4*N+i0*4+1, (layer+1)*4*N+i0*4+0] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+0, layer*4*N+i0*4+1] = tc
|
||||||
|
# h00[layer*4*N+i0*4+3, (layer+1)*4*N+i0*4+2] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+2, layer*4*N+i0*4+3] = tc
|
||||||
|
|
||||||
|
# # AA stacking
|
||||||
|
# h00[layer*4*N+i0*4+0, (layer+1)*4*N+i0*4+0] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+0, layer*4*N+i0*4+0] = tc
|
||||||
|
# h00[layer*4*N+i0*4+1, (layer+1)*4*N+i0*4+1] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+1, layer*4*N+i0*4+1] = tc
|
||||||
|
# h00[layer*4*N+i0*4+2, (layer+1)*4*N+i0*4+2] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+2, layer*4*N+i0*4+2] = tc
|
||||||
|
# h00[layer*4*N+i0*4+3, (layer+1)*4*N+i0*4+3] = tc
|
||||||
|
# h00[(layer+1)*4*N+i0*4+3, layer*4*N+i0*4+3] = tc
|
||||||
|
return h00
|
||||||
|
|
||||||
|
def h01_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num):
|
||||||
|
h01_modified = h01_of_modified_Haldane_model(N, M, t1, t2, phi, sign=1)
|
||||||
|
h01_Haldane = h01_of_Haldane_model(N, M, t1, t2, phi, sign=1)
|
||||||
|
h01 = np.zeros((4*N*layer_num, 4*N*layer_num), dtype=complex)
|
||||||
|
for layer in range(layer_num):
|
||||||
|
if np.mod(layer,2) == 0:
|
||||||
|
h01[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = h01_modified
|
||||||
|
if np.mod(layer,2) == 1:
|
||||||
|
h01[layer*4*N+0:layer*4*N+4*N, layer*4*N+0:layer*4*N+4*N] = h01_Haldane
|
||||||
|
return h01
|
||||||
|
|
||||||
|
def bands_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num):
|
||||||
|
k_array = np.linspace(0, 2*pi, 300)
|
||||||
|
hamiltonian = functools.partial(hamiltonian_of_bilayer_model, N=N, M=M, t1=t1, t2=t2, phi=phi, tc=tc, layer_num=layer_num)
|
||||||
|
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian, print_show=1)
|
||||||
|
plt, fig, ax = guan.import_plt_and_start_fig_ax(labelsize=25)
|
||||||
|
guan.plot_without_starting_fig_ax(plt, fig, ax, k_array, eigenvalue_array, xlabel='$\mathrm{k_x}$', ylabel='$\mathrm{E}$', style='k', fontsize=30, y_max=0.2, y_min=-0.2,linewidth=None, markersize=None, color=None, fontfamily='Times New Roman')
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
def conductance_of_bilayer_model_with_disorder_array(N, M, t1, t2, phi, tc, layer_num):
|
||||||
|
h00 = h00_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num)
|
||||||
|
h01 = h01_of_bilayer_model(N, M, t1, t2, phi, tc, layer_num)
|
||||||
|
fermi_energy = 0
|
||||||
|
disorder_intensity_array = np.arange(0, 2.5, .05)
|
||||||
|
conductance_array = guan.calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, disorder_intensity_array, length=100, calculation_times=3, print_show=1) # length=2000, calculation_times=20
|
||||||
|
guan.plot(disorder_intensity_array, conductance_array, xlabel='$\mathrm{W_d}$', ylabel='$\mathrm{G(e^2/h)}$', style='o-')
|
||||||
|
|
||||||
|
if __name__ == '__main__':
|
||||||
|
main()
|
||||||
11
2024.10.21_python_format_output/python_format_output.py
Normal file
11
2024.10.21_python_format_output/python_format_output.py
Normal file
@ -0,0 +1,11 @@
|
|||||||
|
# 小数的格式化输出（浮点）
|
||||||
|
value = 3.141592653589793
|
||||||
|
print(f"pi={value:.2f}")
|
||||||
|
print("pi={:.2f}".format(value))
|
||||||
|
print("pi=%.2f" % value)
|
||||||
|
|
||||||
|
# 整数的格式化输出
|
||||||
|
value = 13
|
||||||
|
print(f"a={value:5d}")
|
||||||
|
print("a={:5d}".format(value))
|
||||||
|
print("a=%5d" % value)
|
||||||
Loading…
x
Reference in New Issue
Block a user