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Create Kane_Mele_model.m

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guanjihuan 2021-12-09 12:13:22 +08:00
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academic_codes/2020.06.26_Hamiltonian_and_bands_of_Kane_Mele_model_without considering_Rashba_SOC/Kane_Mele_model.m Normal file
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% Purpose: Plot Kane-Mele's bands
% Date: Dec 07, 2021 @HNU
% Author: Ji-Huan Guan;
% Modify by Zhong-Fu Li;
% More code can be found in https://www.guanjihuan.com/
close all
clc
clear all
tic;
k0 = linspace(0,2*pi,100);
for kk = 1:100
k = k0(kk);
H1 = HH(k);
[VV,DD] = eig(H1);
Ds(:,kk) = sort(diag(DD),'ascend'); % sort eigenvalue
end
plot(k0/2/pi,Ds,'k.');
ylim([-1 1])
set(gca,'xtick',[0:0.5:1])
set(gca,'XTickLabel',{'\bf 0','\bf \pi','\bf 2\pi'})
set(gcf,'color','w');
set(gca,'fontsize',16,'LineWidth',1.1);
ylabel('Energy(a.u.)','fontname','Arial');
toc
% define Hamiltonian
function H = HH(k)
N = 10;
M = 0;
t1 = 1;
t2 = 0.03;
phi = pi/2;
h00 = zeros(2 * 4 * N, 2 * 4 * N);
h01 = zeros(2 * 4 * N, 2 * 4 * N);
for spin = 1:2
for ii = 0:N-1
% nearest neighbor couplings
h00(ii * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 1 * 2 + spin) = t1;
h00(ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 0 * 2 + spin) = t1;
h00(ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin) = t1;
h00(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 1 * 2 + spin) = t1;
h00(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t1;
h00(ii * 4 * 2 + 3 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin) = t1;
%next nearest neighbor couplings
h00(ii * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin) = t2 * exp(-1j * phi) * sign_spin(spin);
h00(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 0 * 2 + spin) = conj(h00(...
ii * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin));
h00(ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t2 * exp(-1j * phi) * sign_spin(spin);
h00(ii * 4 * 2 + 3 * 2 + spin, ii * 4 * 2 + 1 * 2 + spin) = conj(h00(...
ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin));
%
end
for ii = 0:N-2
% nearest neighbor couplings
h00(ii * 4 * 2 + 3 * 2 + spin, (ii + 1) * 4 * 2 + 0 * 2 + spin) = t1;
h00((ii + 1) * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t1;
% next nearest neighbor couplings
h00(ii * 4 * 2 + 2 * 2 + spin, (ii + 1) * 4 * 2 + 0 * 2 + spin) = t2 *exp(1j * phi) * sign_spin(spin);
h00((ii + 1) * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin) = conj(h00(...
ii * 4 * 2 + 2 * 2 + spin, (ii + 1) * 4 * 2 + 0 * 2 + spin));
h00(ii * 4 * 2 + 3 * 2 + spin, (ii + 1) * 4 * 2 + 1 * 2 + spin) = t2 * exp(1j * phi) * sign_spin(spin);
h00((ii + 1) * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = conj(h00(...
ii * 4 * 2 + 3 * 2 + spin, (ii + 1) * 4 * 2 + 1 * 2 + spin) );
end
% hopping of intercell h01
for ii = 0:N-1
% nearest neighbor couplings
h01(ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 0 * 2 + spin) = t1;
h01(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t1;
% next nearest neighbor couplings
h01(ii * 4 * 2 + 0 * 2 + spin, ii * 4 * 2 + 0 * 2 + spin) = t2 * exp(1j * phi) * sign_spin(spin);
h01(ii * 4 * 2 + 1 * 2 + spin, ii* 4 * 2 + 1 * 2 + spin) = t2 * exp(-1j * phi) * sign_spin(spin);
h01(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 2 * 2 + spin) = t2 * exp(1j * phi) * sign_spin(spin);
h01(ii * 4 * 2 + 3 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t2 * exp(-1j * phi) * sign_spin(spin);
h01(ii * 4 * 2 + 1 * 2 + spin, ii * 4 * 2 + 3 * 2 + spin) = t2 * exp(1j * phi) * sign_spin(spin);
h01(ii * 4 * 2 + 2 * 2 + spin, ii * 4 * 2 + 0 * 2 + spin) = t2 * exp(-1j * phi) * sign_spin(spin);
if ii ~= 0
h01(ii * 4 * 2 + 1 * 2 + spin, (ii - 1) * 4 * 2 + 3 * 2 + spin) = t2 * exp(1j * phi) * sign_spin(spin);
end
end
for ii = 0:N-2
h01(ii * 4 * 2 + 2 * 2 + spin, (ii + 1) * 4 * 2 + 0 * 2 + spin) = t2 *exp(-1j * phi) * sign_spin(spin);
end
end
H = h00 + h01 * exp(1j * k) + h01' * exp(-1j * k);
end
function sign = sign_spin(spin)
if spin == 0
sign = 1;
else
sign = -1;
end
end