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TBG.m
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classdef TBG < handle
%UNTITLED3 Summary of this class goes here
% Detailed explanation goes here
properties
theta = 0;
m=1;
n=1;
a0=1;
c0=3;
a;
A; % Superlattice lattice vectors
B; % Reciprocal lattice vectors
p; % p(:,:,1) and p(:,:,2) are the coordinates lattice points on layer 1 and 2 respectively
c; % c(:,:,1), c(:,:,2) are atom coordinates on layer 1 and 2
hintra; % Cell array storing adjacent vectors and hopping energy
hinter;
N;
A0; % Hopping cutoff distance
Vpi=-2.7;
Vsigma=0.48; % Hopping energy for pi and sigma bonding
%Vsigma=0;
delta; % Hopping energy decaying discance
MAXK=50; % Max hopping neighbors
H0;
end
methods
function tbg = TBG(n, m, varargin)
tbg.a0 = 0.142/197;
tbg.A0 = 4.01*tbg.a0;
tbg.delta = 0.184*tbg.a0;
tbg.c0 = 0.335/197;
tbg.n = n;
tbg.m = m;
tbg.theta = acos((n^2+4*m*n+m^2)/(2*(n^2+n*m+m^2)))*sign(n-m);
a1 = [1.5; -0.5*sqrt(3)] * tbg.a0;
a2 = [1.5; 0.5*sqrt(3)] * tbg.a0;
R1 = [cos(tbg.theta/2), -sin(tbg.theta/2); sin(tbg.theta/2), cos(tbg.theta/2)];
R2 = [cos(tbg.theta/2), sin(tbg.theta/2); -sin(tbg.theta/2), cos(tbg.theta/2)];
A1 = R1 * ( n*a1 + m*a2);
A2 = R1 * (-m*a1 + (n+m)*a2);
B1 = 2*pi/sum(cross([A1;0],[A2;0]))*cross([A2;0],[0;0;1]);B1 = B1(1:2);
B2 = 2*pi/sum(cross([A1;0],[A2;0]))*cross([0;0;1],[A1;0]);B2 = B2(1:2);
a11 = R1 * a1;
a21 = R1 * a2;
a12 = R2 * a1;
a22 = R2 * a2;
tbg.A = [A1, A2];
tbg.B = [B1, B2];
tbg.a = [a1, a2];
p1 = find_points(tbg, n, m, a11, a21);
p2 = find_points(tbg, m, n, a12, a22);
assert(size(p1,1) == n^2+m^2+n*m);
assert(size(p2,1) == n^2+m^2+n*m);
tbg.p(:,:,1) = p1;
tbg.p(:,:,2) = p2;
tbg.N = n^2+m^2+n*m;
T = inv(tbg.A); % Transformation from real coordinates to lattice coordinates
c1 = [tbg.p(:,:,1) + 1/3 * repmat((a11 + a21)',tbg.N,1);tbg.p(:,:,1) - 1/3 * repmat((a11 + a21)',tbg.N,1)]; % Real coordinates of atoms in layer 1
% c2 = [tbg.p(:,:,2);tbg.p(:,:,2) - 1/3 * repmat((a12 + a22)',tbg.N,1)]; % and layer 2 (Bernal-stacked when theta=0)
c2 = [tbg.p(:,:,2) + 1/3 * repmat((a12 + a22)',tbg.N,1);tbg.p(:,:,2) - 1/3 * repmat((a12 + a22)',tbg.N,1)]; % and layer 2 (Bernal-stacked when theta=0)
C1 = mod(c1*T', 1); % Transform to lattice coordinates and move everything back to the unit cell
C2 = mod(c2*T', 1);
tbg.c(:,:,1) = C1*tbg.A'; % Transform back to real coordinates
tbg.c(:,:,2) = C2*tbg.A';
if nargin==2 || varargin{1}
calcHopping(tbg);
end
disp('Twisted bilayer graphene initialized');
disp(['Twist angle: ',num2str(tbg.theta/pi*180),' degrees']);
disp(['Superlattice potential period: ',num2str(norm(A1)*197/abs(n-m)),' nm']);
end
function [E, P]=getDispersion(tbg, kx, ky, V1, V2)
NK = numel(kx); % Number of k points
kx=kx(:);% reshape different k values to the first dimension
ky=ky(:);
k=[kx,ky];
if V1~=0
% add external potential
H=repmat(shiftdim(diag([repmat(-V1/2,2*tbg.N,1);repmat(V1/2,2*tbg.N,1)]),-1),[NK,1,1]);
else
H=zeros(NK, 4*tbg.N, 4*tbg.N);
end
if(V2~=0)
% V2 adds a asymmetry to the sublattice
% Use this for adding the same amount to both layers
%H=H + repmat(shiftdim(diag([repmat(-V2/2,tbg.N,1);repmat(V2/2,tbg.N,1);repmat(-V2/2,tbg.N,1);repmat(V2/2,tbg.N,1)]),-1),[NK,1,1]);
% Use this to add only to one layer, i.e. graphene/h-BN
H=H + repmat(shiftdim(diag([repmat(-V2/2,tbg.N,1);repmat(V2/2,tbg.N,1);zeros(tbg.N,1);zeros(tbg.N,1)]),-1),[NK,1,1]);
end
H=double(H); % Truncate precision to save memory
% hop: p*2 array (p is number of neighbors). pos: index of
% current atom. layer: index of current layer (0 or 1)
function map(hop, pos, layer1, layer2)
%H(:, pos+layer1*2*tbg.N, hop(:,1)+layer2*2*tbg.N) = ...
% H(:, pos+layer1*2*tbg.N, hop(:,1)+layer2*2*tbg.N) + reshape(exp(1i*(k*hop(:,3:4)')).*repmat(hop(:,2)',NK,1), NK, 1, []);
%disp([num2str(pos),',',num2str(layer1),',',num2str(layer2)]);
for j=1:size(hop,1)
H(:, pos+layer1*2*tbg.N, hop(j,1)+layer2*2*tbg.N) = ...
H(:, pos+layer1*2*tbg.N, hop(j,1)+layer2*2*tbg.N) + exp(1i*(k*hop(j,3:4)'))*hop(j,2);
end
end
fprintf('Map 1\n');
cellfun(@map, tbg.hintra(:,1), num2cell((1:2*tbg.N)'), num2cell(zeros(2*tbg.N,1)), num2cell(zeros(2*tbg.N,1))); % Map intralayer hoppings to the upper-left quadrant of the hamiltonian
fprintf('Map 2\n');
cellfun(@map, tbg.hintra(:,2), num2cell((1:2*tbg.N)'), num2cell(ones(2*tbg.N,1)), num2cell(ones(2*tbg.N,1))); % Map intralayer hoppings to the lower-right quadrant of the hamiltonian
fprintf('Map 3\n');
cellfun(@map, tbg.hinter(:,1), num2cell((1:2*tbg.N)'), num2cell(zeros(2*tbg.N,1)), num2cell(ones(2*tbg.N,1))); % Map interlayer hoppings to the upper-right quadrant of the hamiltonian
fprintf('Map 4\n');
cellfun(@map, tbg.hinter(:,2), num2cell((1:2*tbg.N)'), num2cell(ones(2*tbg.N,1)), num2cell(zeros(2*tbg.N,1))); % Map interlayer hoppings to the lower-left quadrant of the hamiltonian
fprintf('Hermitianize\n');
H = (H + conj(permute(H,[1,3,2])))/2; % Force H to be hermitian, so that the eigen problem can be solved MUCH FASTER
%tbg.H0=H;
disp('Hamiltonian Constructed and Hermitianized');
% Now we have the Hamiltonian. Solve it! (for each k)
E = double(zeros(NK, 4*tbg.N));
P = double(zeros(NK, 4*tbg.N, 4*tbg.N));
%E = zeros(NK, 20);
for i=1:NK
starttime=datetime;
fprintf('%d start...',i);
[V1,D]=eig(squeeze(H(i,:,:)));
[E(i,:), I] = sort(real(diag(D)));
P(i,:,:) = V1(:, I);
fprintf('ended in');
disp(datetime-starttime);
end
end
% Get eigenvalue and eigen state at a specified k point
% Input is fraction of reciprocal lattice vector
function D=getState(tbg, skx, sky, V1, V2)
K = tbg.B(:,1) * skx + tbg.B(:,2) * sky;
[D.E, D.P] = tbg.getDispersion(K(1), K(2), V1, V2);
end
% Get dispersion in the first Brillouin zone
function D=getBrillouin(tbg, res, div, V1, V2, saveState)
B1 = tbg.B(:,1);
B2 = tbg.B(:,2);
% [px,py] = meshgrid(linspace(0,1,res),linspace(0,1,res));
% kx = px * B1(1) + py * B2(1);
% ky = px * B1(2) + py * B2(2);
% D.kx = kx;
% D.ky = ky;
% D.E = tbg.getDispersion(kx,ky,V);
K = 2/3 * [1;0] + 1/3 * [-1/2;sqrt(3)/2];
Kp = 1/3 * [1;0] + 2/3 * [-1/2;sqrt(3)/2];
%pv=[K,[0;0],[0.5;0],K]';
%pv=[[0;0],[1;0],[0.5;sqrt(3)/2],[-0.5;sqrt(3)/2],[0;0]]';
pv=[K,Kp,[-K(1);K(2)],-K,-Kp,[K(1);-K(2)],K]';
%fh=@(p,a) min(min(0.5/res+5/res*abs(dcircle(p,K(1),K(2),0)),0.5/res+5/res*abs(dcircle(p,Kp(1),Kp(2),0))), 5/res);
fh=@(p,a) min(min(min(min(min(min(min(...
0.5/res+5/res*abs(dcircle(p,K(1),K(2),0)),...
0.5/res+5/res*abs(dcircle(p,Kp(1),Kp(2),0))),...
0.5/res+5/res*abs(dcircle(p,-K(1),K(2),0))),...
0.5/res+5/res*abs(dcircle(p,-K(1),-K(2),0))),...
0.5/res+5/res*abs(dcircle(p,-Kp(1),-Kp(2),0))),...
0.5/res+5/res*abs(dcircle(p,K(1),-K(2),0))),...
0.5/res+5/res*abs(dcircle(p,0,0,0))),...
5/res);
[pt,tri]=distmesh2d(@dpoly,fh,0.5/res, [-0.5,-sqrt(3)/3;0.5,sqrt(3)/3], pv, pv);
T1 = [1, -1/2; 0, sqrt(3)/2];
T2 = [B1, B2];
k = T2 / T1 * pt';
kx = k(1,:)';
ky = k(2,:)';
D.kx = kx;
D.ky = ky;
D.fn=@(p) dpoly(p, pv);
triplot(tri,kx,ky);
fprintf('# of points: %d\n', length(kx));
if div == 0
if(saveState)
[D.E, D.P] = tbg.getDispersion(kx,ky,V1,V2);
else
[D.E, ~] = tbg.getDispersion(kx,ky,V1,V2);
end
else
i=1;
D.E = double(zeros(length(kx), 4*tbg.N));
if(saveState)
D.P = double(zeros(length(kx), 4*tbg.N, 4*tbg.N));
end
while i<=length(kx)
if(saveState)
[D.E(i:min(i+div-1,length(kx)), :),D.P(i:min(i+div-1,length(kx)), :, :)] = tbg.getDispersion(kx(i:min(i+div-1,length(kx))), ky(i:min(i+div-1,length(kx))), V1);
else
[D.E(i:min(i+div-1,length(kx)), :),~] = tbg.getDispersion(kx(i:min(i+div-1,length(kx))), ky(i:min(i+div-1,length(kx))), V1, V2);
end
i = i+div;
fprintf('%g%% finished\n', max(i,length(kx))/length(kx)*100);
end
end
D.B = tbg.B;
D.t = tri;
%D.E = reshape(D.E, length(kx), []);
plotDispersion(D);
end
% Get dispersion on high symmetrical points and lines
function D=getHighSymmetrical(tbg, res, div, V1, V2)
B1 = tbg.B(:,1);
B2 = tbg.B(:,2);
K = (2/3 * B1 + 1/3 * B2)';
Kp = (1/3 * B1 + 2/3 * B2)';
Gamma = [0,0];
M = (K + Kp) / 2;
t=linspace(0,1,res+1)'; t=t(1:end-1);
% K -- Gamma
kxy = repmat(K, res, 1) + t * (Gamma - K);
T = t * norm(Gamma - K);
% Gamma -- M
kxy = [kxy ; repmat(Gamma, res, 1) + t * (M - Gamma)];
T = [T; norm(Gamma - K) + t * norm(M - Gamma)];
% M -- Kp
kxy = [kxy ; repmat(M, res, 1) + t * (Kp - M)];
T = [T; norm(Gamma - K) + norm(M - Gamma) + t * norm(Kp - M)];
% Kp
kxy = [kxy ; Kp];
T = [T; norm(Gamma - K) + norm(M - Gamma) + norm(Kp - M)];
kx = kxy(:,1);
ky = kxy(:,2);
i=1;
D.E = zeros(size(kx,1), 4*tbg.N);
while i<=size(kx,1)
[D.E(i:min(i+div-1,size(kx,1)), :),~] = tbg.getDispersion(kx(i:min(i+div-1,size(kx,1))), ky(i:min(i+div-1,size(kx,1))), V1, V2);
i = i + div;
end
D.kx = kx;
D.ky = ky;
D.t = T;
plotHighSymmetric(D);
end
% find all possible lattice coordinates in a superlattice. Basic
% idea: In a TBG, the SUPERLATTICE BASE VECTORS corresponds to (n,
% m) and (-m, n+m) in LAYER 1 (rotated counterclockwise for
% theta/2). It corresponds to (m,n) and (-n, n+m) in LAYER 2
% (rotated clockwise for theta/2). The purpose of this function is
% to find out what possible combinations of (n',m') are inside the
% region defined by the superlattice base vectors. The result
% should contain exactly n^2+m^2+nm points. For LAYER 1, pass n, m
% to this function and m, n for LAYER 2. a1 and a2 should be set to
% the base vector of the corresponding layer.
function points = find_points(~, p, q, a1, a2)
% P and Q stores all possible points in lattice coordinates
[P, Q] = meshgrid(-q:p, 0:(p+2*q));
r = p^2 + q^2 + p*q;
% The linear transformation transforms the permitted area into
% a unit square
P1 = ((p+q) * P + q * Q) ./ r;
Q1 = ( -q * P + p * Q) ./ r;
% Now rule out those points that are not in the unit square
% after transformation
In = (P1 >= 0) & (P1 < 1)...
& (Q1 >= 0) & (Q1 < 1);
% Convert the lattice coordinates back to real coordinates
% using provided base vector
points = P(In) * a1' + Q(In) * a2';
disp('Complete');
end
function calcHopping(tbg)
tbg.hinter = cell(2*tbg.N,2);% (i,j,k) i: atom index j: index/distance k:layer index
tbg.hintra = cell(2*tbg.N,2);
A1 = tbg.A(:,1)';
A2 = tbg.A(:,2)';
E1 = [tbg.c(:,:,1);...
tbg.c(:,:,1)+repmat(A1, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(A1+A2, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(A1-A2, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(A2, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(-A2, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(-A1, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(-A1-A2, 2*tbg.N, 1);...
tbg.c(:,:,1)+repmat(-A1+A2, 2*tbg.N, 1);...
];
E2 = [tbg.c(:,:,2);...
tbg.c(:,:,2)+repmat(A1, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(A1+A2, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(A1-A2, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(A2, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(-A2, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(-A1, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(-A1-A2, 2*tbg.N, 1);...
tbg.c(:,:,2)+repmat(-A1+A2, 2*tbg.N, 1);...
];
[idx11, d11] = knnsearch(E1, tbg.c(:,:,1), 'K', tbg.MAXK+1);
[idx22, d22] = knnsearch(E2, tbg.c(:,:,2), 'K', tbg.MAXK+1);
[idx12, d12] = knnsearch(E2, tbg.c(:,:,1), 'K', tbg.MAXK);
[idx21, d21] = knnsearch(E1, tbg.c(:,:,2), 'K', tbg.MAXK);
d12 = sqrt(d12.^2 + tbg.c0^2);
d21 = sqrt(d21.^2 + tbg.c0^2);
C11 = cat(3, mod(idx11(:,2:end)-1, 2*tbg.N)+1, d11(:,2:end), reshape(E1(reshape(idx11(:,2:end),[],1), :)-tbg.c(repmat((1:2*tbg.N)',size(idx11,2)-1,1),:,1), 2*tbg.N, [], 2));
C22 = cat(3, mod(idx22(:,2:end)-1, 2*tbg.N)+1, d22(:,2:end), reshape(E2(reshape(idx22(:,2:end),[],1), :)-tbg.c(repmat((1:2*tbg.N)',size(idx22,2)-1,1),:,2), 2*tbg.N, [], 2));
C12 = cat(3, mod(idx12-1, 2*tbg.N)+1, d12, reshape(E2(reshape(idx12,[],1), :)-tbg.c(repmat((1:2*tbg.N)',size(idx12,2),1),:,1), 2*tbg.N, [], 2));
C21 = cat(3, mod(idx21-1, 2*tbg.N)+1, d21, reshape(E1(reshape(idx21,[],1), :)-tbg.c(repmat((1:2*tbg.N)',size(idx21,2),1),:,2), 2*tbg.N, [], 2));
cell11 = cellfun(@(X) num2cell(squeeze(X(1,X(1,:,2)<tbg.A0,:)),[1,2]), num2cell(C11, [2,3])); % Each row is combined into a cell, and filtered with A0
cell22 = cellfun(@(X) num2cell(squeeze(X(1,X(1,:,2)<tbg.A0,:)),[1,2]), num2cell(C22, [2,3])); % Each row is combined into a cell, and filtered with A0
cell12 = cellfun(@(X) num2cell(squeeze(X(1,X(1,:,2)<tbg.A0,:)),[1,2]), num2cell(C12, [2,3])); % Each row is combined into a cell, and filtered with A0
cell21 = cellfun(@(X) num2cell(squeeze(X(1,X(1,:,2)<tbg.A0,:)),[1,2]), num2cell(C21, [2,3])); % Each row is combined into a cell, and filtered with A0
function out=intrahop(in) % convert distance to hopping energy
in(:,2)=tbg.Vpi*exp(-(in(:,2)-tbg.a0)./tbg.delta); % Only pi bonding in intralayer hopping
out=num2cell(in, [1,2]);
end
function out=interhop(in) % convert distance to hopping energy
in(:,2)=tbg.Vpi*exp(-(in(:,2)-tbg.a0)./tbg.delta).*(1 - (tbg.c0./in(:,2)).^2)... % PI bonding in intralayer hopping
+tbg.Vsigma*exp(-(in(:,2)-tbg.c0)./tbg.delta).*(tbg.c0./in(:,2)).^2;
out=num2cell(in, [1,2]);
end
cell11 = cellfun(@intrahop, cell11);
cell22 = cellfun(@intrahop, cell22);
cell12 = cellfun(@interhop, cell12);
cell21 = cellfun(@interhop, cell21);
tbg.hintra(:, 1) = cell11; % The first element is always itself for intralayer. Remove it
tbg.hintra(:, 2) = cell22;
tbg.hinter(:, 1) = cell12;
tbg.hinter(:, 2) = cell21;
end
function plot(tbg)
% N = tbg.n+tbg.m;
% a = tbg.a0;
% th = tbg.theta;
% R1 = [cos(th/2), -sin(th/2); sin(th/2), cos(th/2)];
% R2 = [cos(th/2), sin(th/2); -sin(th/2), cos(th/2)];
% c1 = 1.5 * a;
% c2 = sqrt(3) / 2 * a;
% c3 = 0.5 * a;
% figure;
% axis equal tight;
% hold on;
% for i=-max(tbg.n, tbg.m)-2:max(tbg.n, tbg.m)+2
% for j=-2:2*N
% % Convert lattice coordinate to space coordinate
% x = c1 * double(i + j);
% y = c2 * double(j - i);
% p1 = [x;y] + [-a; 0];
% p2 = [x;y] + [-c3; c2];
% p3 = [x;y] + [c3; c2];
% p4 = [x;y] + [a; 0];
% line1 = [R1*p1, R1*p2, R1*p3, R1*p4];
% line2 = [R2*p1, R2*p2, R2*p3, R2*p4];
% plot(line1(1,:), line1(2,:), 'k', line2(1,:), line2(2,:), 'k');
% end
% end
%
t1 = tbg.A(:,1);
t2 = tbg.A(:,2);
% plot([0; t1(1)], [0; t1(2)], 'g', 'LineWidth', 1.5);
% plot([0; t2(1)], [0; t2(2)], 'g', 'LineWidth', 1.5);
% plot([t1(1); t1(1) + t2(1)], [t1(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
% plot([t2(1); t1(1) + t2(1)], [t2(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
% hold off
figure
axis equal tight
title 'Lattice Positions'
hold on
plot([0; t1(1)], [0; t1(2)], 'g', 'LineWidth', 1.5);
plot([0; t2(1)], [0; t2(2)], 'g', 'LineWidth', 1.5);
plot([t1(1); t1(1) + t2(1)], [t1(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
plot([t2(1); t1(1) + t2(1)], [t2(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
scatter(tbg.p(:,1,1), tbg.p(:,2,1),36, 'red');
scatter(tbg.p(:,1,2), tbg.p(:,2,2),36, 'blue');
hold off;
figure
axis equal tight
title 'Atom Positions'
hold on
plot([0; t1(1)], [0; t1(2)], 'g', 'LineWidth', 1.5);
plot([0; t2(1)], [0; t2(2)], 'g', 'LineWidth', 1.5);
plot([t1(1); t1(1) + t2(1)], [t1(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
plot([t2(1); t1(1) + t2(1)], [t2(2); t1(2) + t2(2)], 'g', 'LineWidth', 1.5);
plot([(t1(1)+t2(1))/3; (t1(1)+t2(1))*2/3], [(t1(2)+t2(2))/3; (t1(2)+t2(2))*2/3], 'b', 'LineWidth', 1.5);
plot([t1(1); t2(1)], [t1(2); t2(2)], 'b', 'LineWidth', 1.5);
scatter3(tbg.c(:,1,1), tbg.c(:,2,1),zeros(tbg.N*2,1),36, 'r^');
scatter3(tbg.c(:,1,2), tbg.c(:,2,2),repmat(tbg.c0,tbg.N*2,1),36, 'blue');
hold off;
TBG.plotadj(tbg.c(:,:,1),tbg.c(:,:,1),tbg.hintra(:,1),0,'Layer 1 intra');
TBG.plotadj(tbg.c(:,:,2),tbg.c(:,:,2),tbg.hintra(:,2),0,'Layer 2 intra');
TBG.plotadj(tbg.c(:,:,1),tbg.c(:,:,2),tbg.hinter(:,1),1,'Layer 1 -> 2 inter');
TBG.plotadj(tbg.c(:,:,2),tbg.c(:,:,1),tbg.hinter(:,2),1,'Layer 2 -> 1 inter');
figure
title 'Brillouin Zone'
hold on
axis equal tight
K1=K(tbg.a0,tbg.theta/2);
K2=K(tbg.a0,-tbg.theta/2);
for i=1:6
K1n=[0.5,-0.5*sqrt(3); 0.5*sqrt(3), 0.5]*K1;
K2n=[0.5,-0.5*sqrt(3); 0.5*sqrt(3), 0.5]*K2;
plot([K1(1),K1n(1)],[K1(2),K1n(2)],'r');
plot([K2(1),K2n(1)],[K2(2),K2n(2)],'b');
K1=K1n;
K2=K2n;
end
kc=K(tbg.a0,tbg.theta/2)-tbg.B(:,1)*2/3-tbg.B(:,2)/3;
Ks=tbg.B(:,1)*2/3+tbg.B(:,2)/3;
for i=1:6
Ksn=[0.5,-0.5*sqrt(3); 0.5*sqrt(3), 0.5]*Ks;
plot([Ks(1)+kc(1),Ksn(1)+kc(1)],[Ks(2)+kc(2),Ksn(2)+kc(2)],'g','LineWidth',1.5);
Ks=Ksn;
end
hold off
end
end
methods(Static)
function plotadj(c1,c2,h,inter,tit)
figure
axis equal tight
title(tit);
hold on
for i=1:size(c1,1)
adj = cell2mat(h(i)); % Index of layer 1 intralayer adjacents
x=c1(i,1);
y=c1(i,2);
quiver(repmat(x,size(adj,1),1), repmat(y,size(adj,1),1), adj(:,2).*adj(:,3), adj(:,2).*adj(:,4),0.3+inter*2);
end
scatter(c2(:,1), c2(:,2),36, 'red');
if inter
scatter(c1(:,1), c1(:,2),24, 'blue');
end
hold off
end
end
end