# coding: utf-8 # In[1]: translations_dir = '/l/necadam1/translations-precalc/diracpoints-newdata/222' TMatrix_file ='/m/home/home4/46/necadam1/unix/tmatrix-experiments/twisted_triangle/silver/twisted_triangle.TMatrix.nonan' pdfout = '/m/home/home4/46/necadam1/unix/tmp/pdf_out/inv-2-mag10-10.pdf' hexside = 375e-9 epsilon_b = 2.3104 gaussianSigma = None # hexside * 222 / 7 factor13inc = 10 factor13scat=10 ops = ( # co, typ operace (symetrizace / transformace / kopie), specifikace (operace nebo zdroj), # co: 0, 1, (0,1), (0,), (1,), #NI: 'all' # typ operace: sym, tr, copy # specifikace: # sym, tr: 'σ_z', 'σ_y', 'C2'; sym: 'C3', # copy: 0, 1 (zdroj) ((0,1), 'sym', 'σ_z'), #((0,1), 'sym', 'σ_x'), #((0,1), 'sym', 'σ_y'), ((0,1), 'sym', 'C3'), ((1), 'tr', 'C2'), ) interpfreqfactor = 0.5 import qpms import numpy as np import os, sys import warnings import math from matplotlib import pyplot as plt from matplotlib.backends.backend_pdf import PdfPages from scipy.constants import hbar, e as eV, pi, c from scipy import interpolate nx = None s3 = math.sqrt(3) pdf = PdfPages(pdfout) # In[2]: #TODO později #import argparse #parser = argparse.ArgumentParser() #parser.add_argument('--sym', 'mz', 'my', 'mx', 'C3', 'C2' type=str, help='symmetrize both particles') #args = parser.parse_args() # In[3]: # specifikace T-matice zde cdn = c/ math.sqrt(epsilon_b) TMatrices_orig, freqs_orig, freqs_weirdunits_orig, lMax = qpms.loadScuffTMatrices(TMatrix_file) my, ny = qpms.get_mn_y(lMax) nelem = len(my) ž = np.arange(2*nelem) tž = ž // nelem mž = my[ž%nelem] nž = ny[ž%nelem] TEž = ž[(mž+nž+tž) % 2 == 0] TMž = ž[(mž+nž+tž) % 2 == 1] č = np.arange(2*2*nelem) žč = č % (2* nelem) tč = tž[žč] mč = mž[žč] nč = nž[žč] TEč = č[(mč+nč+tč) % 2 == 0] TMč = č[(mč+nč+tč) % 2 == 1] TMatrices = np.array(np.broadcast_to(TMatrices_orig[:,nx,:,:,:,:],(len(freqs_orig),2,2,nelem,2,nelem)) ) TMatrices[:,:,:,:,:,ny==3] *= factor13inc TMatrices[:,:,:,ny==3,:,:] *= factor13scat xfl = qpms.xflip_tyty(lMax) yfl = qpms.yflip_tyty(lMax) zfl = qpms.zflip_tyty(lMax) c2rot = qpms.apply_matrix_left(qpms.yflip_yy(3),qpms.xflip_yy(3),-1) for op in ops: if op[0] == 'all': targets = (0,1) elif isinstance(op[0],int): targets = (op[0],) else: targets = op[0] if op[1] == 'sym': if op[2] == 'σ_z': for t in targets: TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2 elif op[2] == 'σ_y': for t in targets: TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2 elif op[2] == 'σ_x': for t in targets: TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)))/2 elif op[2] == 'C3': # FIXME fuj fuj fuj, použij regex!!! rotN = 3 TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_) for t in targets: for i in range(rotN): rotangle = 2*np.pi*i / rotN rot = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle])) rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle])) TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1) TMatrices[:,t] = np.sum(TMatrix_contribs, axis=0) / rotN elif op[2] == 'C2': for t in targets: TMatrices[:,t] = (TMatrices[:,t] + qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1))/2 else: raise elif op[1] == 'tr': if op[2] == 'σ_z': for t in targets: TMatrices[:,t] = qpms.apply_ndmatrix_left(zfl,qpms.apply_ndmatrix_left(zfl, TMatrices[:,t], (-4,-3)),(-2,-1)) elif op[2] == 'σ_y': for t in targets: TMatrices[:,t] = qpms.apply_ndmatrix_left(yfl,qpms.apply_ndmatrix_left(yfl, TMatrices[:,t], (-4,-3)),(-2,-1)) elif op[2] == 'σ_x': for t in targets: TMatrices[:,t] = qpms.apply_ndmatrix_left(xfl,qpms.apply_ndmatrix_left(xfl, TMatrices[:,t], (-4,-3)),(-2,-1)) elif op[2] == 'C3': # TODO use regex and generalize rotN = 3 TMatrix_contribs = np.empty((rotN,TMatrices.shape[0],2,nelem,2,nelem), dtype=np.complex_) for t in targets: for i in range(rotN): rotangle = 2*np.pi*i / rotN rot = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,rotangle])) rotinv = qpms.WignerD_yy_fromvector(lMax,np.array([0,0,-rotangle])) TMatrix_contribs[i] = qpms.apply_matrix_left(rot,qpms.apply_matrix_left(rotinv, TMatrices[:,t], -3),-1) elif op[2] == 'C2': for t in targets: TMatrices[:,t] = qpms.apply_matrix_left(c2rot,qpms.apply_matrix_left(c2rot, TMatrices[:,t], -3),-1) elif op[1] == 'copy': raise else: raise TMatrices_interp = interpolate.interp1d(freqs_orig*interpfreqfactor, TMatrices, axis=0, kind='linear',fill_value="extrapolate") # In[4]: om = np.linspace(np.min(freqs_orig), np.max(freqs_orig),100) TMatrix0ip = np.reshape(TMatrices_interp(om)[:,0], (len(om), 2*nelem*2*nelem)) f, axa = plt.subplots(2, 2, figsize=(15,15)) print(TMatrices.shape) #plt.plot(om, TMatrices[:,0,0,0,0].imag,'r',om, TMatrices[:,0,0,0,0].real,'r--',om, TMatrices[:,0,2,0,2].imag,'b',om, TMatrices[:,0,2,0,2].real,'b--')) ax = axa[0,0] ax2 = ax.twiny() ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar]) ax.plot( om, TMatrix0ip[:,:].imag,'-',om, TMatrix0ip[:,:].real,'--', ) ax = axa[0,1] ax2 = ax.twiny() ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar]) ax.plot( om, abs(TMatrix0ip[:,:]),'-' ) ax.set_yscale('log') ax = axa[1,1] ax2 = ax.twiny() ax2.set_xlim([ax.get_xlim()[0]/eV*hbar,ax.get_xlim()[1]/eV*hbar]) ax.plot( om, np.unwrap(np.angle(TMatrix0ip[:,:]),axis=0),'-' ) pdf.savefig(f) # In[ ]: kdensity = 66 bz_0 = np.array((0,0,0.,)) bz_K1 = np.array((1.,0,0))*4*np.pi/3/hexside/s3 bz_K2 = np.array((1./2.,s3/2,0))*4*np.pi/3/hexside/s3 bz_M = np.array((3./4, s3/4,0))*4*np.pi/3/hexside/s3 k0Mlist = bz_0 + (bz_M-bz_0) * np.linspace(0,1,kdensity/5)[:,nx] kMK1list = bz_M + (bz_K1-bz_M) * np.linspace(0,1,kdensity)[:,nx] kK10list = bz_K1 + (bz_0-bz_K1) * np.linspace(0,1,kdensity)[:,nx] k0K2list = bz_0 + (bz_K2-bz_0) * np.linspace(0,1,kdensity/5)[:,nx] kK2Mlist = bz_K2 + (bz_M-bz_K2) * np.linspace(0,1,kdensity/5)[:,nx] B1 = 2* bz_K1 - bz_K2 B2 = 2* bz_K2 - bz_K1 klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0) kxmaplist = np.concatenate((np.array([0]),np.cumsum(np.linalg.norm(np.diff(klist, axis=0), axis=-1)))) # In[ ]: n2id = np.identity(2*nelem) n2id.shape = (2,nelem,2,nelem) extlistlist = list() leftmatrixlistlist = list() minsvTElistlist=list() minsvTMlistlist=list() nan = float('nan') omegalist = list() filecount = 0 for trfile in os.scandir(translations_dir): filecount += 1 try: npz = np.load(trfile.path, mmap_mode='r') k_0 = npz['precalc_params'][()]['k_hexside'] / hexside omega = k_0 * c / math.sqrt(epsilon_b) if(omega < 2.4e15 or omega > 2.7e15 ): continue except: print ("Unexpected error, trying to continue with another file:", sys.exc_info()[0]) continue try: tdic = qpms.hexlattice_precalc_AB_loadunwrap(trfile.path, return_points=True) except: print ("Unexpected error, trying to continue with another file:", sys.exc_info()[0]) continue k_0 = tdic['k_hexside'] / hexside omega = k_0 * c / math.sqrt(epsilon_b) omegalist.append(omega) print(filecount, omega/eV*hbar) a_self = tdic['a_self'][:,:nelem,:nelem] b_self = tdic['b_self'][:,:nelem,:nelem] a_u2d = tdic['a_u2d'][:,:nelem,:nelem] b_u2d = tdic['b_u2d'][:,:nelem,:nelem] a_d2u = tdic['a_d2u'][:,:nelem,:nelem] b_d2u = tdic['b_d2u'][:,:nelem,:nelem] unitcell_translations = tdic['self_tr']*hexside*s3 u2d_translations = tdic['u2d_tr']*hexside*s3 d2u_translations = tdic['d2u_tr']*hexside*s3 if gaussianSigma: unitcell_envelope = np.exp(-np.sum(unitcell_translations**2,axis=-1)/(2*gaussianSigma**2)) u2d_envelope = np.exp(-np.sum(u2d_translations**2,axis=-1)/(2*gaussianSigma**2)) d2u_envelope = np.exp(-np.sum(d2u_translations**2,axis=-1)/(2*gaussianSigma**2)) TMatrices_om = TMatrices_interp(omega) minsvTElist = np.full((klist.shape[0]),np.nan) minsvTMlist = np.full((klist.shape[0]),np.nan) leftmatrixlist = np.full((klist.shape[0],2,2,nelem,2,2,nelem),np.nan,dtype=complex) isNaNlist = np.zeros((klist.shape[0]), dtype=bool) # sem nějaká rozumná smyčka for ki in range(klist.shape[0]): k = klist[ki] if (k_0*k_0 - k[0]*k[0] - k[1]*k[1] < 0): isNaNlist[ki] = True continue phases_self = np.exp(1j*np.tensordot(k,unitcell_translations,axes=(0,-1))) phases_u2d = np.exp(1j*np.tensordot(k,u2d_translations,axes=(0,-1))) phases_d2u = np.exp(1j*np.tensordot(k,d2u_translations,axes=(0,-1))) if gaussianSigma: phases_self *= unitcell_envelope phases_u2d *= u2d_envelope phases_d2u *= d2u_envelope leftmatrix = np.zeros((2,2,nelem, 2,2,nelem), dtype=complex) leftmatrix[0,0,:,0,0,:] = np.tensordot(a_self,phases_self, axes=(0,-1)) # u2u, E2E leftmatrix[1,0,:,1,0,:] = leftmatrix[0,0,:,0,0,:] # d2d, E2E leftmatrix[0,1,:,0,1,:] = leftmatrix[0,0,:,0,0,:] # u2u, M2M leftmatrix[1,1,:,1,1,:] = leftmatrix[0,0,:,0,0,:] # d2d, M2M leftmatrix[0,0,:,0,1,:] = np.tensordot(b_self,phases_self, axes=(0,-1)) # u2u, M2E leftmatrix[0,1,:,0,0,:] = leftmatrix[0,0,:,0,1,:] # u2u, E2M leftmatrix[1,1,:,1,0,:] = leftmatrix[0,0,:,0,1,:] # d2d, E2M leftmatrix[1,0,:,1,1,:] = leftmatrix[0,0,:,0,1,:] # d2d, M2E leftmatrix[0,0,:,1,0,:] = np.tensordot(a_d2u, phases_d2u,axes=(0,-1)) #d2u,E2E leftmatrix[0,1,:,1,1,:] = leftmatrix[0,0,:,1,0,:] #d2u, M2M leftmatrix[0,0,:,1,1,:] = np.tensordot(b_d2u, phases_d2u,axes=(0,-1)) #d2u,M2E leftmatrix[0,1,:,1,0,:] = leftmatrix[0,0,:,1,1,:] #d2u, E2M leftmatrix[1,0,:,0,1,:] = np.tensordot(b_u2d, phases_u2d,axes=(0,-1)) #u2d,M2E leftmatrix[1,1,:,0,0,:] = leftmatrix[1,0,:,0,1,:] #u2d, E2M #leftmatrix is now the translation matrix T for j in range(2): leftmatrix[j] = -np.tensordot(TMatrices_om[j], leftmatrix[j], axes=([-2,-1],[0,1])) # at this point, jth row of leftmatrix is that of -MT leftmatrix[j,:,:,j,:,:] += n2id #now we are done, 1-M leftmatrixlist[ki] = leftmatrix nnlist = np.logical_not(isNaNlist) leftmatrixlist_s = np.reshape(leftmatrixlist,(klist.shape[0], 2*2*nelem,2*2*nelem))[nnlist] leftmatrixlist_TE = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TEč,TEč)] leftmatrixlist_TM = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TMč,TMč)] minsvTElist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TE, compute_uv=False), axis=-1) minsvTMlist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TM, compute_uv=False), axis=-1) minsvTMlistlist.append(minsvTMlist) minsvTElistlist.append(minsvTElist) # In[ ]: minsvTElistarr = np.array(minsvTElistlist) minsvTMlistarr = np.array(minsvTMlistlist) omegalist = np.array(omegalist) omlist = np.broadcast_to(omegalist[:,nx], minsvTElistarr.shape) kxmlarr = np.broadcast_to(kxmaplist[nx,:], minsvTElistarr.shape) klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0) # In[ ]: import matplotlib.pyplot as plt from matplotlib.path import Path import matplotlib.patches as patches f, ax = plt.subplots(1, figsize=(20,15)) sc = ax.scatter(kxmlarr, omlist/eV*hbar, c = np.sqrt(minsvTMlistarr), s =40, lw=0) ax.plot(kxmaplist, np.linalg.norm(klist,axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1-B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1-2*B2, axis=-1)*cdn/eV*hbar, '-', # kxmaplist, np.linalg.norm(klist+2*B2-B1, axis=-1)*cdn, '-', # kxmaplist, np.linalg.norm(klist+2*B1-B2, axis=-1)*cdn, '-', ) ax.set_xlim([np.min(kxmlarr),np.max(kxmlarr)]) #ax.set_ylim([2.15,2.30]) ax.set_ylim([np.min(omlist/eV*hbar),np.max(omlist/eV*hbar)]) ax.set_xticks([0, kxmaplist[len(k0Mlist)-1], kxmaplist[len(k0Mlist)+len(kMK1list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)+len(kK2Mlist)-1]]) ax.set_xticklabels(['Γ', 'M', 'K', 'Γ', 'K\'','M']) f.colorbar(sc) pdf.savefig(f) # In[ ]: import matplotlib.pyplot as plt from matplotlib.path import Path import matplotlib.patches as patches f, ax = plt.subplots(1, figsize=(20,15)) sc = ax.scatter(kxmlarr, omlist/eV*hbar, c = np.sqrt(minsvTElistarr), s =40, lw=0) ax.plot(kxmaplist, np.linalg.norm(klist,axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist+B2+B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B2-B1, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1-B2, axis=-1)*cdn/eV*hbar, '-', kxmaplist, np.linalg.norm(klist-2*B1-2*B2, axis=-1)*cdn/eV*hbar, '-', # kxmaplist, np.linalg.norm(klist+2*B2-B1, axis=-1)*cdn, '-', # kxmaplist, np.linalg.norm(klist+2*B1-B2, axis=-1)*cdn, '-', ) ax.set_xlim([np.min(kxmlarr),np.max(kxmlarr)]) #ax.set_ylim([2.15,2.30]) ax.set_ylim([np.min(omlist/eV*hbar),np.max(omlist/eV*hbar)]) ax.set_xticks([0, kxmaplist[len(k0Mlist)-1], kxmaplist[len(k0Mlist)+len(kMK1list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)-1], kxmaplist[len(k0Mlist)+len(kMK1list)+len(kK10list)+len(k0K2list)+len(kK2Mlist)-1]]) ax.set_xticklabels(['Γ', 'M', 'K', 'Γ', 'K\'','M']) f.colorbar(sc) pdf.savefig(f) # In[ ]: pdf.close() # In[ ]: unitcell_translations # In[ ]: