CMP Technical Report No. 92 DOS Department of Computational Nanomaterials Design ISIR, Osaka University

CMP Technical Report No. 92 DOS Department of Computational Nanomaterials Design ISIR, Osaka University

1 1 2 1 3 GaAs 3 3.1 SCF..................................... 3 3.2 DOS pwbcd.......................... 4 3.3 tetrahedron pdosdr...................... 6 3.3.1 pwbcd................................... 7 3.3.2 pdosdr.................................. 9 3.3.3 aydosp.................................. 11 3.4.............................. 12 3.5 pdos............................... 14 4 pdosdr k 14 5 16 A label of m components 17 B colors in aydosp 17 0

1 Osaka2k Technical Report [1, 2, 3] pwm VersionNo = 1.72 VersionDate = 08 Jul 2006 pwbcd VersionNo = 0.90 VersionDate = 27 Jun 2006 2 κ lm ϕ κ lm (r) = uκ l (r)y lm(θ, φ) (1) a κ lm ϕ k,alm (r) = R exp[ik (R + R a )] ϕ κ lm (r R R a) (2) ψ k (r) ψ k ϕ κ lm (3) 3G ψ k k + G k + G ϕ κ lm = ψk (k + G)ϕκ lm (k + G) (4) G G 1

ψk (k + G) ϕ κ lm (q) = ϕ κ lm (r)e iq r dr = (2l + 1)i l u κl (r)j l (qr)r 2 dr Y lm (ˆq)P l (cos θ)dω 1 0 = 4πi l u κl (r)j l (qr)r 2 dry lm (ˆq) (5) I κ 0 l (q) = 4πil u κl (r)j l (qr)r 2 dr (6) 0 {Il κ (q)} 4 a S a (q) ψ k ϕ κ lm = q ψ k (q)iκ l (q)y lm(ˆq)s a (q) (7) 7 ϕ κ lm I κ l (q) Y lm(ˆq) S a (q) ϕ k,alm 1 2 k ψ k (r) = G c k+g e i(k+g) r (8) k G 8 2 1 Y lm (ˆq) 2

k k {ϕ k,alm (r)} 2 k 3 GaAs GaAs DOS DOS 3.1 SCF SCF ==================== K-Space Setup ============================== k sampling point set Nkpts = 2 No NM index in p in c A/gmin i/o star WTK 1 LD -1-1 -1/ 4-1 -1-1/ 4 0.25000 1 4 0.25000 2 XY 1-1 -1/ 4-3 1 1/ 4 0.47871 1 12 0.75000 ==================== PW_Expansion ============================== Cutoff in the reciprocal space am = 3.10000 (rel. units) kcut = 3.15801 (ab^-1) with 2Pi Ecut = 9.97300 (Ry) UNIT of K 1.01871 (a.u.) Planewave expansion with NHDIM = 169 Name: LD -1-1 -1/ 4 Nstr= 4 WTK= 0.250000 NPW= 162 Name: XY 1-1 -1/ 4 Nstr= 12 WTK= 0.750000 NPW= 164 ==================== atomic PPOT ============================== Ga ca nrl nc pseudopotential read from tape atom-lda 8-JAN- 2 Improved Troullier - Martins potential 4s( 2.00) rc= 2.50 4p( 1.00) rc= 2.35 As ca nrl nc pseudopotential read from tape atom-lda 8-JAN- 2 Improved Troullier - Martins potential 4s( 2.00) rc= 2.50 4p( 3.00) rc= 2.50 SCF ====================SCF calculation==================== convergence parameters max iteration : 15 iter Eel dee Xsi nst/bk aglmax (Ry/cell) (Ry/cell) (Ry^2/cell) ==== =============== ============ ============ ======== ============= 3

1-0.0090254029-6.9760E+00 7.0425E-02 5/ 0 0.624308035 2-0.4061363678-3.9711E-01 9.0575E-04 5/ 0 0.237960989 3-0.4127710828-6.6347E-03 3.2210E-05 5/ 1 0.021868549 4-0.4129192995-1.4822E-04 6.4211E-07 5/ 7 0.003967351 5-0.4129231853-3.8858E-06 2.5645E-08 5/ 16 0.000715309 6-0.4129233887-2.0347E-07 5.1295E-10 5/ 11 0.000085793 7-0.4129232409 1.4781E-07 3.4848E-11 3/ 8 0.000021200 CG process is stopped because increase in Eel 1.4781E-07 Etot Eel delta E resid iter ============== ============= ========== ========== === -17.25697453-0.41292324 1.478E-07 3.485E-11 7 ===== KS levels ===== -0.513307 0.047161 0.283862 0.283862-0.417444-0.103171 0.106391 0.193900 3.2 DOS pwbcd DOS DOS Osaka2k DOS pwbcd bcd.para JobType dos Input file name gaas.prim number of division (nkdiv) 8 number of levels you want to draw (NBUP) usually NEPC 8 scan zone only (iscan) 1 print control (ilp) 1 use symmetry (isymm) 1 energy unit (ienun=0 for Ry, 1 for ev) 0 pwbcd dos gaas.out ========================= DOSMain ============================== nkdiv per line : 8 nk3dim : 512 N of bands (NBUP) : 8 dim0eng : 4096 Use of symmetry for diagonalization Decomposition of DOS ON using pa n sample k points (nktot: 47 n total k points (nkfull: 564 Upper energy to limit DO: 5.000 (Ry) 4

50 DOS of GaAs 40 States/Ry. 30 20 10-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy \Ry.\ 1: Total DOS of GaAs. DOS ========================= FindEf ============================== Nel0prim = 8 fixocc = 2.00000E+00 N of electrons 8 are occupied in the ascending order in energy. N of occupation processe 189 residual of electron num 0.000000 === Fermi Sort Summary === Fermi_Level = 0.424483 (Ry) at 1 th k-point GM 0 0 0/ 8 (p) 0 0 0/ 8 (c) Valence Top = 0.424483 (Ry) at 1 th k-point GM 0 0 0/ 8 (p) 0 0 0/ 8 (c) Conduction Bottom = 0.428412 (Ry) at 42 th k-point X 4 4 0/ 8 (p) 0 0 8/ 8 (c) Energy Gap = 0.003930 (Ry) with energy resolution for degeneracy 1.00E-03 (Ry) pwbcd fort.2 pdosdr DOS pdosdr pdosdr.inp gaas. NONM 4 4 4 0-0.6 1.0 0.001 8 1 12 5

Osaka2k pdosdr fort.13 aydosp aydosp.inp 61-0.6 1.0 150.0 120.0 10.0 50.0 0.376 1 1 0 DOS of GaAs DOS 1 3.3 tetrahedron pdosdr pdosdr DOS DOS 2 JobType dos... nkdiv 8... OPTION BEGIN decompdos ON OPTION END gaas. NONMSPIN-ORBIT 4 4 4 8 MAXCMP 4 NCOMP 1 Ga2s 2 Ga4p 5 As4s 6 As4p -0.6 1.0 0.001 8 1 12 ======================== Decomposition of DOS parameters maxcmp : 8 ncmp0dos in pdoddr.inp contracted decomposition by nkat= 2 NO ik at l 1 1 ga 0 2 1 ga 1 5 2 as 0 6 2 as 1 The actual n of lm components calculated = 4 N of Bloch functions with G block 3 renumbering 61-0.6 1.0 150.0 120.0 1.0 10.0 0.376 1 4 1 2 3 4 pdos of GaAs 2: Flow of the parameters for pdos calculation 6

3.3.1 pwbcd DOS pwbcd bcd.para OPTION BEGIN decompdos ON OPTION END pwbcd DOS dos gaas.out DOS ========================= Decomposition of DOS parameters maxcmp : 8 The array dimension for pdos Write this number for ncmp0dos in pdoddr.inp contracted decomposition by nkat = 2 NO ik at l 1 1 ga 0 2 1 ga 1 5 2 as 0 6 2 as 1 The actual n of lm components calculated = 4 N of Bloch functions with G block 3 Total number of Bloch functions = 15 1 1-1 2 2-9 3 10-15 Type of atomic orbital: psuedo-wavefunction DOS maxcmp nkat s p d f maxcmp = nkat 4 (9) pdosdr s p d f s p d f 0 DOS Ga4s Ga4p As4s As4p 1 2 5 6 fort.12 fort.13 ik dos gaas.out ϕ a lm ϕ a l m ϕ a lm δl l,m m 7

Normalization factor Normality of atom 1 1.36E-01 6.11E-20 5.90E-20 6.10E-20 2.33E-20 2.67E-02 1.34E-19 7.35E-19 2.82E-20 1.34E-19 2.67E-02 1.01E-18 2.69E-20 7.35E-19 1.01E-18 2.67E-02 Normality of atom 2 9.50E-02 1.61E-19 1.63E-19 1.56E-19 4.69E-20 5.17E-02 3.93E-19 1.34E-18 4.83E-19 3.93E-19 5.17E-02 2.11E-18 4.41E-20 1.34E-18 2.09E-18 5.17E-02 ϕ a l m ϕ a lm spx p y p z Ga As sp x p y p z ϕ a l m ϕ b lm Orthgonality Combination atom 1-2 8.55E-02 9.31E-11 9.31E-11 9.31E-11 9.86E-11 7.66E-03 3.69E-10 3.69E-10 9.86E-11 3.69E-10 7.66E-03 3.69E-10 9.86E-11 3.69E-10 3.69E-10 7.66E-03 a b E ab Slater Koster a b s p E s,x = αv spσ (10) (α, β, γ) E s,x (R 1, R 2 ) 0 A B 3: (Left) a combination of atom A and B. (Right) atomic orbital representation in a crystal 8

R R = R l + R b R l R b (lb) (lmn, b) l = (lmn) pwbcd R b R l l zincblende E s,x (1, 2) E s,x ((000, 1), (000, 2)) E s,x = E s,x ((0, 1), (000, 2)) + E s,x ((0, 1), ( 1 10, 2))+ E s,x ((0, 1), ( 10 1, 2)) + E s,x ((0, 1), (0 1 1, 2)) (11) 10 3.3.2 pdosdr pdosdr pdosdr.inp gaas. NONM 4 4 4 8 4 1 Ga4s 2 Ga4p 5 As4s 6 As4p -0.6 1.0 0.001 8 1 12 3.3.1 pwbcd 1 pdosdr Osaka2k DOS MAXCMP NCOMP FORTRAN 9

pdos of GaAs 5 4 States/Ry. 3 2 1-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy \Ry.\ 4: Partial DOS of GaAs. DOS 9 GaAs Ga As s p d f MAXCMP DOS Ga4s Ga4p As4s As4p NCOMP DOS pdos *.prim Number of atom species 2 No Name Zat Zval 1 ga 31 3 2 as 33 5 Kind of atoms 2 Number of atoms 2 L.L. AND U.U. VALENCE ELEMENT 1 1 3.0000 1 ga 2 2 5.0000 2 as Ga As nkat nkat 2 nspec p f dos *.out 2 nkmax0dos 6 10

1: input form of pdosdr.inp. When MAXCMP=0, specification NCOMP is not required. NAME MAGNET NX, NY, NZ MAXCMP (NCOMP ESTART, ENEND, DE NELEC, NB1, NB2 description name of the crystal with a period specify the magnetic state (NONM, MAGN, SPIN) segments of BZ dimension of decomposed orbitals number of selected orbitals followed by each name of selected orbitals) energy scale begin at E =ESTART end at E =ENEND with spacing DE number of electrons spanning from band NB1 to NB2 Number of atom species Decomposition of DOS parameters maxcmp : 8 contracted decomposition by nkat = 2 NO ik at l 1 1 ga 0 2 1 ga 1 5 2 as 0 6 2 as 1 pdosdr.inp pdosdr fort.13 DOS DOS pdosdr.inp pdos DOS pdos 3.3.3 aydosp aydosp pdosdr fort.13 PS aydosp.inp 61-0.6 1.0 150.0 120.0 20.0 5.0 0.376 1 11

4 1 2 3 4 DOS of GaAs 2: input form of aydosp.inp IFIL EO, EM, XM, YM, DDOS, DOSM, EF, ISPIN NLINE, JLINE(NLINE) D description specify file number minimum and maximum of energy scale of x- and y- axes (mm) the tick and full scale of DOS Fermi level and spin status number of pdos lines followed by each pdos specification title DOS pdosdr fort.13 pdosdr.inp fort.13 DOS DOS 0 NLINE, JLINE(NLINE) no SPIN 1 0 -> 1 data; total DOS only 2 0 2 -> 2 data; total DOS and a partial DOS of #2 3 1 3 4 -> 3 data: 3 partial DOSs of #1, 3, and 4 SPIN 2 0 1 -> 2 data: up and down total DOSs DOS 4 3.4 ϕ k,alm (r) = R exp[ik (R + R a )] ϕ κ lm (r R R a) (12) k 12 4 DOS 12 12

pdos of GaAs States/Ry. 10 9 8 7 6 5 4 3 2 1-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy \Ry.\ 5: Partial DOS of GaAs. ψ nl 12 k k 6 k 1st BZ k + G G G {Il κ (q)} k + G k + G The actual n of lm components calculated = 4 N of Bloch functions with G block 3 Total number of Bloch functions = 15 1 1-1 2 2-9 3 10-15 k + G 5 4 DOS k + G s p 13

G X k 6: Bloch sum of s orbital for excited states and s band in the band structure. 3.5 pdos pdos 7 ψ k ϕ κ lm ψ k ϕ κ lm 2 4 m ψ k ϕ κ lm 2 (13) m m ψ k ϕ κ lm (14) 7 4 pdosdr k pdosdr DOS Tetrahedron DOS pdosdr k Osaka2k 14

States/Ry. 5 4 3 2 1 pdos of GaAs sum of abs^2 States/Ry. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 pdos of GaAs sqrt sum -0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy \Ry.\ -0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy \Ry.\ 7: Comparison of two ways of pdos. The left is the sum of square of the matrix element, while the right is the sum of absolute value of the elements. pwbcd pdosdr k 4 3: Appropriate mesh points between pwbcd and pdosdr crystal ndiv notes system pwbcd pdosdr on pdosdr P n n n should be even F 2n n I 2n n C 2n (n, n, 2n) R 3n n monoclinic orthorhombic pdosdr k pwbcd pdosdr k pdosdr rhombohedral system pdosdr fort.2 k NDFAC= 1 ISO= 1 15

1 0 0 0 6 1 GM 1 1 2 21 1 0 0 0 6 1 GM 2 1 2 7 2 0 0-3 6 1 LD 1 1 4 37 2 0 0-3 6 1 LD 2 1 4 12 2 0 0-3 6 1 LD 3 2 4 37 3 0 1-1 6 1 YP 1 1 6 37 3 0 1-1 6 1 YP 2 1 6 37 4 1 0-2 6 1 XP 1 1 6 37 4 1 0-2 6 1 XP 2 1 6 37 5 0 1-4 6 1 YP 1 1 6 37 5 0 1-4 6 1 YP 2 1 6 37... 31 0 3 6 6 1 F 4 1 3 37 32 2 1-8 6 1 GN 1 1 12 37 NBAND= 37 1 37 pwbcd 6 6 6 pdosdr pdosdr k 2 2 2 GENERATED KPOINT NO KX, KY, KZ 1 0 0 0 2 1 2 0 0 1 2 2 3 0 1 0 2 20 4 0 1 1 2 24 5 0 2 0 2 10 6 0 2 1 2 21 7 1 0 0 2 20 8 1 0 1 2 25 9 1 1 0 2 31 10 1 1 1 2 24 11 1 2 0 2 20 12 1 2 1 2 24 13 2 0 0 2 10 14 2 0 1 2 2 15 2 1 0 2 20 16 2 1 1 2 25 17 2 2 0 2 1 18 2 2 1 2 2 5 pwm pdosdr MAXCMP NCOMP l m bcd.para 16

4: Options for bcd.para Option Default Description toggle options decompdos OFF decomposition to partial DOS mdecomp0dos OFF decomposition to the m level value options targetatom0dos none atom specification to pdos ngblck0input 1 n of blocks G in Bloch sums cutoff0kc modify NHDIM with this factor A label of m components Osaka2k DOS m DOS B colors in aydosp aydosp c c c c c c c c c c 1:Black 2:Red 3:Green 4:Blue 5:Orange 6:lavender 7:pink 8:lime 9:yellow 10:bright Blue [1] Technical Report No. 28 [2] Technical Report No. 61 DOS [3] Technical Report No. 83 Osaka2k pdosdr k 17

5: definition of real-valued spherical harmonics in Osaka2k. The normalization factor is ignored. l m Y lm 0 0 1 1-1 x 0 y 1 z 2-2 xy -1 zx 0 z 2 x 2 y 2 1 yz 2 y 2 x 2 3-3 x(3y 2 x 2 ) -2 xyz -1 x(4z 2 x 2 y 2 ) 0 z(2z 2 3(x 2 + y 2 )) 1 y(4z 2 x 2 y 2 ) 2 z(y 2 x 2 ) 3 y(y 2 3x 2 ) 18