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Yusuke Nomura and Valerio Vitale
26 March, 2020 Wannier90 School
Collaborators (SAWF part): Yoshiro Nohara, Takashi Koretsune, and Ryotaro Arita
Symmetry-adapted Wannier functions lecture and tutorials
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If you have questions, please put them in chat ! Mute your audio and unmute it when necessary
Now available in Wannier90 ※ Please use version 3.1.0
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Wannier State Bloch state
Maximally localized Wannier functionsN. Marzari and D. Vanderbilt, Phys. Rev. B. 56 12847 (1997) I. Souza et al., ibid. 65, 035109 (2001)
The unitary matrix U is obtained by minimizing the spread functional Ω
where,
Symmetry breaking of “maxloc" Wannier functions : CopperI. Souza et al., Phys. Rev. B 65 035109 (2001)
initial projections with atom-centered s and d orbitals, i.e., 6 orbital model → results in interstitial-centered s-like “maxloc”
(“maxloc” procedure does not care about symmetry at all)
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Symmetry-adapted Wannier functions = “maxloc” procedure + symmetry constraint → obtain irreducible representations of a subgroup of full symmetry group
(irreducible representations of site-symmetry group)
Now available in Wannier90 ※ Please use version 3.1.0 !!!
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5
Site-symmetry group
Example: two-dimensional square latticeFull symmetry group : 8 symmetry operations (sym. ops.)
(0,0) (1/2,0)
A subgroup of full-symmetry group, whose elements leave the site-position unchanged
Wyckoff position (0,0) : Site-symmetry group : 8 sym. ops. Multiplicity : 1
Wyckoff position (1/2,0), (0,1/2) : Site-symmetry group : 4 sym. ops. (without C4) Multiplicity : 2
(0,1/2)
Multiplicity = (# full sym. ops.)/(# sym. ops. in site-symmetry group)
Concept of Symmetry-adapted Wannier functions (SAWF)
SAWF = “maxloc" procedure + symmetry constraint → obtain irreducible representations of site-symmetry group
“maxloc” Wannier (global minimum)
SAWF (local minimum)
All unitary transformation Umn(k)
symmetry-adapted Umn(k)
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Symmetry-adapted Wannier functionsRei Sakuma, Phys. Rev. B 87 235109 (2013)
Symmetry-adapted Wannier functions = “maxloc” procedure + symmetry constraint → obtain irreducible representations of a subgroup of full symmetry group
(irreducible representations of site-symmetry group)
U(Rk) = d̃(g,k)U(k)D†(g,k)<latexit sha1_base64="54K67hgXmjqmCJGTvIuKLHGYeHU=">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</latexit><latexit sha1_base64="54K67hgXmjqmCJGTvIuKLHGYeHU=">AAACwHichVHLahRBFD3paIxjHmOyEdw0GRImIMPtEDAIgRBduEwm6SQwnQzdPTU9xfQr3TUDSTM/4A+4cKUgIn6FuPEHXOQLRNwoEdy48E5PE4kheouqOnXqnlunqpzYl6kiOhvTxm/cnLg1ebt0Z2p6ZrZ8d24vjXqJK0w38qPkwLFT4ctQmEoqXxzEibADxxf7TvfxcH+/L5JURuGuOonFYWB7oWxL11ZMNcsNs1rPLKetdwfLur6uW0r6LZG1Bno1swJbdZJA9wYPLlLM6gV8cpRZLdvzRHJNcrNcoRrloV8FRgEqKGIrKr+BhRYiuOghgEAIxdiHjZRbAwYIMXOHyJhLGMl8X2CAEmt7nCU4w2a2y6PHq0bBhrwe1kxztcun+NwTVupYpE/0ls7pI72jL/Tr2lpZXmPo5YRnZ6QVcXP22b2dn/9VBTwrdP6o/ulZoY213Ktk73HODG/hjvT90+fnO4/qi9kSvaKv7P8lndEHvkHY/+G+3hb1FyjxBxh/P/dVsLdSM6hmbK9WNjaLr5jEfSygyu/9EBt4ii2YfO57fMY3fNc2tY4WacejVG2s0MzjUminvwGi+6t5</latexit><latexit sha1_base64="54K67hgXmjqmCJGTvIuKLHGYeHU=">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</latexit><latexit sha1_base64="54K67hgXmjqmCJGTvIuKLHGYeHU=">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</latexit>
U(k) = d̃(gk,k)U(k)D†(gk,k)<latexit sha1_base64="+mOCY/nxjbE7FYJh1nB9vy9mWuY=">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</latexit><latexit sha1_base64="+mOCY/nxjbE7FYJh1nB9vy9mWuY=">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</latexit><latexit sha1_base64="+mOCY/nxjbE7FYJh1nB9vy9mWuY=">AAACz3ichVFNaxNBGH6yftW0mmgvhV6WhpYKEt4VQSkUSu3BY9M2SaGpYXcz2UyzX+xOUtol4lX/gAdPFkSkP6MXj1489CdIjxV7KeibzeJX0b7DzLzzzPO888yMFboyVkTHOe3K1WvXb4zdzI9P3LpdKN65W4uDXmSLqh24QbRpmbFwpS+qSipXbIaRMD3LFXWr+2S4X++LKJaBv6H2QrHtmY4v29I2FUPN4k51PmlYbb07uKfri3pDSbclktZAZ9gzVSfydGfQzCj3f1J/U608Sxot03FEdImoWSxRmdLQLyZGlpSQxWpQfI8GWghgowcPAj4U5y5MxNy2YIAQMraNhLGIM5nuCwyQZ22PWYIZJqNdHh1ebWWoz+thzThV23yKyz1ipY5Z+kwf6JQ+0iF9ofN/1krSGkMvezxbI60Im4VXU+tnl6o8nhU6v1T/9azQxuPUq2TvYYoMb2GP9P3916frC2uzyRwd0An7f0vHdMQ38Ptf7XcVsfYGef4A4+/nvpjUHpQNKhuVh6Wl5ewrxjCNGczzez/CEp5iFVU+9xO+4XsOWkXb1Z5rL0ZULZdpJvFHaC9/AD7hsMo=</latexit><latexit sha1_base64="+mOCY/nxjbE7FYJh1nB9vy9mWuY=">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</latexit>
Constraint on U(k) for k in irreducible BZ
Unitary matrix for other k points
matrices related to symmetry
gkk = k<latexit sha1_base64="Fi8TiozTDHaidk4kBO1rq4pb/Lk=">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</latexit><latexit sha1_base64="Fi8TiozTDHaidk4kBO1rq4pb/Lk=">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</latexit><latexit sha1_base64="Fi8TiozTDHaidk4kBO1rq4pb/Lk=">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</latexit><latexit sha1_base64="Fi8TiozTDHaidk4kBO1rq4pb/Lk=">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</latexit>
Important quantities: D and d matrices ~
num_wann×num_wann matrix
num_bands×num_bands matrix
Transformation of symmetry-adapted (Wannier-gauge) Bloch functions by sym. ops.
Transformation of Kohn-Sham Bloch functions by sym. ops.
written in seedname.dmn file8
Flow of calculation (after nscf calculations and creating .nnkp file)
pw2wannier90.x
seedname.win site_symmetry = .true.
pw2wan.in write_dmn = .true.
input executable output/input
seedname.wout …
seedname.dmn (on top of amn, mmn)
wannier90.x
seedname.sym (not used in wannier90.x)
9
Example of Dmn : CaCuO2 d-p model
Famous family of high-Tc cuprates
Quasi-2D (layered) material
16 symmetry operations (P4/mmm)
CuO2 layer
Ca layer
10
x2-y2 px
py
Example of Dmn : CaCuO2 d-p modelEnergy (eV)
Γ X M Γ Z R A Z
D matrix → how does the SAWF transform by sym. ops.
11
(We do not discuss d matrix because the global phase of KS wave function can be random)~
1 dim. irrep. site multiplicity: 2
1 dim. irrep. site multiplicity: 1
1 dim. irrep. site multiplicity: 2
Example of Dmn (90° rotation, Γ): CaCuO2 d-p modelafter 90° rotation
Wannier-gauge Bloch at Γ ΨΓ,x2-y2,(0,0,0)
→ (-1)ΨΓ,x2-y2,(0,0,0)
ΨΓ,px,(1/2,0,0) ΨΓ,py,(0,1/2,0)
→ ΨΓ,py,(0,1/2,0) → (-1)ΨΓ,px,(1/2,0,0)
R̂⇡/2 �n(r) =X
m
Dmn �m(r)
12
Example of Dmn (90° rotation, Γ): CaCuO2 d-p modelafter 90° rotation
Wannier-gauge Bloch at Γ ΨΓ,x2-y2,(0,0,0)
→ (-1)ΨΓ,x2-y2,(0,0,0)
ΨΓ,px,(1/2,0,0) ΨΓ,py,(0,1/2,0)
→ ΨΓ,py,(0,1/2,0) → (-1)ΨΓ,px,(1/2,0,0)
R̂⇡/2 �n(r) =X
m
Dmn �m(r)
D =
0
@�1 0 00 0 �10 1 0
1
A
px pyx2-y2
Block diagonal for each irrep. (block size: dimension of irrep × site multiplicity)
13
Energy (eV)
Γ X M Γ Z R A Z
x2-y2 px
py
In this case, SAWF = “maxloc” Wannier function
SAWFs : CaCuO2 d-p model
14
SAWFs : CopperRei Sakuma, Phys. Rev. B 87 235109 (2013)
15
Applications to H3S ①
bcc, 48 sym. ops.
Γ H N Γ P N
0
20
40
Energy (eV)
Band structure of Im-3m H3S
A. P. Drozdov et al., Nature 2015 M. Einaga et al., Nat. Phys. 2016 R. Akashi et al., PRL 2016
16
Im3-m H3SMaximally localized Wannier functions
Applications to H3S ②
S s
S p
S d
H s
17
Im3-m H3SSymmetry adapted Wannier functions
Applications to H3S ③
S s
S p
S d
H s
18
Examples in Wannier90
example21: Gallium Arsenide - Symmetry-adapted Wannier functions
example22: Copper - Symmetry-adapted Wannier functions
—— atom_centered_As_sp —— atom_centered_Ga_p —— atom_centered_Ga_s —— atom_centered_Ga_sp —— bond_centered
—— s_at_0.00 —— s_at_0.25 —— s_at_0.50
You can try SAWF ※ Please use version 3.1.0 !!!
19
Be careful …
One cannot always get atom-centered Wannier orbitals with symmetry-adapted mode
Example: MoS2 monolayer
sulphur p orbitals cannot be exactly atom-centered 20
Summary and future perspective
SAWF = “maxloc" procedure + symmetry constraint → obtain irreducible representations of site-symmetry group
“maxloc” Wannier (global minimum)
SAWF (local minimum)
All unitary transformation Umn(k)
symmetry-adapted Umn(k)
Summary
Future perspective Frozen window (need to be symmetry-adapted) Extension to noncolliner case
21
22
Tutorials
23
Instructions
Tutorials can be found in “Tutorials_SAWF”
Basic tutorial: “GaAs”
(A little bit) advanced tutorials: “H3S” and “Cu”
Work flow “GaAs” → “H3S” and “Cu”
Follow the instruction pdf file or README in each directory
For “GaAs” and “Cu”, refer also to Wannier90 Tutorials and Tutorial Solutions
24
Flow of calculation (after nscf calculations and creating .nnkp file)
pw2wannier90.x
seedname.win site_symmetry = .true.
pw2wan.in write_dmn = .true.
input executable output/input
seedname.wout …
seedname.dmn (on top of amn, mmn)
wannier90.x
seedname.sym (not used in wannier90.x)
25
Reference: H3S
Γ H N Γ P N
0
20
40
Energy (eV)
12 band model
Γ H N Γ P N
0
20
40
Energy (eV)
7 band model
26
Flow of calculation in Cu tutorial : advanced usage (after nscf calculations and creating .nnkp file)
pw2wannier90.x
seedname.win site_symmetry = .true.
pw2wan.in write_dmn = .true. read_sym = .true.
input executable output/input
seedname.wout …
seedname.dmn (on top of amn, mmn)
wannier90.x
seedname.sym (prepare it by ourselves)
27