organic materials database / dirac...
TRANSCRIPT
Organic Materials Database / Dirac MaterialsElectronic Structure Database with Focus on Data Mining
Stanislav Borysov, Matthias Geilhufe and Alexander Balatsky
omdb.diracmaterials.org
Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Villum Foundation
A data mining approach for the search of organic Diracmaterials
Stanislav Borysov1,2, Matthias Geilhufe1,2, Alexander Balatsky1,2
1 Center for Quantum Materials, Stockholm2 Nordita, KTH Royal Institute of Technology and Stockholm University
1 / 17
Organic Materials DatabaseOnline Database with Focus on Data Mining
omdb.diracmaterials.org
Accelerated Materials Discovery
https://www.whitehouse.gov/sites/default/files/microsites/ostp/materials_genome_initiative-final.pdf
Organic Materials
• Flexible electronics• Organic LED• Organic solar cells
http://www.flickr.com/photos/rdecom/4146880795/
Dirac Materials
DataMining
Large-ScaleCalculations
• Graphene• Topological insulators• Weyl semi-metals
General Context and Motivation
2
Dirac materials
3
Schrödinger fermions Dirac fermions
d-wave superconductors, graphene, topological insulators,…
CuO2 plane
Graphene sheet
Bi2Se3
Peng
etal.,NatureMat.
9,225
(200
9)
What is a Dirac material?
Dirac materials (DMs): low-energy fermionic excitations are described by a Dirac Hamiltonian
Examples:
Dirac equation: Dirac Hamiltonian:
→ d-wave superconductors, superfluid He-3→ 2D DM: graphene, TI, TCI
→ 3D DM: Dirac/Weyl semimetals→ artificial DM→ bosonic DM
in condensed matter
T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Advances in Physics
(2014)
E
kykx
Universal properties:
Landau levels
minimum cond.Eres ≃ −1/U
impurity resonances
density of states
specific heat
e-e interactions
DM as a framework:
Example of classification:
Carl Linnaeus 1707-1778
• The formal introduction of this system of naming species is credited to Swedish natural scientist Carl Linnaeus
• The value of the binomial nomenclature system derives primarily from its economy, its widespread use, and the uniqueness and stability of names it generally favors:
• Economy, Clarity, Robustness, Predictive
Challenge of classification
Metals
Nonmetals
Dirac Materials: characterization of functional response
Not a chemical characterization, nor group theoretical
Functoinal characterization
Dirac materials vs metalsMetals
FS
E=v(k-k_F)
Diracmaterials(3Heincluded)
E=vk,k_F=0
empty
occupied
Definingfeature:Symmetryofthebandstructureortopology
Dimensionalityofzeroenergystatesinoneless(atleast)DM/WM>Topologicalstates
DMBettercontrolofresponse– gapopening,lessdissipationatlowT.Importantforfutureenergyanddeviceapplications.
D_node = d-2, d-3D_node = d-1
T. Wehling, A Black-Schaffer and A. V. Balatsky, Dirac Materials, Adv Phys, v 63, p 1 (2014)
Many-body instability in DM N(E)
E
E
kykx
4
gapless sate gapped sateKotov et al., RMP 84, 1067 (2012)
αc≈1 in graphene
but no gap observed in suspended graphene with α=2.2
2D DM:
N(E)
Eµ
N(E)
Eµeµh
pumpµE
k
µe
µh
l Linear dispersion → vanishing DOS at the nodel
l Critical coupling for many-body instabilitiesl
l
l
l
l
l
l Dirac nodes are stable against interactionsl
dimensionless coupling in DM
Need to create long-livednon-equilibrium e and hpopulations, e.g. populationinversion, in a DM.
E
kE
nF(E,T)
equilibrium pump relaxation
tt<0 t=0
rapid thermalization
E
nF(E,T)
population inversion
carrier-carrier(150fs-1ps)phonons(1-15ps)
cooling & recombination→(10-150fs)
(timscales for graphene)
Bosonic Dirac MaterialsHonecomb lattices with Dirac Dispersion
• Any particle: fermion or boson on honeycomb, • Kagome and other lattices
Dirac cone dispersion:𝑡"#𝑂"∗𝑂# - O can be any particle
O – fermion – TI, Graphene, SC
O- boson – plasmonic crystals, acoustic, polaritons
• Dirac Materials extended to bosons : Josepshon Junction circuits and Magnons
Phonons on an non-bravaislattice
BEC of polaritons in Driven Dirac nodes
Direct Observation of Dirac Cones and aFlatband in a Honeycomb Lattice for Polaritons T. Jacqmin et al, PRL 112, 116402 (2014)
Polaritons Dirac cone
Dirac Magnons
Dirac magnons – transition metal trihalides
Br-
Cr3+
J
Jz
l CrBr3 lattice
Magnon energy spectrum
Dirac crossing
Neutron scattering experiments on CrB3 from 70s:W. B. Yelon and R. Silberglitt, Phys. Rev. B 4, 2280 (1971).E. J. Samuelsen, R. Silberglitt, et al., Phys. Rev. B 3, 157 (1971).
Renormalization of Large-Wave-Vector Magnons in Ferromagnetic Cr ...
link.aps.org/doi/10.1103/PhysRevB.4.2280
Google Scholarvon WB Yelon - 1971 - Zitiert von: 5 - Ähnliche Artikel
... Studied by Inelastic Neutron Scattering: Spin-Wave Correlation Effects. W. B. Yelon and Richard Silberglitt.
Phys. Rev. B 4, 2280 – Published 1 October 1971.
How we do it
crystallography.netMore than 100,000 organic compounds
to calculate (~20,000 are ready)
Standard DFT calculations to capture trends
Borysov SS, Geilhufe RM, Balatsky AV, Organic materials database: An open-access online database for data mining,
PLoS ONE 12(2), e0171501 (2017)
22
Organic Materials Database: Content~20,000 Electronic Structures
(Oct 22, 2017)
23
Organic Materials Database: Gap Search
24
Organic Materials Database: Gap Search at Fermi Level
25
114 metals (gap = 0 eV)58 semiconductors with 0 < gap <= 0.1 eV
Organic Materials Database: Online Pattern Search
E (
eV
)
X Γ Y,L Γ Z,N Γ M,R Γ-1.2
-1.15
-1.1
-1.05
-1
-0.95
Highcharts.com
Arbitrary pattern
Search results
S.S. Borysov, B. Olsthoorn, M.B. Gedik, R.M. Geilhufe, A.V. Balatsky,To be submitted (2017)
26
Organic Materials Database: Online Pattern Search
S.S. Borysov, B. Olsthoorn, M.B. Gedik, R.M. Geilhufe, A.V. Balatsky,To be submitted (2017)
1. Represent data and query as vectors 2. Approximate nearest neighbor search
27
https://www.cs.umd.edu/~mount/ANN/
~b2~b3
E(~k)
R
~b3
E(~k)
~b2
D
Dirac points (SG 19) Dirac lines (SG 14)
Geilhufe RM, Borysov SS, Bouhon A, Balatsky AV,Data Mining for Three-Dimensional Organic Dirac
Materials: Focus on Space Group 19, Scientific Reports 7, 7298 (2017)
Geilhufe RM, Bouhon A, Borysov SS, Balatsky AV,Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry: A data mining approach,
Physical Review B 95, 041103(R) (2017)
Online Pattern Search: Dirac Materials
28
Organic Materials Database: DOS Similarity Search
2
most
similar
top-terp
henyl.
REFERENCE
MATERIA
LP-T
ERPHENYL
Cry
stalstru
cture
and
electro
nic
structu
re
The
organic
compou
nd
p-terp
henyl
or1,4-
Diphenylb
enzen
ecrystallizes
with
ina
mon
oclinic
crystalstru
cture
obeyin
gthespace
group
P21 /a
(14).The
molecu
leitself
has
the
chem
icalsum
formula
C18 H
14 ,
exhibitin
gthefollow
ingskeletal
formula:
Accord
ingto
Ref.
[27],thelattice
param
etersare
givenby
a=
8.10A,b=
5.61A,c=
13.61A
and�=
92.02�.
The
electronic
structu
reof
p-terp
henyl
fora
non
-op
timized
unit
cellwith
ionic
position
saccord
ing
toRef.
[27]is
illustrated
inFig.
1.Thecrystal
itselfis
alarge
ban
dgap
insulator
with
acalcu
latedban
dgap
of3eV
.Theban
dstru
cture
(Fig.
1a)exh
ibits
alocal-
izedan
dwell
isolatedflat
ban
dright
below
theFerm
ilevel
which
isalso
seenin
theden
sityof
statesshow
nin
Fig.
1b.
Such
flat
ban
dsare
common
with
intheban
dstru
cture
oforgan
icsdueto
theweak
hop
pingof
elec-tron
sbetw
eenthemolecu
larorb
itals.Both
below
and
above
thegap
,theDOSshow
slocalized
features
with
inan
energy
range
ofab
out2eV
.After
astru
ctural
opti-
mization
oftheion
icposition
s,theban
dstru
cture
and
den
sityof
statesrem
ainqu
alitativelysim
ilar.Theban
dgap
itselfslightly
decreases
toab
out2.8
eV,whereas
the
spectral
gapbetw
eenthelocalized
ban
dbelow
theFerm
ilevel
tothesecon
den
ergeticallylow
erbran
chof
ban
ds
slightlyincreases
toab
out0.8
eV.
Computa
tionaldeta
ils
Theelectron
icstru
cture
ofthereferen
cematerial
p-
terphenyl
was
calculated
inthefram
ework
oftheden
-sity
function
altheory
[28–30]by
applyin
gapseu
dop
o-tential
projector
augm
ented-w
avemeth
od[31–34],
asim
-plem
entedin
theVien
naAbinitio
Sim
ulation
Package
(VASP)[35–38].
Durin
gthecalcu
lations,
theexch
ange-
correlationfunction
alwas
approxim
atedby
the
gen-
eralizedgrad
ientap
proxim
ationaccord
ing
toPerd
ew,
Burke
andErnzerh
of[39](P
BE).T
hestru
cturalin
forma-
tionwas
takenfrom
theCam
brid
geStru
ctural
Datab
ase(C
SD)[27,
40]an
dtran
sferredinto
POSCAR
files
us-
ingVESTA
(Visu
alizationfor
Electron
ican
dSTructu
ralAnalysis)
[41].Theen
ergycu
t-o↵was
setto
400eV
.Dueto
thelight
atomsinvolved
,thecalcu
lationswere
perform
edspin-
-2 -1 0 1 2 3 4
ΓZ
CY
AE
DB
AΓ
D
Energy (eV)
b1
b3
b2
Z
D
Y
AB
C
�
E
(a)bandstru
cture
alongva
rioushighsymmetry
path
swith
inth
eBrillo
uin
zone
�2
02
46
W1
W2
Energy
(eV)
DOS
(b)den
sityofsta
tesinclu
dingth
etw
oen
ergy
window
sW
1andW
2used
forth
esim
ilaritysea
rch
FIG
.1:
Electron
icstru
cture
ofp-terp
henyl.
polarized
butwith
outspin-orb
itcou
plin
g.For
thein-
tegrationin
~k-sp
ace,a6⇥
6⇥6�-centered
mesh
accord-
ingto
Mon
khorst
andPack
[42]was
chosen
durin
gthe
self-consistent
cycle.Ban
dstru
cture
calculation
swere
perform
edin
twoways.
First,
thecrystal
structu
rewas
keptfixed
asprovid
edby
theexp
eriment
[27],which
isin
correspon
den
ceto
theelectron
icstru
cture
calculation
sstored
with
intheOMDB
[2].Secon
d,theion
icposition
swere
optim
izedby
incorp
oratingvan
der
Waals
correc-tion
swith
inthefram
ework
oftheden
sitydep
endent
dis-
persion
correctionaccord
ingto
Stein
man
nan
dCorm
in-
boeu
f[43]
tocross-ch
eckthestab
ilityof
theelectron
icstru
cture
with
respect
toslight
structu
ralchan
ges.
DOS
SIM
ILARIT
YSEARCH
TOOL
Toidentify
materials
with
intheOMDB
havin
gDOS
similar
top-terp
henyl,
we
develop
eda
DOS
similar-
itysearch
toolwhich
ismad
efreely
available
onlin
eat
https://omdb.diracmaterials.org/search/dos.
It
Reference material
4
E (
eV
)
Γ Y HC EM_1 A X H_1,M D Z,Y D
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 10 20 30 40 50
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(a) OMDB-ID 12336, COD-ID 2212018, C8H8Br2
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D
-2
0
-3.5
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 20 40 60 80
-2
0
-3.5
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(b) OMDB-ID 261, COD-ID 4062949, C8H5O
E (
eV
)
X Γ Y,L Γ Z,N Γ M,R Γ
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 20 40 60 80
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(c) OMDB-ID 12231, COD-ID 2203730, C18H18O2
FIG. 2: Electronic structure of the three mostpromising materials with similarity to the electronicstructure of p-terphenyl within the valence bands.
almost planar molecules comparable to p-terphenyl.
The mechanisms guiding the high-temperature super-conductivity in p-terphenyl are still unclear. The firstattempts were reported by Mazziotti et al. [45] propos-ing that the driving mechanism is the quantum resonancebetween di↵erent superconducting gaps near a Lifshitz
E (
eV
)
X Γ Y,L Γ Z,N Γ M,R Γ2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
Values
0 25 50 75 100 125
2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
(a) OMDB-ID 20042, COD-ID 2222905, C13H9FO3
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D2
4
2.5
3
3.5
4.5
5
Highcharts.com
Values
0 50 100 150 200 250 300 350
2
4
2.5
3
3.5
4.5
5
Highcharts.com
(b) OMDB-ID 21466, COD-ID 7153064, C16H12ClN3O
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
Values
0 50 100 150 200 250 300 350
2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
(c) OMDB-ID 19325, COD-ID 1542706,C12H14N2O5
FIG. 3: Electronic structure of the three mostpromising materials with similarity to the electronicstructure of p-terphenyl within the conduction bands.
transition.Considering a BCS-type mechanism to induce super-
conductivity, the transition temperature Tc increaseswith increasing DOS at the Fermi level N(EF) and cou-pling constant g,
Tc ⇠ e�1/|g|N(EF). (1)
Search results
29
Organic Materials Database: High-Tc SC Search
Ren-Shu Wang, Yun Gao, Zhong-Bing Huang, Xiao-Jia Chen, Superconductivity above 120 kelvin in a chain link molecule,
arXiv preprint arXiv:1703.06641 (2017)
30
100 110 120 130 140 150
-0.6
-0.4
-0.2
0.0
0.2
100 110 120 130 140 150-0.8
-0.6
-0.4
-0.2
0.0
0.2
100 110 120 130 140 150
-0.6
-0.4
-0.2
0.0
100 110 120 130 140 150
-0.6
-0.4
-0.2
0.0
χ (1
0-6 e
mu
g-1 O
e-1 )
Temperature (K)
ZFC
FC
H=50 Oe
H=100 Oe
Temperature (K)
ZFC
FC
χ (1
0-6 e
mu
g-1 O
e-1 )
FC
χ (1
0-6 e
mu
g-1 O
e-1 )
Temperature (K)
H=200 OeZFC
FC
χ (1
0-6 e
mu
g-1 O
e-1 )
Temperature (K)
H=300 Oe
ZFC
Figure 1.
11
P-Terphenyl (Tc ~ 120 K)
Organic Materials Database: DOS Similarity Search
Geilhufe RM, Borysov SS, Kalpakchi D, Balatsky AV, Novel Organic High-Tc Superconductors: Data Mining using Density of States Similarity Search,
arXiv preprint arXiv:1709.03151 (2017)
31
4
E (
eV
)
Γ Y HC EM_1 A X H_1,M D Z,Y D
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 10 20 30 40 50
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(a) OMDB-ID 12336, cod-id 2212018, C8H8Br2
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D
-2
0
-3.5
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 20 40 60 80
-2
0
-3.5
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(b) OMDB-ID 261, cod-id 4062949, C8H5O
E (
eV
)
X Γ Y,L Γ Z,N Γ M,R Γ
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
Values
0 20 40 60 80
-2
0
-3
-2.5
-1.5
-1
-0.5
Highcharts.com
(c) OMDB-ID 12231, cod-id 2203730, C18H18O2
FIG. 2: Electronic structure of the three mostpromising materials with similarity to the electronicstructure of p-terphenyl within the valence bands.
almost planar molecules comparable to p-terphenyl.
The mechanisms guiding the high-temperature super-conductivity in p-terphenyl are still unclear. The firstattempts were reported by Mazziotti et al. [45] propos-ing that the driving mechanism is the quantum resonancebetween di↵erent superconducting gaps near a Lifshitz
E (
eV
)
X Γ Y,L Γ Z,N Γ M,R Γ2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
Values
0 25 50 75 100 125
2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
(a) OMDB-ID 20042, cod-id 2222905, C13H9FO3
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D2
4
2.5
3
3.5
4.5
5
Highcharts.com
Values
0 50 100 150 200 250 300 350
2
4
2.5
3
3.5
4.5
5
Highcharts.com
(b) OMDB-ID 21466, cod-id 7153064, C16H12ClN3O
E (
eV
)
Γ Y H C E M_1 A X H_1,M D Z,Y D2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
Values
0 50 100 150 200 250 300 350
2
4
2.5
3
3.5
4.5
5
5.5
Highcharts.com
(c) OMDB-ID 19325, cod-id 1542706,C12H14N2O5
FIG. 3: Electronic structure of the three mostpromising materials with similarity to the electronicstructure of p-terphenyl within the conduction bands.
transition.Considering a BCS-type mechanism to induce super-
conductivity, the transition temperature Tc increaseswith increasing DOS at the Fermi level N(EF) and cou-pling constant g,
Tc ⇠ e�1/|g|N(EF). (1)
Valence Bands
2
most similar to p-terphenyl.
REFERENCE MATERIAL P-TERPHENYL
Crystal structure and electronic structure
The organic compound p-terphenyl or 1,4-Diphenylbenzene crystallizes within a monocliniccrystal structure obeying the space group P21/a (14).The molecule itself has the chemical sum formulaC18H14, exhibiting the following skeletal formula:
According to Ref. [27], the lattice parameters are givenby a = 8.10 A, b = 5.61 A, c = 13.61 A and � = 92.02�.
The electronic structure of p-terphenyl for a non-optimized unit cell with ionic positions according toRef. [27] is illustrated in Fig. 1. The crystal itself isa large band gap insulator with a calculated band gapof 3 eV. The band structure (Fig. 1a) exhibits a local-ized and well isolated flat band right below the Fermilevel which is also seen in the density of states shown inFig. 1b. Such flat bands are common within the bandstructure of organics due to the weak hopping of elec-trons between the molecular orbitals. Both below andabove the gap, the DOS shows localized features withinan energy range of about 2 eV. After a structural opti-mization of the ionic positions, the band structure anddensity of states remain qualitatively similar. The bandgap itself slightly decreases to about 2.8 eV, whereas thespectral gap between the localized band below the Fermilevel to the second energetically lower branch of bandsslightly increases to about 0.8 eV.
Computational details
The electronic structure of the reference material p-terphenyl was calculated in the framework of the den-sity functional theory [28–30] by applying a pseudopo-tential projector augmented-wave method [31–34], as im-plemented in the Vienna Ab initio Simulation Package(VASP) [35–38]. During the calculations, the exchange-correlation functional was approximated by the gen-eralized gradient approximation according to Perdew,Burke and Ernzerhof [39] (PBE). The structural informa-tion was taken from the Cambridge Structural Database(CSD) [27, 40] and transferred into POSCAR files us-ing VESTA (Visualization for Electronic and STructuralAnalysis) [41].
The energy cut-o↵ was set to 400 eV. Due to the lightatoms involved, the calculations were performed spin-
-2
-1
0
1
2
3
4
Γ Z C Y A E D B A Γ D
En
erg
y (e
V)
b1
b3
b2
Z
D
Y
AB
C
�
E
(a) band structure along various high symmetry paths within theBrillouin zone
�2 0 2 4 6
W1 W2
Energy (eV)
DOS
(b) density of states including the two energywindows W1 and W2 used for the similarity
search
FIG. 1: Electronic structure of p-terphenyl.
polarized but without spin-orbit coupling. For the in-tegration in ~k-space, a 6⇥ 6⇥ 6 �-centered mesh accord-ing to Monkhorst and Pack [42] was chosen during theself-consistent cycle. Band structure calculations wereperformed in two ways. First, the crystal structure waskept fixed as provided by the experiment [27], which isin correspondence to the electronic structure calculationsstored within the OMDB [2]. Second, the ionic positionswere optimized by incorporating van der Waals correc-tions within the framework of the density dependent dis-persion correction according to Steinmann and Cormin-boeuf [43] to cross-check the stability of the electronicstructure with respect to slight structural changes.
DOS SIMILARITY SEARCH TOOL
To identify materials within the OMDB having DOSsimilar to p-terphenyl, we developed a DOS similar-ity search tool which is made freely available onlineat https://omdb.diracmaterials.org/search/dos. It
Reference material (p-terphenyl)
Conduction Bands
Collaboration with experimentalists
32
Computational challenges
Borysov SS, Geilhufe RM, Balatsky AV, Organic materials database: An open-access online database for data mining,
PLoS ONE 12(2), e0171501 (2017)
33
Machine Learning to Approximate DFT for Crystals
34
DFT + Tight binding
t
t
Now learn:
Map from tight binding model
Online Materials Hub: Know, Discover, Interact
35
36
02468
1012141618
New users per month
0
50
100
150
200
250
300
6-2017 7-2017 8-2017 9-2017 10-2017
Total material views per month
Users by country
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Total: 94
Total: 726
OMDB Users Report (27-10-2017)
