Overview: P₄

Structure info
Layer group	pman
Layer group number	42
Structure origin	original03-18
COD id of parent bulk structure	COD 9012486
ICSD id of parent bulk structure	ICSD 36434
Mono/few-layer report(s)	10.1038/nnano.2014.35

Stability
Energy above convex hull [eV/atom]	0.039
Heat of formation [eV/atom]	0.039
Dynamically stable	Yes

Basic properties
Magnetic	No
Band gap [eV]	0.903
Band gap (HSE06) [eV]	1.511
Band gap (G₀W₀) [eV]	2.025

Repeat: 1234   Download: XYZ CIF JSON

Axis	x [Å]	y [Å]	z [Å]	Periodic
1	4.631	0.000	0.000	Yes
2	0.000	3.306	0.000	Yes
3	0.000	0.000	17.110	No

Lengths [Å]	4.631	3.306	17.110
Angles [°]	90.000	90.000	90.000

Crystal structure

Symmetries
2D Bravais type	Rectangular (op)
Layer group number	42
Layer group	pman
Space group number (bulk in AA-stacking)	53
Space group (bulk in AA-stacking)	Pmna
Point group	mmm
Inversion symmetry	Yes

Structure data
Formula	P4
Stoichiometry	A
Number of atoms	4
Unit cell area [Å2]	15.312
Thickness [Å]	2.110

Stability

Convex hull

P4 (4P-1)
Heat of formation [eV/atom]	0.04
Energy above convex hull [eV/atom]	0.04

Monolayers from C2DB
P4, (4P-1)	0.04 eV/atom
P2 (2P-1)	0.04 eV/atom

Bulk crystals from OQMD123
P42	0.00 eV/atom

Phonons

Minimum eigenvalue of Hessian [eV/Ų]

-0.00

Linear deformations

Deformation potentials

DVB [eV]	xx	yy	xy
Γ	-2.69	0.06	-0.00
X	-7.80	1.41	-0.00
S	-2.44	0.04	-1.44
Y	-0.23	-2.79	-0.00
kVBM	-2.69	0.06	-0.00

	xx	yy	xy
Band gap [eV]	4.25	4.88	0.00

DCB [eV]	xx	yy	xy
Γ	1.56	4.94	0.00
X	-1.21	-12.64	-0.00
S	-2.71	0.56	3.07
Y	1.34	3.66	-0.00
kCBM	1.56	4.94	0.00

Stiffness tensor

Cij (N/m)	xx	yy	xy
xx	23.59	17.00	-0.00
yy	16.92	101.96	0.00
xy	0.00	0.00	44.68

Stiffness tensor eigenvalues
Eigenvalue 0	20.08 N/m
Eigenvalue 1	44.68 N/m
Eigenvalue 2	105.47 N/m

Electronic bands

Band structure and DOS

Electronic band structure (HSE06@PBE)

Details
Band gap (HSE06) [eV]	1.511
Direct band gap (HSE06) [eV]	1.511
Valence band maximum wrt. vacuum level (HSE06) [eV]	-5.400
Conduction band minimum vs. vacuum (HSE06) [eV]	-3.889

Electronic band structure (G₀W₀@PBE)

Details
Band gap (G₀W₀) [eV]	2.025
Direct band gap (G₀W₀) [eV]	2.025
Valence band maximum wrt. vacuum level (G₀W₀) [eV]	-5.955
Conduction band minimum vs. vacuum (G₀W₀) [eV]	-3.930

Effective masses

Property (VBM)	Value
Min eff. mass	0.13 m0
Max eff. mass	8.16 m0
DOS eff. mass	1.03 m0
Crystal coordinates	[0.000, -0.029]
Warping parameter	-0.000
Barrier height	0.4 meV
Distance to barrier	0.0063 Å-1

Property (CBM)	Value
Min eff. mass	0.13 m0
Max eff. mass	1.24 m0
DOS eff. mass	0.41 m0
Crystal coordinates	[-0.000, -0.000]
Warping parameter	0.005
Barrier height	> 43.3 meV
Distance to barrier	> 0.0189 Å-1

Electronic properties

Born charges

ZPij	ux	uy	uz
Px	-0.00	-0.00	-0.35
Py	0.00	0.00	-0.00
Pz	-0.01	0.00	-0.00

ZPij	ux	uy	uz
Px	0.00	0.00	0.35
Py	-0.00	0.00	-0.00
Pz	0.01	0.00	0.00

ZPij	ux	uy	uz
Px	0.00	0.00	-0.35
Py	-0.00	0.00	0.00
Pz	-0.01	-0.00	0.00

ZPij	ux	uy	uz
Px	-0.00	-0.00	0.35
Py	0.00	0.00	0.00
Pz	0.01	-0.00	-0.00

Bader charges

Atom No.	Chemical symbol	Charges [|e|]
0	P	-0.00
1	P	0.00
2	P	-0.00
3	P	0.00

Berry Phase Spectrum

Optical properties

Optical polarizability

Properties
Interband polarizability (x) [Å]	6.055
Interband polarizability (y) [Å]	4.533
Interband polarizability (z) [Å]	0.343
Plasma frequency (x) [eV Å0.5]	0.000
Plasma frequency (y) [eV Å0.5]	0.000

Infrared polarizability

Static polarizability [Å]
Phonons only (x)	0.23
Phonons only (y)	0.00
Phonons only (z)	0.00
Total (phonons + electrons) (x)	6.29
Total (phonons + electrons) (y)	4.53
Total (phonons + electrons) (z)	0.34

Optical absorption (BSE and RPA)

Exciton binding energy (BSE) [eV]

0.62

Raman spectrum

Mode	Frequency (1/cm)	Degeneracy
Mode 1	0.4	3
Mode 2	128.4	1
Mode 3	187.7	1
Mode 4	225.3	1
Mode 5	350.9	1
Mode 6	426.6	1
Mode 7	433.4	1
Mode 8	437.7	1
Mode 9	465.2	1
Mode 10	468.	1

Miscellaneous

Miscellaneous details
Unique ID	4P-1
Number of atoms	4
Number of species	1
Formula	P4
Reduced formula	P
Stoichiometry	A
Unit cell area [Å2]	15.312
Original file-system folder	/home/niflheim2/cmr/C2DB-ASR/tree/A/P/P4-276f0a298324
Old uid	P4-276f0a298324
Space group (bulk in AA-stacking)	Pmna
Space group number (bulk in AA-stacking)	53
Point group	mmm
Inversion symmetry	Yes
Layer group number	42
Layer group	pman
2D Bravais type	Rectangular (op)
Thickness [Å]	2.110
Structure origin	original03-18
Band gap [eV]	0.903
gap_dir	0.903
gap_dir_nosoc	0.903
Vacuum level [eV]	3.233
Fermi level [eV]	-1.369
minhessianeig	-0.000
Dynamically stable	Yes
Band gap (HSE06) [eV]	1.511
Direct band gap (HSE06) [eV]	1.511
Valence band maximum wrt. vacuum level (HSE06) [eV]	-5.400

Miscellaneous details
Conduction band minimum vs. vacuum (HSE06) [eV]	-3.889
Band gap (G₀W₀) [eV]	2.025
Direct band gap (G₀W₀) [eV]	2.025
Valence band maximum wrt. vacuum level (G₀W₀) [eV]	-5.955
Conduction band minimum vs. vacuum (G₀W₀) [eV]	-3.930
E_B	0.624
Interband polarizability (x) [Å]	6.055
Interband polarizability (y) [Å]	4.533
Interband polarizability (z) [Å]	0.343
Static polarizability (phonons) (x) [Å]	0.232
Static polarizability (phonons + electrons) (x) [Å]	6.287
Static polarizability (phonons) (y) [Å]	0.000
Static polarizability (phonons + electrons) (y) [Å]	4.533
Static polarizability (phonons) (z) [Å]	0.000
Static polarizability (phonons + electrons) (z) [Å]	0.343
Plasma frequency (x) [eV Å0.5]	0.000
Plasma frequency (y) [eV Å0.5]	0.000
Energy [eV]	-21.301
ICSD id of parent bulk structure	ICSD 36434
COD id of parent bulk structure	COD 9012486
Mono/few-layer report(s)	10.1038/nnano.2014.35
Magnetic	No
Spin axis	z
Magnetic anisotropy energy, xz [meV/unit cell]	0.000
Magnetic anisotropy energy, yz [meV/unit cell]	0.000
topology	Not checked
Energy above convex hull [eV/atom]	0.039
Heat of formation [eV/atom]	0.039