Overview: Ge₂

Structure info
Layer group	p-3m1
Layer group number	72
Structure origin	original03-18
ICSD id of parent bulk structure	ICSD 192507
Mono/few-layer report(s)	10.1088/1367-2630/16/9/095002

Stability
Energy above convex hull [eV/atom]	0.482
Heat of formation [eV/atom]	0.482
Dynamically stable	Yes

Basic properties
Magnetic	No
Topology	Z2=1
Band gap (PBE) [eV]	0.025
Band gap (HSE06) [eV]	0.025

Repeat: 1234   Download: XYZ CIF JSON

Axis	x [Å]	y [Å]	z [Å]	Periodic
1	4.047	-0.000	0.000	Yes
2	-2.023	3.505	0.000	Yes
3	0.000	0.000	15.200	No

Lengths [Å]	4.047	4.047	15.200
Angles [°]	90.000	90.000	120.000

Crystal structure

Symmetries
2D Bravais type	Hexagonal (hp)
Layer group number	72
Layer group	p-3m1
Space group number (bulk in AA-stacking)	164
Space group (bulk in AA-stacking)	P-3m1
Point group	-3m
Inversion symmetry	Yes

Structure data
Formula	Ge2
Stoichiometry	A
Number of atoms	2
Unit cell area [Å2]	14.183
Thickness [Å]	0.688

Stability

Convex hull

Ge2 (2Ge-1)
Heat of formation [eV/atom]	0.48
Energy above convex hull [eV/atom]	0.48

Monolayers from C2DB
Ge2, (2Ge-1)	0.48 eV/atom
Ge2 (2Ge-2)	0.49 eV/atom

Bulk crystals from OQMD123
Ge2	0.00 eV/atom

Phonons

Minimum eigenvalue of Hessian [eV/Ų]

-0.00

Linear deformations

Stiffness tensor

Cij (N/m)	xx	yy	xy
xx	48.87	16.22	-0.00
yy	16.08	48.83	-0.00
xy	-0.00	0.00	33.30

Stiffness tensor eigenvalues
Eigenvalue 0	32.70 N/m
Eigenvalue 1	33.30 N/m
Eigenvalue 2	65.00 N/m

Electronic bands

Band structure and DOS

Key values [eV]
Band gap (PBE)	0.025
Direct band gap (PBE)	0.025
Valence band maximum wrt. vacuum (PBE)	-4.477
Conduction band minimum wrt. vacuum (PBE)	-4.451

Electronic band structure (HSE06@PBE)

Key values [eV]
Band gap (HSE06)	0.025
Direct band gap (HSE06)	0.025
Valence band maximum wrt. vacuum (HSE06)	-4.511
Conduction band minimum wrt. vacuum (HSE06)	-4.486

Effective masses

Property (VBM)	Value
Min eff. mass	0.01 m0
Max eff. mass	0.01 m0
DOS eff. mass	0.01 m0
Crystal coordinates	[0.333, 0.333]
Warping parameter	-0.000
Barrier height	> 339.5 meV
Distance to barrier	> 0.0178 Å-1

Property (CBM)	Value
Min eff. mass	0.01 m0
Max eff. mass	0.01 m0
DOS eff. mass	0.01 m0
Crystal coordinates	[0.333, 0.333]
Warping parameter	0.000
Barrier height	> 317.0 meV
Distance to barrier	> 0.0178 Å-1

Electronic properties

Bader charges

Atom No.	Chemical symbol	Charges [|e|]
0	Ge	0.00
1	Ge	-0.00

Berry phase spectrum

Optical properties

Optical polarizability

Properties
Interband polarizability (x) [Å]	13.134
Interband polarizability (y) [Å]	13.134
Interband polarizability (z) [Å]	0.247
Plasma frequency (x) [eV Å0.5]	0.666
Plasma frequency (y) [eV Å0.5]	0.666

Optical absorption (BSE and RPA)

Raman spectrum

Mode	Frequency (1/cm)	Degeneracy
Mode 1	0.1	3
Mode 2	171.5	1
Mode 3	295.5	2

Miscellaneous

Miscellaneous details
Unique ID	2Ge-1
Number of atoms	2
Number of species	1
Formula	Ge2
Reduced formula	Ge
Stoichiometry	A
Unit cell area [Å2]	14.183
Original file-system folder	/home/niflheim2/cmr/C2DB-ASR/tree/A/Ge/Ge2-bbbd76379a3d
Old uid	Ge2-bbbd76379a3d
Space group (bulk in AA-stacking)	P-3m1
Space group number (bulk in AA-stacking)	164
Point group	-3m
Inversion symmetry	Yes
Layer group number	72
Layer group	p-3m1
2D Bravais type	Hexagonal (hp)
Thickness [Å]	0.688
Structure origin	original03-18
Band gap (PBE) [eV]	0.025
Direct band gap (PBE) [eV]	0.025
gap_dir_nosoc	0.000
Vacuum level [eV]	2.134
Fermi level wrt. vacuum (PBE) [eV]	-4.464
Valence band maximum wrt. vacuum (PBE) [eV]	-4.477

Miscellaneous details
Conduction band minimum wrt. vacuum (PBE) [eV]	-4.451
minhessianeig	-0.000
Dynamically stable	Yes
Band gap (HSE06) [eV]	0.025
Direct band gap (HSE06) [eV]	0.025
Fermi level wrt. vacuum (HSE) [eV]	-4.499
Valence band maximum wrt. vacuum (HSE06) [eV]	-4.511
Conduction band minimum wrt. vacuum (HSE06) [eV]	-4.486
Interband polarizability (x) [Å]	13.134
Interband polarizability (y) [Å]	13.134
Interband polarizability (z) [Å]	0.247
Plasma frequency (x) [eV Å0.5]	0.666
Plasma frequency (y) [eV Å0.5]	0.666
Energy [eV]	-8.068
ICSD id of parent bulk structure	ICSD 192507
Mono/few-layer report(s)	10.1088/1367-2630/16/9/095002
Magnetic	No
Spin axis	z
Magnetic anisotropy energy, xz [meV/unit cell]	0.000
Magnetic anisotropy energy, yz [meV/unit cell]	0.000
Topology	Z2=1
Energy above convex hull [eV/atom]	0.482
Heat of formation [eV/atom]	0.482