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Bychkov-Rashba effect is dependent on the relative position of the system in the cell
Date: 2016/09/21 18:06
Name: Dubois S.   <simon.dubois@uclouvain.be>

Dear all,

I am working on spin-relaxation processes in 2D systems. Currently, I am interested in the impact of intrinsic and Rashba spin-orbit coupling (SOC) in carbon systems. I have used OpenMX v3.8 to simulate the band splittings induced by SOC in Haeckelites (i.e. planar carbon systems made of pentagonal, hexagonal and heptagonal rings) and the computed splittings accurately reproduce my reference all-electron calculations.

However, I am facing an issue when I am adding a perpendicular electric-field to investigate the Byckov-Rashba effect. Indeed, the value of the SOC induced bands splitting then appears to strongly depend (by a factor of 20) on the relative position of the atomic plane along the 'z'-axis.

Here below, I copy two of my input files that only differ with respect to the relative position of the carbon plane along the z-axis. I am quite new to OpenMX and I haven't been able to figure out where this 'z' dependence comes from.....

Any suggestion is welcome!
Thanks for your help!

S. Dubois

######################### INPUT 1 ##################################

System.CurrrentDirectory ./ # default=./
System.Name haeck
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 1 # default=1 (0-2)

data.path /home/ucl/naps/sdubois/PROGS/openmx3.8/DFT_DATA13

#
# Definition of Atomic Species
#

Species.Number 1
<Definition.of.Atomic.Species
C C6.0-s2p2d2 C_CA13
Definition.of.Atomic.Species>

#
# Atoms
#

Atoms.Number 16
Atoms.SpeciesAndCoordinates.Unit FRAC # Ang|AU
<Atoms.SpeciesAndCoordinates
1 C 0.0000000000000000 0.0000000000000000 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
2 C 0.1857263654461506 0.4337764424795359 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
3 C 0.5662235875204666 0.7519499369666159 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
4 C 0.2480500630333841 0.8142736495538542 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
5 C 0.4337764424795359 0.1857263654461506 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
6 C 0.7519499369666159 0.5662235875204666 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
7 C 0.8142736495538542 0.2480500630333841 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
8 C 0.1127550425495183 0.5893033626500752 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
9 C 0.4106966373499250 0.5234516648994383 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
10 C 0.4765483351005616 0.8872449724504865 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
11 C 0.5893033626500752 0.1127550425495183 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
12 C 0.5234516648994383 0.4106966373499250 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
13 C 0.8872449724504865 0.4765483351005616 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
14 C 0.0000000000000000 0.2097460630122455 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
15 C 0.7902539219877569 0.7902539219877569 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
16 C 0.2097460630122455 0.0000000000000000 0.000000000000000 2.0 2.0 0. 0. 0. 0. 0 off
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
7.0254943780836001 0.0000000000000000 0.0000000000000000
-3.5127471890887807 6.0842566055863347 0.0000000000000000
0.0000000000000000 0.0000000000000000 20.0000000000000000
Atoms.UnitVectors>

#
# SCF or Electronic System
#

scf.XcType LSDA-PW # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization NC # On|Off|NC
scf.SpinOrbit.Coupling on
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 300.0 # default=150 (Ry)
scf.maxIter 200 # default=40
scf.EigenvalueSolver cluster # DC|GDC|Cluster|Band
scf.Kgrid 11 11 1 # means n1 x n2 x n3
scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.30 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.400 # default=0.40
scf.Mixing.History 50 # default=5
scf.Mixing.StartPulay 5 # default=6
scf.criterion 1.0e-10 # default=1.0e-6 (Hartree)
scf.lapack.dste dstevx # dstevx|dstedc|dstegr,default=dstevx
scf.Electric.Field 0. 0. 1.

#
# MD or Geometry Optimization
#

MD.Type nomd # Nomd|Opt|NVE|NVT_VS|NVT_NH
# Constraint_Opt|DIIS
MD.maxIter 1 # default=1
MD.TimeStep 1.0 # default=0.5 (fs)
MD.Opt.criterion 1.0e-4 # default=1.0e-4 (Hartree/bohr)


#
# Bands Dispersion
#
Band.dispersion on # on|off, default=off
<Band.KPath.UnitCell
7.0254943780836001 0.0000000000000000 0.0000000000000000
-3.5127471890887807 6.0842566055863347 0.0000000000000000
0.0000000000000000 0.0000000000000000 20.0000000000000000
Band.KPath.UnitCell>
Band.Nkpath 3
<Band.kpath
30 0.00000000000 0.00000000000 0.00000000000 0.50000000000 0.00000000000 0.00000000000 g M
30 0.50000000000 0.00000000000 0.00000000000 0.33333333333 0.33333333333 0.00000000000 M K
30 0.33333333333 0.33333333333 0.00000000000 0.00000000000 0.00000000000 0.00000000000 K g
Band.kpath>

######################### INPUT 2 ##################################

System.CurrrentDirectory ./ # default=./
System.Name haeck
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 1 # default=1 (0-2)

data.path /home/ucl/naps/sdubois/PROGS/openmx3.8/DFT_DATA13

#
# Definition of Atomic Species
#

Species.Number 1
<Definition.of.Atomic.Species
C C6.0-s2p2d2 C_CA13
Definition.of.Atomic.Species>

#
# Atoms
#

Atoms.Number 16
Atoms.SpeciesAndCoordinates.Unit FRAC # Ang|AU
<Atoms.SpeciesAndCoordinates
1 C 0.0000000000000000 0.0000000000000000 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
2 C 0.1857263654461506 0.4337764424795359 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
3 C 0.5662235875204666 0.7519499369666159 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
4 C 0.2480500630333841 0.8142736495538542 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
5 C 0.4337764424795359 0.1857263654461506 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
6 C 0.7519499369666159 0.5662235875204666 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
7 C 0.8142736495538542 0.2480500630333841 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
8 C 0.1127550425495183 0.5893033626500752 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
9 C 0.4106966373499250 0.5234516648994383 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
10 C 0.4765483351005616 0.8872449724504865 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
11 C 0.5893033626500752 0.1127550425495183 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
12 C 0.5234516648994383 0.4106966373499250 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
13 C 0.8872449724504865 0.4765483351005616 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
14 C 0.0000000000000000 0.2097460630122455 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
15 C 0.7902539219877569 0.7902539219877569 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
16 C 0.2097460630122455 0.0000000000000000 0.250000000000000 2.0 2.0 0. 0. 0. 0. 0 off
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
7.0254943780836001 0.0000000000000000 0.0000000000000000
-3.5127471890887807 6.0842566055863347 0.0000000000000000
0.0000000000000000 0.0000000000000000 20.0000000000000000
Atoms.UnitVectors>

#
# SCF or Electronic System
#

scf.XcType LSDA-PW # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization NC # On|Off|NC
scf.SpinOrbit.Coupling on
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 300.0 # default=150 (Ry)
scf.maxIter 200 # default=40
scf.EigenvalueSolver cluster # DC|GDC|Cluster|Band
scf.Kgrid 11 11 1 # means n1 x n2 x n3
scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.30 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.400 # default=0.40
scf.Mixing.History 50 # default=5
scf.Mixing.StartPulay 5 # default=6
scf.criterion 1.0e-10 # default=1.0e-6 (Hartree)
scf.lapack.dste dstevx # dstevx|dstedc|dstegr,default=dstevx
scf.Electric.Field 0. 0. 1.

#
# MD or Geometry Optimization
#

MD.Type nomd # Nomd|Opt|NVE|NVT_VS|NVT_NH
# Constraint_Opt|DIIS
MD.maxIter 1 # default=1
MD.TimeStep 1.0 # default=0.5 (fs)
MD.Opt.criterion 1.0e-4 # default=1.0e-4 (Hartree/bohr)


#
# Bands Dispersion
#
Band.dispersion on # on|off, default=off
<Band.KPath.UnitCell
7.0254943780836001 0.0000000000000000 0.0000000000000000
-3.5127471890887807 6.0842566055863347 0.0000000000000000
0.0000000000000000 0.0000000000000000 20.0000000000000000
Band.KPath.UnitCell>
Band.Nkpath 3
<Band.kpath
30 0.00000000000 0.00000000000 0.00000000000 0.50000000000 0.00000000000 0.00000000000 g M
30 0.50000000000 0.00000000000 0.00000000000 0.33333333333 0.33333333333 0.00000000000 M K
30 0.33333333333 0.33333333333 0.00000000000 0.00000000000 0.00000000000 0.00000000000 K g
Band.kpath>

###################################################################

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Re: Bychkov-Rashba effect is dependent on the relative position of the system in the cell ( No.1 )
Date: 2016/09/21 18:58
Name: Artem Pulkin

"to strongly depend (by a factor of 20) on the relative position of the atomic plane along the 'z'-axis."

My first guess is that your electrons are trapped somewhere away from the material. Plot the charge density and check if it is the case. Also plot the potential profile to see if the sawtooth potential discontinuity does not happen in the vicinity of the material.
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Re: Bychkov-Rashba effect is dependent on the relative position of the system in the cell ( No.2 )
Date: 2016/10/16 21:45
Name: T. Ozaki

Hi,

The dependence comes from the use of fractional coordinate in the specification of
atomic coordinates.

In the use of fractional coordinate in the specification of atomic coordinates,
the origin of the unit cell is always set to (0,0,0), and the atomic coordinates
in xyz are generated starting from the origin (0,0,0). On the hand, the origin electric
field potential of the sawtooth shape is set to (the origin of the unit cell - the center
of the system). Therefore, when you shift the system along the c-axis, the relative position
of the sawtooth shape is also changed. That's why you had the dependence.

The dependency disappears if you use Cartesian coordinates for the specification of atomic
coordinates. In this case, the origin of the unit cell is determined by referring the atomic
coordinates you give.

Regards,

TO
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