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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. 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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