Graphene on Ir(111) surface: interplay between chemical bonding and

van der Waals

Predrag Lazić, Nicolae Atodiresei, Vasile Caciuc, Radovan Brako and Stefan Blügel

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

INSTITUT FÜR FESTKÖRPERFORSCHUNG (IFF) , FZ JÜLICH

RUDJER BOSKOVIC INSTITUTE

plazic@mit.edu

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

MOTIVATION: Experiment

Structure – Moiré 10×10 Graphene on 9×9 Iridium (111)

Typical STM images (there are also “strange” ones)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

Straightforward calculation – 4 layers of Iridium (324 atoms)- graphene 200 C atoms

Rather large supercell

Cutoff 400 eV

3×3 k-points

VASP

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

Straightforward calculation – 4 layers of Iridium (324 atoms)- graphene 200 C atoms

Rather large supercell

Cutoff 400 eV

3×3 k-points

VASP

BUT PROBLEM OCCURS! WE GET NO BINDING IN GGA (PBE)!

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

Straightforward calculation – 4 layers of Iridium (324 atoms)- graphene 200 C atoms

Rather large supercell

Cutoff 400 eV

3×3 k-points

VASP

BUT PROBLEM OCCURS! WE GET NO BINDING IN GGA (PBE)!

MOST PROBABLE CAUSE LACK OF vdW INTERACTION!

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Two ways out of the problem but within DFT framework

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Two ways out of the problem but within DFT framework

Use LDA

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Two ways out of the problem but within DFT framework

Use LDA Use some nonlocal density Functional like vdW-DF (2004)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Two ways out of the problem but within DFT framework

Use LDA Use some nonlocal density Functional like vdW-DF (2004)

Numerically cheapNumerically (very) expensive

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Two ways out of the problem but within DFT framework

Use LDA Use some nonlocal density Functional like vdW-DF (2004)

Numerically cheapNumerically (very) expensive

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

vdW-DF (Dion et al.)M. Dion, H. Rydberg, E. Schröder, D.C. Langreth and B.I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)

Nonselfconsistent implementation (post processing – i.e. no forces for relaxation!)

Trick – for relaxation we use Grimme’s semiempirical approachAnd for the final position we run a vdW-DF energy calculation with our JuNoLo code.Lazić P. et al. 2010 Comput. Phys. Commun. 181 371

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Grimme’s approach for forces (relaxation) + vdW-DF for energy (only at final relaxed position)

Grimme theory – semiempirical one, two coeffiecients for each element C6 and R0.S. Grimme J. Comput. Chem. 27, 1787 (2006)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Grimme’s approach for forces (relaxation) + vdW-DF for energy (only at final relaxed position)

Grimme theory – semiempirical one, two coeffiecients for each element C6 and R0.S. Grimme J. Comput. Chem. 27, 1787 (2006)

Minor problem C6 is not given for Ir.

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

Grimme’s approach for forces (relaxation) + vdW-DF for energy (only at final relaxed position)

Grimme theory – semiempirical one, two coeffiecients for each element C6 and R0.S. Grimme J. Comput. Chem. 27, 1787 (2006)

Minor problem C6 is not given for Ir.

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

LACK OF vdW IN “STANDARD” DFT

C6 for Ir, we determined by:

-Comparing adsorption of Bz on Ir(111) (energies) calculated with Grimme’s approach and vdW-DF calculation

-Comparing Grimme’s approach and vdW-DF for 1x1 commensurate Ir/GrapheneCell (compressed Iridium)

-Final check for C6, calculation of energy with vdW-DF for final configuration of a big (9×9/10×10) cell.

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

THEORETICAL DFT STRUCTURE WITH vdW

dzC=3.4±0.2 Å

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

THEORETICAL DFT STRUCTURE WITH vdW

Adsorption energy (per C atom, in graphite ~-50 meV):

EGGA=+20 meV

Etotal=-44 meV (vdW-DF, PBE exchange) Etotal=-50 meV (Grimme, so Ir C6 is quite OK!)

If we use revPBE for exchange (as vdW-DF suggests) we getEtotal=-11 meV

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

THEORETICAL DFT STRUCTURE WITH vdW

Adsorption energy (per C atom, in graphite ~-50 meV):

EGGA=+20 meV

Etotal=-44 meV (vdW-DF, PBE exchange) Etotal=-50 meV (Grimme, so Ir C6 is quite OK!)

If we use revPBE for exchange (as vdW-DF suggests) we getEtotal=-11 meV

Very interesting result – graphene buckling alone costs almost no energy!0.2 meV per C atom only! (~0.4 Å corrugation)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURE

Even though graphene is dominantly vdW binded there is some charge transfer in the system from graphene to Ir(111).

p-doped graphene

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURECharge transfer

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURECharge transfer

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURECharge transfer

Shift of Dirac’s cone +0.2 eV

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURENonlocal binding energy (almost as seeing vdW!)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

ELECTRONIC STRUCTURENonlocal binding energy (almost as seeing vdW!)

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

GROWTH, NOT SPOTTING THE PROBLEM TILL THE FULL MONOLAYER

n=19

Ref. [1] P. Lacovig et al., Phys. Rev. Lett. 103 166101 (2009).

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals

CONCLUSIONS

GGA is incapable of describing this system properly

Van der Waals interaction plays an important role

vdW-DF is too expensive for such a system to be used directlybut in combination with semiempirical method seems to give goodresults so that is the approach that should be considered for other systemsin which vdW plays a significant role

2010 APS March Meeting March 15–19, 2010; Portland, Oregon

Graphene on Ir(111) surface: interplay between chemical bonding and van der Waals