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 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 cheap Numerically (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 cheap Numerically (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, (2004)‏ Nonselfconsistent implementation (post processing – i.e. no forces for relaxation!)‏ Trick – for relaxation we use Grimme’s semiempirical approach And for the final position we run a vdW-DF energy calculation with our JuNoLo code. Lazić P. et al Comput. Phys. Commun

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 C 6 and R 0. 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 C 6 and R 0. S. Grimme J. Comput. Chem. 27, 1787 (2006)‏ Minor problem C 6 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 C 6 and R 0. S. Grimme J. Comput. Chem. 27, 1787 (2006)‏ Minor problem C 6 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 C 6 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/Graphene Cell (compressed Iridium)‏ -Final check for C 6, 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 dz C =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): E GGA =+20 meV E total =-44 meV (vdW-DF, PBE exchange) E total =-50 meV (Grimme, so Ir C 6 is quite OK!)‏ If we use revPBE for exchange (as vdW-DF suggests) we get E total =-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): E GGA =+20 meV E total =-44 meV (vdW-DF, PBE exchange) E total =-50 meV (Grimme, so Ir C 6 is quite OK!)‏ If we use revPBE for exchange (as vdW-DF suggests) we get E total =-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 STRUCTURE Charge 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 STRUCTURE Charge 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 STRUCTURE Charge 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 STRUCTURE Nonlocal 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 STRUCTURE Nonlocal 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 (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 directly but in combination with semiempirical method seems to give good results so that is the approach that should be considered for other systems in 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