Patterns in strained epitaxial layers: Beyond the Frenkel-Kontorova model

Although the structures of strained overlayers have been understood in terms of the classical Frenkel-Kontorova model [1], our recent work indicates that these structures can have a quantum mechanical origin. Experimental STM studies show that the second layer of Ag on Pt(111) forms a striped pattern [2]. We simulated the striped phase with a combination of DFT, to quantify Ag pair interactions up to the 53$^{rd}$ neighbor [3], and Monte Carlo (MC). Our MC simulations yield a striped phase with the experimental characteristics: stripes along the $[112] $ direction that alternate between fcc and hcp sites. Although our DFT pair potential can be fit in an average way to a theoretical expression with radial symmetry [4], this fit cannot produce the striped phase, indicating that angular variations in the potential are important in producing this phase. [1] J. Frenkel and T. Kontorova, Journal of Physics-USSR 1, 137 (1939). [2] H. Brune, H. Roder, C. Boragno, and K. Kern, Phys. Rev. B 49, 2997 (1994). [3] W. Luo and K. A. Fichthorn, Phys. Rev. B 72, 115433 (2005). [4] P. Hyldgaard and M. Persson, J. Phys: Cond. Matter 12, 2981 (2000).