Effects of the cubic vs quartic anharmonicity in gap and surface localized modes of diatomic chains

In this paper we discuss in detail the gap localized vibrational modes in a diatomic anharmonic chain. We consider a finite (even or odd9 number of particles interacting with nearest neighbours harmonic and cubic and quartic anharmonic force constants. The analysis of the effect of these anharmonic interactions shows that in the gap there are localized modes arising from the top of the acoustic branch with odd parity if they are centerewd on a heavy atom and even parity if they are centered on a light atom. These acoustic gap modes are related to the quartic anharmonicity, while there are localized modes arising from the bottom of the optical branch in presence of cubic anharmonicity. Th optical odd parity modes are centered on a light atom and the even parity modes are centered on a heavy atom. In addition to these gap modes we have found two types of surface modes. One which is remenescent of the surface mode occurring on a finite diatomic harmonic chain and the other entirely due to the anhermonicity.