Correlated hopping in honeycomb lattice: tracer diffusion coefficient at arbitrary lattice gas concentration

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Abstract
The tracer diffusion coefficient is investigated for a correlated diffusion of a tracer, which is a particle of the lattice gas. The lattice gas consists of particles of arbitrary concentration hopping on a two-dimensional honeycomb lattice, which interact only as repulsing point hard cores. Exchange between different particles is excluded, and any particle can jump only to the nearest-neighbour empty sites. The tracer diffusion coefficient is studied in a wide range of concentrations by the Monte Carlo simulations and compared with different theoretical predictions. It is shown that the Nakazato and Kitahara theory (1980) as well as the Tahir-Kheli and Elliot (1982) one give a good description of the simulation data. Moreover, it is proved that the traditional tracer diffusion coefficient that results from direct correlations over two consecutive jumps of a tracer is in distinct disagreement with the simulation data. Therefore a generalised expression for the tracer diffusion coefficient is derived; it includes direct correlations over an arbitrary number of jumps expressed in terms of integrals over 'waiting-time distributions'. The description of the data is much improved already by taking into account direct correlations over four jumps. Hence, it is concluded that the Nakazato and Kitahara theory as well as that of Tahir-Kheli and Elliott must include direct correlations over several consecutive jumps of a tracer-particle, which is not evident from the formalisms of these authors.