Metal-Insulator Transitions at Surfaces

Various types of metal-insulator transitions are discussed to find conditions for which an ideal surface of a bulk insulator is metallic. It is argued that for the correlation-driven Mott metal-insulator transition the surface phase diagram should be expected to have the same topology as the phase diagram for magnetic order at surfaces: The corresponding linearized mean-field descriptions, a simplified dynamical mean-field theory of the Hubbard model and the Weiss mean-field theory for the Ising model, are found to be formally equivalent. A new kind of surface state appears in the low-energy part of the one-particle excitation spectrum as a precursor effect of the Mott transition. The Mott metal-insulator transition at a crystal surface is a subject that touches different areas in solid-state theory which are usually treated as being disjoined: many-body theory of the correlation-driven metal-insulator transition, the general theory of surface phase transitions, and the theory of electronic surface states. It is the intention of the present paper to show that a corresponding combination of different concepts can be fruitful and allows for some new theoretical predictions. 1 Surface Phase Transitions The large variety of novel and interesting phenomena in surface physics is closely related with the occurrence of surface phase transitions. As has been pointed out by Mills [1], the surface of a system may undergo a phase transition at a critical temperature Tc,s being different from the bulk critical temperature Tc, i.e. the surface may undergo its own phase transition. Critical exponents, for example, can be defined and determined which are specific for the transition at the surface and which cannot be fully reduced to the bulk critical exponents [2,3]. Different kinds of surface phase transitions are conceivable and have been found, e.g. structural transitions, such as deviating geometrical order of the atoms near the surface of a single crystal (surface reconstruction), the loss of long-range crystalline order at the surface prior to a bulk melting transition (surface melting) or enrichment of one component at the surface of a solid binary alloy (surface segregation) [2]. Typical examples for surface phase transitions are also found among magnetically ordered systems: For example, the (0001) surface of ferromagnetic Gd is believed to have a Curie temperature which is higher than the bulk TC [4].