Thermodynamic Behavior near a Metal-Insulator Transition

Abstract

Measurements of the low-temperature specific heat of phosphorus-doped silicon for densities near the metal-insulator transition show an enhancement over the conduction-band itinerant-electron value. The enhancement increases toward lower temperatures but is less than that found for the spin susceptibility. The data are compared with various theoretical models; the large ratio of the spin susceptibility to specific heat indicates the presence of localized spin excitations in the metallic phase as the metalinsulator transition is approached. PACS numbers: 71.30.+h, 65.40.Em, 71.55.Jv The simple and well-understood microscopic physics of shallow impurities in semiconductors, such as phosphorus-doped silicon (Si:P), makes these systems especially attractive for a study of the metal-insulator (MI) transition in disordered systems. 1 In the insulating phase at low phosphorus concentrations, n, the donor electrons are bound to the phosphorus nuclei in a hydrogenic Is state. The Coulomb interactions between the electrons on different donors lead to an effective antiferromagnetic Heisenberg exchange interaction between the electron spins. The random locations of the donor nuclei lead to large variations in the magnitude of the exchange interaction. The resulting Heisenberg spin-y antiferromagnet was modeled successfully by Bhatt and Lee 2 where they showed that pairs of spins gradually condense into singlets with falling temperature according to a highly correlated, hierarchical scheme. The experimental data are consistent with such a model even close to the critical density n c , at sufficiently low temperatures. 3 " 6 In the metallic phase the electrons delocalize and well above the MI transition (n^2n c ) their interactions can be adequately described in terms of a disordered Fermi liquid. However, in the critical regime just above n c (n c ;S n < 2n c ) we have, at the moment, only a qualitative understanding of the electronic properties. Even though temperature and magnetic field dependences of the electrical conductivity in this dirty-metal regime are in reasonable agreement with the perturbative expansion of the scaling theories, 7 " 11 the critical conductivity exponent 0.5 remains poorly understood. The electron spin susceptibility 12 " 15 and specific heat 16 ' 17 are observed to be greatly enhanced over the expected degenerate-electron values. Such trends are predicted by the Brinkman-Rice treatment 18 for interacting electrons near the MI transition in a Hubbard model without disorder, as well as by the scaling theory of interacting electrons in disordered media. 10,11 Alternatively, an enhancement in the spin susceptibility is obtained if one assumes localized or nearly localized magnetic moments in the metallic phase just above n C9 similar to those in the n <n c insulating regime. 512 " 1519 An experimental distinction between the various theoretical scenarios has not yet been made. This is in part due to a lack of adequate data on properly characterized samples, and also because of the many adjustable p...

RKKY interactions and the Mott transition

“…Another interesting class of systems where both the Kondo effect and the RKKY correlations are believed to be crucial are exemplified by doped semiconductors 3 near the metal-insulator transition. In these systems, non-Fermi liquid 4,5 metallic behavior is observed, suggesting the coexistence of local moments and conduction electrons that seem decoupled from each other -another manifestation of the "twofluid" behavior 6 . There are many further examples where these effects are of key importance.…”

Effects of Disorder on Ferromagnetism in Diluted Magnetic Semiconductors

“…While it is generally accepted that the ferromagnetism is due to an effective interaction between the magnetic ions (Mn) mediated by mobile carriers (holes, since Mn, a group II element substitutes for Ga, a group III element), different models differ in detail, e.g. whether the interaction is RKKY or not, and also the approximations used to model the system.In nonmagnetic doped semiconductors, such as phosphorus doped silicon [8], there has been no evidence for ferromagnetism due to carriers. Indeed, carrier hopping at low doping concentrations in the insulating phase is known to induce antiferromagnetic interactions between localized states, leading to a valence-bond-glass like state down to the lowest observable temperatures [9].…”

“…In nonmagnetic doped semiconductors, such as phosphorus doped silicon [8], there has been no evidence for ferromagnetism due to carriers. Indeed, carrier hopping at low doping concentrations in the insulating phase is known to induce antiferromagnetic interactions between localized states, leading to a valence-bond-glass like state down to the lowest observable temperatures [9].…”

Disordered quantum spin chains with long-range antiferromagnetic interactions

“…At the same time, the power α m of the divergence of the magnetic susceptibility is experimentally observed to converge to a constant value as the doping concentration is increased beyond the MIT (in Si:P α m → .64 11 , α m → .62 10 and α m → .5 1,12 ). This situation has been modeled by a phenomenological two-fluid model 6,9,15,16 . It presumes that the antiferromagnetic interaction between localized magnetic moments is dominant even in the metallic phase, leading to the formation of a random singlet phase.…”