Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

Abstract

Electron localization in a metal, ultimately leadingto a metalinsulator (MI) transition, can occur because of disorder (Anderson transition) or electron-electron interactions (Mott-Hubbard transition). Both effects play a role in heavily doped semiconductors which have become prototype systems for the study of MI transitions. In this review we focus on phosphorus-doped Si. The statistical distribution of donor atoms on an atomic scale as the origin of random disorder can be checked by scanning tunneling microscopy. Long-range Coulomb interactions lead to AltshulerAronov corrections to the density of states N(EF) at the Fermi level and the electrical conductivity a(T) on the metallic side of the MI transition, and to a soft Coulomb gap at EF and Efros-Shklovskii variable-range hopping on the insulating side. On-site Coulomb interactions, on the other hand, lead to the formation of localized magnetic moments and the Kondo effect on the metallic side, and to a Hubbard splitting of thedonor band on the insulating side. The MI transition in Si:P can be tuned by varying the P concentration or -for barely insulating samples -by application of uniaxial stress S. The continuous stress tuning allows the observation of dynamic scaling of a(T,S) and hence a reliable determination of the critical exponent # of the extrapolated zero-temperature conductivity a(0)~l S -S¢ Iv, i.e. # --1, and of the dynamical exponent z --3. IntroductionThe problem of the metal-insulator (MI) transition in heavily doped semiconductors has come of age. Although these materials have become prototype systems for the study of a MI transition driven by the combined effects of disorder (Anderson transition) and electron-electron interactions (Mott-Hubbard transition), these effects are only beginning to be disentangled experimentally. In a strict sense, the MI transition viewed as a transition from extended to localized states at the Fermi level, occurs only at T = 0 because at finite temperature T thermally activated charge transport may occur. Hence a metal is defined by a finite dc conductivity a(T) for T --~0, while for an insulator a(0) = 0. Zero-point quantum fluctuations become important at a quantum phase transition between these two groundstates [1]. The determination of the critical exponent # describing how a(0) vanishes at T = 0 as a function of a control parameter 5 at a critical value 5c, i.e. a(0)~1 5 -5c I", has been a subject of considerable controversy, as will be discussed below. However, using both carrier concentration N and uniaxial stress S to

Disordered quantum spin chains with long-range antiferromagnetic interactions

“…These moments can be created from localized states in the tail of the band with onsite interactions 4,8 , or they may be created due to an instability of the disordered Fermi liquid with long-range interactions 5 . 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 .…”

“…Surprisingly, both magnetic susceptibility and specific heat measurements indicate that there remains a finite density of magnetic moments at the metal-insulator transition 1 . In P:Si about 10% of all dopants are magnetic at the metalinsulator transition (MIT)…”

“…Additionally we study the localization of spin excitations for ξ = ∞ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at αc = α * . The magnetic susceptibility of doped semiconductors such as P-doped Si is known to diverge at low temperature with an anomalous power law 1 . This can be taken as evidence for local magnetic moments, formed in localized states due to interactions [2][3][4][5] , that are positioned randomly, and coupled by exchange interactions [6][7][8][9] , as illustrated in Fig.…”

“…(1). From a numerical perspective, the onedimensional models offer the possibility of exploring larger length scales, and hopefully clearer asymptotic behavior.…”

Ferromagnetism and Metal-Insulator Transitions in Correlated Electron Systems with Alloy Disorder

“…For this reason disorder also requires a non-perturbative treatment. The simultaneous presence of interactions and disorder therefore leads to a highly non-trivial many-body problem [1][2][3][4] which is still far from understood.…”