Electron‐electron interactions and the metal‐insulator transition in heavily doped silicon

Abstract

This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.The metal-insulator (MI) transition in Si:P can be tuned by varying the P concentration or -for barely insulating samples -by application of uniaxial stress S. On-site Coulomb interactions lead to the formation of localized magnetic moments and the Kondo effect on the metallic side, and to a Hubbard splitting of the donor band on the insulating side. Continuous stress tuning allows the observation of finite-temperature dynamic scaling of σ(T, S) and hence a reliable determination of the critical exponent μ of the extrapolated zero-temperature conductivity σ(0) ∼ |S − Sc| µ , i.e., μ = 1, and of the dynamical exponent z = 3. The issue of half-filling vs. away from half-filling of the donor band (i.e., uncompensated vs. compensated semiconductors) is discussed in detail.

Dilute magnetic topological semiconductors

“…Performing the perturbative analysis up to the 2 R order, we obtain where we introduced a shorthand notation of δ (4) …”

“…The role of localized magnetic moments in metal-insulator transitions [1] lies at the heart of modern condensed matter physics, for example, the mechanism of high-T c superconductivity [2], the nature of non-Fermi-liquid physics near heavyfermion quantum criticality [3], and the problem of metalinsulator transitions in doped semiconductors [4][5][6]. Dilute magnetic semiconductors had been investigated for more than twenty years [7], where such spin-polarized electric currents have been realized but at low temperatures much below room temperature, prohibiting us from device applications.…”

Electronic disorder of P- and B-doped Si at the metal–insulator transition investigated by scanning tunnelling microscopy and electronic transport

“…These different behaviours all occur in the range of S up to 4 kbar. Still, the scaling behaviour of σ (S,T) is the same regardless of whether S [110] or [100], as long as we restrict our data to the region where σ (S, 4.2 K) increases monotonically with S. In both cases similar critical exponents are obtained: z ≈ 3 for the dynamical exponent and y ≈ 1 for the correlation-length exponent [45,47]. Even more, roughly the same exponents are found when applying σ (N,T) scaling for different samples close to N c [48] although here the scatter between different samples is larger than that between different uniaxial strains for a given (single) sample.…”

“…In addition, STM provides proof for a minimal distance between P or B dopants. We note that away from criticality, the on-site Coulomb interaction becomes decisive and affects the electronic properties resulting in the splitting of the DOS into a lower and an upper Hubbard band [47]. In particular, features of a Mott-Hubbard transition come into play away from N c .…”

“…Recent detailed work on Si:P demonstrates a strong directional strain dependence of the conductivity σ measured at 4.2 K [47]. Strain along [110] leads to a monotonic increase of σ (S), strain along [100] shows a non-monotonic σ (S) dependence, while strain along [111] leads to a weak overall decrease of σ (S).…”