We report new measurements of the electrical conductivity σ of the canonical three-dimensional metal-insulator system Si:P under uniaxial stress S. The zero-temperature extrapolation of σ(S, T → 0) ∼| S − Sc | µ shows an unprecidentedly sharp onset of finite conductivity at Sc with an exponent µ = 1. The value of µ differs significantly from that of earlier stress-tuning results. Our data show dynamical σ(S, T ) scaling on both metallic and insulating sides , viz. σ(S, T ) = σc(T ) · F(| S − Sc | /T y ) where σc(T ) is the conductivity at the critical stress Sc. We find y = 1/zν = 0.34 where ν is the correlation-length exponent and z the dynamic critical exponent. 71.30.+h, 71.55.Cu, 72.80.Cw Quantum phase transitions have become of steadily increasing interest in recent years [1]. These continuous transitions ideally occur at temperature T = 0 where quantum fluctuations play the role corresponding to thermal fluctuations in classical phase transitions. In particular, certain types of metal-insulator transitions (MIT) such as localization transitions have been studied extensively. Experimentally, the MIT may be driven by an external parameter t such as carrier concentration N , uniaxial stress S, or electric or magnetic fields. Generally, electron localization might arise from disorder (Anderson transition) or from electron-electron (e-e) interactions (Mott-Hubbard transition) [2]. In Nature, these two features go hand in hand. For instance, the disorderinduced MIT occurring as a function of doping in threedimensional (d = 3) semiconductors where the disorder stems from the statistical distribution of dopant atoms in the crystalline host, bears signatures of e-e interactions as evidenced from the transport properties in both metallic [3] and insulating regimes [4]. This makes a theoretical treatment of the critical behavior of a MIT exceedingly difficult. Even for purely disorder-induced transitions, the critical behavior of the zero-temperature dc conductivity, σ(0) ∼| t − t c | µ where t c is the critical value of t, is not well understood. Theoretically, µ is usually inferred from the correlation-length critical exponent ν via Wegner scaling µ = ν(d−2). Numerical values of ν range between 1.3 and 1.6 [5,6].Experimentally, it has long been suggested that the critical behavior of the conductivity falls into two classes: µ ≈ 0.5 for uncompensated semiconductors and µ ≈ 1 for compensated semiconductors and amorphous metals [7]. However, there appears to be no clear physical distinction between these materials that would justify different universality classes. While many different materials were reported to show µ ≈ 1, the exponent µ ≈ 0.5 was largely based on the very elegant experiments by Paalanen and coworkers [8][9][10], where uniaxial stress was used to drive an initially insulating uncompensated Si:P sample metallic. This allows to fine-tune the MIT since the stress can be changed continuously at low T thus eliminating geometry errors incurring when different samples are employed in concentration tuning ...

The low‐temperature electrical conductivity σ(T) of uncompensated insulating Si : P with P concentration N just below the metal–insulator transition (MIT), i.e. 30×1018 cm–3 ≲ N ≲ 3.5 × 1018 cm–3, was measured between 0.05 and 5 K. With decreasing N, σ(T) shows a crossover from Mott variable‐range hopping (VRH) to Efros‐Shklovskii VRH. The data on the insulating side can be described by the universal phenomenological scaling function proposed by Aharony et al. From the N dependence of the Mott temperature TM a correlation‐length exponent ν = 1.1 is obtained, compatible with the conductivity exponent μ ≈ 1.3 for metallic samples. Indeed, the data on both sides of the MIT can be combined to yield dynamic scaling of σ(N, T). Upon lowering N on the insulating side further, a change from Efros‐Shklovskii VRH to simple activated conduction is observed near N ≈ 2.7 × 1018 cm–3. This is attributed to the activation from the lower to the upper Hubbard band, as inferred from a sign change in the thermoelectric power and the absence of such a feature in compensated Si:(P, B).

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Barely insulating, uncompensated Si:P samples have been tuned through the metal‐insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — Sc|μ, in disagreement with earlier stress tuning studies along [123‐] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress‐tuning measurements obey finite‐T scaling with a dynamic exponent z = 3.