[Paper Review] Weak-localization type description of conduction in the "anomalous" metallic state

B. L. Altshuler, Geoffroy Martin+5 more|arXiv (Cornell University)|Aug 1, 2000

Surface and Thin Film Phenomena1 references3 citations

TL;DR

This paper proposes that the anomalous metallic-like resistivity behavior in high-mobility Si-MOSFETs—characterized by a positive temperature coefficient of resistivity (dρ/dT > 0) at elevated temperatures—is dominantly due to semiclassical scattering effects, not quantum localization. It demonstrates that the observed resistivity minimum in the crossover regime (T ≈ 0.01–0.1 E_F) can be quantitatively described using conventional weak-localization theory, with good agreement between theoretical predictions and experimental data for carrier densities above ~20×10¹¹ cm⁻².

ABSTRACT

This paper is devoted to the temperature dependence of the resistivity in Si- MOS samples over the wide range of densities in the ``metallic phase'' (n>n_c) but not too close to the critical density n_c. Three domains of different behavior in ρ(T) are identified. These are: [i] quantum domain of `low-temperatures', where a logarithmic T-dependence of ρ(with $dρ/dT<0$) dominates; [ii] semi-classical domain of `high-temperatures', in which Drude resistivity strongly varies with T (with dρ/dT>0); and [ii] crossover between the former two, where a linear T-dependence dominates (with dρ/dT>0). In the crossover regime and at higher densities (n>20x10^{11}/cm^2), ρ(T) goes through a minimum at temperature T_{min}. Both the absolute value of T_{min} and its dependence on density are found to be in an agreement with the conventional weak-localization theory. For n smaller than \sim 20x10^{11}/cm^2, the theoretical estimate for T_{min} falls outside the experimentally accessible temperature range. This explains the absence of the minimum at these densities in the data. In total, over the two decades in the temperature (domains [ii] and [iii]), the two semiclassical effects mimic the metallic like transport properties. Our analysis shows that the behaviour of ρ(T) in the region of ρ<< h/e^2 can be described phenomenologically in terms of the conventional weak-localization theory.

Motivation & Objective

• To clarify the origin of the metallic-like resistivity (dρ/dT > 0) observed in two-dimensional electron systems at low temperatures.
• To distinguish between quantum interference effects (e.g., weak localization) and semiclassical mechanisms in shaping the temperature dependence of resistivity.
• To identify and characterize three distinct regimes—quantum, crossover, and semiclassical—based on temperature and carrier density.
• To test whether the phenomenological weak-localization theory can quantitatively describe the resistivity minimum observed in high-mobility Si-MOSFETs.
• To reconcile discrepancies in prior experimental interpretations by showing that the apparent metallic behavior is a finite-temperature semiclassical artifact, not a sign of a true metallic ground state.

Proposed method

• The authors analyze experimental ρ(T) data from high-mobility Si-MOSFET samples across a wide range of carrier densities (n ≈ 1–35×10¹¹ cm⁻²) and temperatures (0.3–45 K).
• They normalize temperature to the Fermi energy (E_F) to reveal universal scaling behavior and identify three distinct regimes: quantum (T < T_q), crossover (T_q < T < T_cros), and semiclassical (T > T_cros).
• The crossover regime is modeled using a phenomenological approach combining a temperature-dependent Drude resistivity (ρ_Drude(T)) with weak-localization corrections (δρ(T)), assuming δρ(T) ∝ ln(T) at low T.
• The resistivity minimum T_min is determined by solving dρ/dT = 0, where ρ(T) = ρ_Drude(T) + δρ(T), with δρ(T) derived from standard weak-localization theory.
• Theoretical predictions for T_min are compared with experimental data, using both exponential and polynomial fits to ρ(T) in the crossover region.
• The analysis incorporates recent measurements of the quantum coherence time to define T_q ≈ 0.007 E_F and T_cros ≈ 0.07 E_F empirically.

Experimental results

Research questions

• RQ1 What causes the metallic-like temperature dependence of resistivity (dρ/dT > 0) in high-mobility 2D electron systems near the metal-insulator transition?
• RQ2 Can the observed resistivity minimum in the crossover regime be quantitatively explained by conventional weak-localization theory?
• RQ3 How do the relative contributions of quantum interference and semiclassical scattering vary across different temperature and density regimes?
• RQ4 Why is the resistivity minimum absent at low carrier densities (n < 20×10¹¹ cm⁻²) despite the presence of metallic-like behavior at higher temperatures?
• RQ5 To what extent can the full ρ(T) behavior in the regime ρ ≪ h/e² be described by a semiclassical Drude resistivity combined with weak-localization corrections?

Key findings

• The resistivity exhibits three distinct regimes: a quantum domain (T < T_q ≈ 0.007 E_F) with logarithmic T-dependence (dρ/dT < 0), a crossover domain (T_q < T < T_cros ≈ 0.07 E_F) with approximately linear T-dependence (dρ/dT > 0), and a semiclassical domain (T > T_cros) with strong positive T-dependence (dρ/dT > 0).
• For carrier densities ≥ 20×10¹¹ cm⁻², the resistivity minimum T_min is experimentally observable and its position shows good quantitative agreement with predictions from conventional weak-localization theory.
• For densities below ~20×10¹¹ cm⁻², the theoretical T_min falls below the lowest accessible temperature (T_acc ≈ 100 mK), explaining the absence of a minimum in experimental data.
• The position of T_min increases monotonically with carrier density, and the observed T_min(n) dependence is not universal but depends on the specific form of ρ_Drude(T) in each sample.
• The semiclassical T-dependence of resistivity persists down to temperatures as low as ~0.01 E_F, mimicking metallic behavior over a wide temperature range.
• The analysis shows that the observed metallic-like transport in the ρ ≪ h/e² regime can be successfully described by a phenomenological model combining semiclassical Drude resistivity and weak-localization corrections, without requiring a new quantum ground state.