Wigner-Mott scaling of transport near the two-dimensional metal-insulator transition

Electron-electron scattering usually dominates the transport in strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum ${\rho }_{\max }$ increases. Here we show that in this regime, the entire family of resistivity curves displays a characteristic scaling behavior $\rho \left(T\right)/{\rho }_{\max }\approx F(T/T_{\max }),$ while the ${\rho }_{\max }$ and $T_{\max }\sim T^{*}$ assume a power-law dependence on the quasiparticle effective mass $m^{*}$. Remarkably, precisely such trends are found from an appropriate scaling analysis of experimental data obtained from diluted two-dimensional electron gases in zero magnetic fields. Our analysis provides strong evidence that inelastic electron-electron scattering—and not disorder effects—dominates finite-temperature transport in these systems, validating the Wigner-Mott picture of the two-dimensional metal-insulator transition.

Figure 1

Resistivity as a function of temperature from the experiments on Si MOSFET by Pudalov et al. (Ref. 19).

Figure 2

Scaled resistivity as a function of scaled temperature for different electron (hole) concentrations, for (a) Si MOSFET and (b) GaAs heterostructures. The experimental data are taken from Ref. 21 (MOSFETs), Ref. 23 (p-GaAs/AlGaAs, blue symbols), Ref. 24 (n-GaAs/AlGaAs, green symbols), and Ref. 25 (p-GaAs, orange symbols). The solid line is the scaling function obtained for a simple model of the MIT (see Sec. IV).

Figure 3

(a) $T_{\max }$ normalized to Fermi temperature, and (b) maximal resistivity $\delta {\rho }_{\max }={\rho }_{\max }-{\rho }_o$ in units $\pi h/e^2$, as a function of a reduced density. The data are taken from Refs. 21, 23, and 24.

Figure 4

(a) Maximum resistivity $\delta {\rho }_{\max }={\rho }_{\max }-{\rho }_o$ as a function of $T_{\max }$. (b) $T_{\max }$ as a function of inverse effective mass $m^{*}$. $m_b$ is the band mass in Si MOSFETs. The data are taken from Refs. 21 and 26.

Figure 5

Resistivity as a function of temperature scaled as in Ref. 21. Red solid line is the calculated scaling curve.

Figure 6

Scaled resistivity curves for (a) ${\text{UBe}}_{13}$ and (b) $\kappa$-${\left(\text{ET}\right)}_2{\text{Cu}}_2{\left(\text{CN}\right)}_3$, for different external pressure. The data are taken from Refs. 4 and 7.

Figure 7

(a) Resistivity as a function of temperature for several interaction strengths in the half-filled Hubbard model solved within the DMFT. The resistivity is normalized to the Mott limit value, which corresponds to the scattering length of one lattice spacing. (b) Scaled resistivity curves.

Figure 8

(a) Maximum resistivity as a function of the corresponding temperature from the DMFT solution of the Hubbard model. (b) $T_{\max }$ as a function of the inverse effective mass.