Composite fermions without a magnetic field: An application to the metal-insulator transition in a two-dimensional conductor with the long-range Coulomb interaction between electrons

Abstract

It is shown that a composite-fermion (CF) paradigm, which works nicely in the fractional quantum Hall effect, can be applied to the case of a low-density two-dimensional (2D) conductor with long-range Coulomb interactions between electrons without external magnetic field. This approach, based on the unitary Chern-Simons (CS) transformation, relates the physics of the metal-to-insulator transition (MIT) in 2D correlated electron system with the MIT in a 2D system of noninteracting CFs subject to the CS gauge field $b=2{\ensuremath{\Phi}}_{0}\ensuremath{\rho}(\mathbf{r})$ [${\ensuremath{\Phi}}_{0}$ is the flux quantum, $\ensuremath{\rho}(\mathbf{r})$ is the electron density]. The MIT in such system is of the same origin as a well-known transitions observed near the peaks in the diagonal resistivity ${R}_{xx}$ of a 2D electron gas in the integer quantum Hall effect. The calculated longitudinal resistivity changes the sign of the temperature derivative from the metal-like, $d{R}_{xx}/dT>0$, at $\ensuremath{\rho}>{\ensuremath{\rho}}_{c}$ to the insulatorlike, $d{R}_{xx}/dT<0$, at lower densities $\ensuremath{\rho}<{\ensuremath{\rho}}_{c}$. A separatrix ${R}_{xx}^{S}(T)$ demarcating the metal and insulator phases at the critical density ${\ensuremath{\rho}}_{c}$ is temperature independent in the uniform-density approximation $\ensuremath{\rho}(\mathbf{r})=\ensuremath{\rho}$. The CFs do not interact in this case, but if $\ensuremath{\rho}(\mathbf{r})\ensuremath{\ne}\ensuremath{\rho}$ a weak interaction between the CFs makes the separatrix a linear function of $T$. The mechanism of the CF conductivity near the ${\ensuremath{\rho}}_{c}$ is the Mott variable range hopping which, in full agreement with experiments, takes a form ${\ensuremath{\sigma}}_{xx}\ensuremath{\propto}\text{exp}[\ensuremath{-}A{X}^{\ensuremath{\gamma}/2}]$ assuming a scaling with respect to the variable $X=|\ensuremath{\rho}\ensuremath{-}{\ensuremath{\rho}}_{c}|/{T}^{\ensuremath{\kappa}}$, where $\ensuremath{\gamma}$ and $\ensuremath{\kappa}=1/\ensuremath{\gamma}$ are the critical indices of the MIT. External perpendicular magnetic field shifts the value of ${\ensuremath{\rho}}_{c}$ at which the MIT occurs due to the partial compensation of the CS gauge field $b$ but does not change the shape of the resistivity curves ${R}_{xx}(T)$. Reflection symmetry between the ${R}_{xx}$ and ${\ensuremath{\sigma}}_{xx}$ on the opposite sides of the MIT and other relations of the results obtained with experiments in the high-mobility silicon metal-oxide semiconductor field-effect transistors are discussed.