Colloquium: Transport in strongly correlated two dimensional electron fluids

An overview of the measured transport properties of the two dimensional electron fluids in high mobility semiconductor devices with low electron densities is presented as well as some of the theories that have been proposed to account for them. Many features of the observations are not easily reconciled with a description based on the well understood physics of weakly interacting quasiparticles in a disordered medium. Rather, they reflect new physics associated with strong correlation effects, which warrant further study.

Figure 1

(Color online) Critical behavior of the resistivity near the 2D metal-insulator transition in (a) Si-MOSFET, (b) $p\text{−}\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure, (c) $n\text{−}\mathrm{Si}\mathrm{Ge}$ heterostructure, (d) $n\text{−}\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure, and (e) $p\text{−}\mathrm{Si}\mathrm{Ge}$ quantum well. The corresponding ranges of $r_s$ are (a) 14–19, (b) 12–32, (c) 27–47, (d) 5–14, and (e) 7–19. For comparison, we also show the critical behavior of the resistivity in Si:P, (f) a 3D system. Adapted from 78, 63, 85, 90, 24, and 121, respectively.

Figure 2

(Color online) Nonmonotonic temperature dependence of the resistivity in (a) (100) Si-MOSFET, (b) $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well, (c) $p\text{−}\mathrm{Si}\mathrm{Ge}$ quantum well, and (d) (111) Si-MOSFET deep in the metallic regime over an extended temperature range. The bare (nonrenormalized) Fermi temperatures are (a) 7.5, (b) 0.75, and (c) $7\mathrm{K}$. Adapted from 53, 23, and 99, respectively. Panel (d) courtesy of R. N. McFarland and B. E. Kane.

Figure 3

Giant magnetoresistance in a parallel magnetic field in (a) a strongly metallic Si-MOSFET, (b) a $10\text{−}\mathrm{nm}$-wide $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well, (c) a $n\text{−}\mathrm{Al}\mathrm{As}$ quantum well, and (d) a $n\text{−}\mathrm{Si}\mathrm{Ge}$ quantum well. Adapted from 112, 31, 85, and 54, respectively.

Figure 4

Parallel magnetic-field-induced metal-insulator transition in a Si-MOSFET. Adapted from 135.

Figure 5

(Color online) The slope $d\sigma ∕dT$ as a function of the parallel magnetic field (a) in a Si-MOSFET and (b) in a $10\text{−}\mathrm{nm}$-wide $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well. Adapted from 143 and 54, respectively.

Figure 6

(Color online) Magnetoresistance of the strongly correlated metallic 2D systems in a perpendicular magnetic field in (a) a Si-MOSFET and (b) a $10\text{−}\mathrm{nm}$-wide $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well. Adapted from 81 and 56, respectively.

Figure 7

Position of the lowest extended state on a $n\text{−}{B}_{\perp }$ diagram in a “weakly interacting” $(r_s\sim 1)$ $n\text{−}\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure (left-hand side) and in a “strongly interacting” $(r_s\sim 10)$ $p\text{−}\mathrm{Ga}\mathrm{As}$ heterostructure (right-hand side). Adapted from 36.

Figure 8

A map of the extended states for a highly disordered 2D hole system in a $\mathrm{Ge}∕\mathrm{Si}\mathrm{Ge}$ quantum well. The open circles represent the positions of the extended state in the quantum Hall effect regime. The solid circles correspond to the position of the lowest extended state. Numbers show the value of ${\rho }_{xy}h∕e^2$. Adapted from 67.

Figure 9

Bands of the extended states (white areas) in a dilute Si-MOSFET. The shaded area corresponds to localized states. The inset shows the expected floating of the extended states (74; 87). Adapted from 127.

Figure 10

(Color online) The critical magnetic field $B^{*}$ needed for complete spin polarization in a Si-MOSFET as a function of the electron density. Adapted from 126.

Figure 11

(Color online) Metallic $(d\rho ∕dT>0)$ temperature dependence of the resistivity in a $30\text{−}\mathrm{nm}$-wide $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well with $\rho >h∕e^2$ (see four lower curves). 2D hole densities are $6.1\times {10}^9$, $5.9\times {10}^9$, $5.7\times {10}^9$, $5.5\times {10}^9$, $5.3\times {10}^9$, and $5.1\times {10}^9{\mathrm{cm}}^{-2}$ from bottom to top curve. Adapted from 52.

Figure 12

Parallel field magnetoresistance in a Si-MOSFET at different electron densities across the metal-insulator transition. Adapted from 96.

Figure 13

Magnetoresistance of a highly resistive dilute 2D gas (a)–(c) in a perpendicular magnetic field in a Si-MOSFET and (d) in a $30\text{−}\mathrm{nm}$-wide $p\text{−}\mathrm{Ga}\mathrm{As}$ quantum well. Adapted from 32 and 52, respectively.

Figure 14

$R_{xx}\left(B_{\perp }\right)$ in a silicon MOSFET in the presence of a parallel field $B_{\parallel }=3.4\mathrm{T}$ used to suppress the metallic behavior (solid symbols). For comparison, the magnetoresistance in the absence of a parallel magnetic field is shown by the solid line. Adapted from 83.

Figure 15

In-plane magnetotransport data for $p_m=2.15\times {10}^{10}{\mathrm{cm}}^{-2}$ at $T=80$, 175, 250, and $400\mathrm{mK}$. (a) Inset: $\rho$ vs $B_{\parallel }$. Main plot: Data from inset normalized by its $B_{\parallel }=0$ value. (b) Inset: Corresponding data for ${\rho }_D$ vs $B_{\parallel }$. Main plot: Data from inset normalized by its $B_{\parallel }=0$ value. Adapted from 106.

Figure 16

Schematic phase diagram for 2D electrons in a MOSFET with no disorder.

Figure 17

The melting pressure of ${}^3\mathrm{He}$. Adapted from 119.