Toward an artificial Mott insulator: Correlations in confined high-density electron liquids in SrTiO${}_3$

We investigate correlation physics in high-density, two-dimensional electron liquids that reside in narrow SrTiO${}_3$ quantum wells. The quantum wells are remotely doped via an interfacial polar discontinuity and the three-dimensional (3D) carrier density is modulated by changing the width of the quantum well. It is shown that even at 3D densities well below one electron per site, short-range Coulomb interactions become apparent in transport, and an insulating state emerges at a critical density. We also discuss the role of disorder in the insulating state.

Figure 1

(a) Schematic showing the origin of the fixed polar charge at SrTiO${}_3$/GdTiO${}_3$ interfaces, compensated by ∼3.5×10${}^{14}$ cm${}^{-2}$ mobile electrons at each interface. (b), (c) HAADF-STEM images of a unit cell of SrTiO${}_3$ embedded in GdTiO${}_3$. The image in (b) shows a larger field of view, confirming the uniform thickness of the SrTiO${}_3$ quantum well (thin dark region). The image in (c) is a magnified section of the atomic resolution image. The SrTiO${}_3$ appears darker in these images because of the lower atomic number of Sr relative to Gd.

Figure 2

(a) Sheet resistance as a function of $T^2$ for quantum wells of SrTiO${}_3$ embedded in GdTiO${}_3$, with different SrTiO${}_3$ quantum well thicknesses. The solid black lines are fits to Eq. (1). (b) Temperature coefficient $A$ as a function of carrier density for the samples investigated in this study and bulk La${}_x$Sr${}_{1-x}$TiO${}_3$ from the literature [Tokura et al. (Ref. 25) and Okuda et al. (Ref. 24)], respectively. $A$ was obtained from fits to Eq. (1) between ∼40 and 300 K, except for Gd${}_{0.285}$Sr${}_{0.715}$TiO${}_3$ and Gd${}_{0.56}$Sr${}_{0.44}$TiO${}_3$, for which it was obtained from ∼10 to 250 K. The thickness of the SrTiO${}_3$ quantum wells for the GdTiO${}_3$/SrTiO${}_3$/LSAT samples was between 0.4 and 8.6 nm [see Supplemental Material (Ref. 11)] and the 3D carrier concentrations were calculated from the sheet densities as described in the text. The vertical line is a guide to the eye showing the critical carrier density for which $A$ increases as the Mott transition is approached.

Figure 3

Sheet resistance as a function of temperature for insulating SrTiO${}_3$ quantum wells. The solid lines are the experimental data, the red dotted lines fits to an Arrhenius law, and the black dashed lines are fits to the Efros-Shklovskii law ($y=1/2$).