Nonlinear Hall effect and multichannel conduction in ${\text{LaTiO}}_3/{\text{SrTiO}}_3$ superlattices

We report magnetotransport properties of heterointerfaces between the Mott insulator ${\text{LaTiO}}_3$ and the band insulator ${\text{SrTiO}}_3$ in a delta-doping geometry. At low temperatures, we have found a strong nonlinearity in the magnetic field dependence of the Hall resistivity, which can be effectively controlled by varying the temperature and the electric field. We attribute this effect to multichannel conduction of interfacial charges generated by an electronic reconstruction. In particular, the formation of a highly mobile conduction channel revealed by our data is explained by the greatly increased dielectric permeability of ${\text{SrTiO}}_3$ at low temperatures and its electric field dependence reflects the spatial distribution of the quasi-two-dimensional electron gas.

Figure 1

(Color online) (a) Schematic representation of a delta-doped ${\text{LaTiO}}_3/{\text{SrTiO}}_3$ heterostructure and its energy band diagram. The superlattices are denoted as $\left[\text{L}m/\text{S}n\right]$, where L(S) refers to ${\text{LaTiO}}_3$ $\left({\text{SrTiO}}_3\right)$, and $m\left(n\right)$ indicates its thickness in unit cells. (b) RHEED oscillations during the growth of a [L1/S6] superlattice. (c) Cross-sectional Z-contrast image of a test sample with various $\left[\text{L}m/\text{S}n\right]$ superlattices. (d) High-resolution Z-contrast image of a [L2/S6] superlattice (left) and its colorized version (right).

Figure 2

(Color online) (a) Temperature dependence of 2D resistance per interface $R_{2\text{D}}=R_{\text{sheet}}{N}_{\text{IF}}$ for various configurations, where $R_{\text{sheet}}$ and $N_{\text{IF}}$ are the sheet resistance and the number of interfaces, respectively. (b) The carrier density per interface, $n_{2\text{D}}=n_{\text{sheet}}/N_{\text{IF}}$, at $T=100$ and 275 K as a function of La fraction where the sheet carrier density $n_{\text{sheet}}=-1/R_{\text{H}}e$. For comparison, we also plotted the carrier density obtained from optical spectroscopy (Ref. 11), the induced charge, $0.5e$ per unit cell (solid line), which is nominally expected to be transferred across the interfaces and the charge density (dashed line) for $\left(\text{La},\text{Sr}\right){\text{TiO}}_3$ solid solutions (Refs. 18, 19). [(c) and (d)] $R_{xy}\left(H\right)$ at various temperatures for [L1/S10] and [L1/S6] superlattices. The solid lines are fitted curves using the two-channel model. The dashed lines indicate the result of a linear fit of the high-field $R_{xy}\left(H\right)$ data.

Figure 3

(Color online) The temperature dependence of sheet carrier densities $n_i$ and mobilities ${\mu }_i$ $\left(i=1,2\right)$ assuming a two-channel conduction in various ${\text{LaTiO}}_3/{\text{SrTiO}}_3$ superlattices. The majority charge carriers (open circles) have lower mobility while the minority charge carriers (solid circles) have much higher mobility. At high temperatures, where $R_{xy}\left(H\right)$ shows almost linear field dependence (Fig. 2), we estimate the density and the mobility (open squares) for one type of charge carriers, which corresponds to the majority charge carriers. Schematics of the potential profile and wave function of charge carriers are shown in the inset. The LDHM and HDLM carriers stand for the low-density-high-mobility and high-density-low-mobility carriers, respectively. The higher dielectric constant $\epsilon$ of ${\text{SrTiO}}_3$ at low temperatures (left) makes the potential profile much shallower than that at high temperatures (right).

Figure 4

(Color online) (a) Hall resistance of a [L2/S6] superlattice as a function of magnetic field at $T=3\text{K}$ for various gate voltages increasing with a 20 V step between $-200$ and 200 V. The gate electric field was applied across the 0.5-mm-thick ${\text{SrTiO}}_3$ substrate through backside contacts. The solid lines are fitted curves using the two-channel model. (b) Gate voltage dependence of the 2D resistance. (c) Schematics of the effects of external electric field on the potential profile and wave function of charge carriers in a delta-doped superlattice. Here the gate electrode is assumed to be placed on the left side of the delta-doped layer. [(d) and (e)] The gate voltage dependence of carrier densities and mobilities for the two-channel conduction.