Two-Dimensional Superconducting Phase in ${\mathrm{LaTiO}}_3/{\mathrm{SrTiO}}_3$ Heterostructures Induced by High-Mobility Carrier Doping

In this Letter, we show that a superconducting two-dimensional electron gas is formed at the ${\mathrm{LaTiO}}_3/{\mathrm{SrTiO}}_3$ interface whose transition temperature can be modulated by a back-gate voltage. The gas consists of two types of carriers: a majority of low-mobility carriers always present, and a few high-mobility ones that can be injected by electrostatic doping. The calculation of the electron spatial distribution in the confinement potential shows that the high-mobility electrons responsible for superconductivity set at the edge of the gas whose extension can be tuned by the field effect.

Figure 1

Superconducting transition as a function of gate voltage for sample $A$ ($XX$ direction). (a) Sheet resistance of sample A in color scale as a function of temperature and gate voltage from $-50\mathrm{V}$ to $+200\mathrm{V}$; the superconducting transition temperature (defined as a 15% drop in sheet resistance) is superimposed as a white dashed line (see Part I of the Supplemental Material [19] for a discussion on the $T_c$ criterion). (b) Sheet resistance as a function of temperature for selected gate voltages. (c) Sheet resistance at 450 mK (left scale) and superconducting transition temperature (right scale) as a function of gate voltage (see Part II of the Supplemental Material [19] for the $YY$ direction).

Figure 2

Hall effect and two carrier analysis. (a) Hall resistance as a function of magnetic field for different gate voltages measured at 4.2 K on sample $A$ ($YY$ direction). Open symbols correspond to experimental data, and full lines to fits with Eq. (1). An offset, indicated by a black horizontal segment and an arrow, has been added to separate the curves. (b) Sheet resistance (left scale) and carrier density (right scale) extracted from Eq. (1) as a function of gate voltage measured at 4.2 K. $n_1$ ($n_2$) corresponds to LMC (HMC), $n_{\mathrm{total}}$ to the total density of carriers and $n_{\mathrm{Hall}}$ to the low-field Hall number. (c) Mobilities ${\mu }_1$, ${\mu }_2$, and ${\mu }_{\mathrm{Hall}}$ corresponding to LMC, HMC, and the low-field Hall number extracted from Eq. (1).

Figure 3

Evolution of carrier density and mobility as a function of gate voltage and temperature. (a) Low-field (5 T) Hall number of carriers (full lines) and total number of carriers extracted from capacitance measurements (open symbols) as a function of gate voltage measured at different temperatures on sample $B$. Total number (squares) and low-field Hall number (triangles) extracted from the two carrier analysis of high-field experiments (45 T) are superimposed to the other curves, showing a very good agreement. (b) Hall mobility corresponding to low-field measurements as a function of gate voltage at the same temperatures. Beyond 60 K, that is, when the nonlinearity of ${ϵ}_R$ strongly decreases, $n_S$ and ${\mu }_{\mathrm{Hall}}$ recover regular behavior with the gate voltage, that is, a rather constant mobility and a linear increase of the carriers concentration expected for a single carrier fluid.

Figure 4

Subband filling calculation in the interface potential well. (a–c) ${\mathrm{SrTiO}}_3$ band bending calculation for three different gate voltages ($-200\mathrm{V}$, 0 V, $+200\mathrm{V}$) obtained with the experimental sheet carrier densities of Fig. 2c. The figure displays the conduction band profile $E_C$ (black), the Fermi energy $E_F$ (green dashed), the subband energies (red), and the carrier density $n$ (deep blue, left scale) as a function of depth $z$ from the interface. The dielectric constant ${ϵ}_R$ as a function of $z$ is drawn on a log scale from 260 to 26000 (see Fig. 4 of the Supplemental Material [19] for the precise scale). The square modulus of the envelope function of the first and last filled subbands is indicated in arbitrary units (red areas). Inset: conduction band profile $E_C$ at larger scale (0–100 nm) for the three different gate voltages. (d) 2DEG extension from the interface taken as the crossing point of $E_C$ and $E_F$ (left scale) and carrier density $n_2$ of HMC (right scale) as a function of gate voltage. The superconducting transition temperature as measured in Fig. 1c is superimposed with the same scale, as a reminder.