Large negative electronic compressibility of LaAlO${}_3$-SrTiO${}_3$ interfaces with ultrathin LaAlO${}_3$ layers

A two-dimensional electron liquid is formed at the $n$-type interface between SrTiO${}_3$ and LaAlO${}_3$. Here we report on Kelvin probe microscopy measurements of the electronic compressibility of this electron system. The electronic compressibility is found to be negative for carrier densities of $\approx {10}^{13}$/cm${}^2$. At even smaller densities, a metal-to-insulator transition occurs. These local measurements corroborate earlier measurements of the electronic compressibility of LaAlO${}_3$-SrTiO${}_3$ interfaces obtained by measuring the capacitance of macroscopic metal-LaAlO${}_3$-SrTiO${}_3$ capacitors.

Figure 1

Illustration of the experimental configuration. The force sensor consists of a quartz tuning fork.[25] The force between tip and sample is monitored as a function of $V_{\mathrm{ts}}$, the voltage applied between tip and sample. Through the back-gate voltage $V_{\mathrm{G}}$ between the interface and the silver paint at the back of the SrTiO${}_3$ substrate the carrier density at the interface can be tuned. A negative $V_{\mathrm{G}}$ causes the $n$-type interface electron system to be depleted. The current $I$ flowing into the interface and the force between tip and sample are recorded simultaneously.

Figure 2

(a) Topographic frequency-modulation scanning force microscopy image of the LaAlO${}_3$ film acquired at 4.7 K. The image was recorded with a scanning speed of 75 nm/s and a frequency shift of $\Delta f=-1.8$ Hz. The free resonance frequency of the cantilever was $f_0=25926.6$ Hz, the quality factor was $Q=20320$ and the oscillation amplitude was set to $A=3.4$ Å. The white dots in the scan are caused by adsorbates on the sample surface.(b) Profile taken along the blue line plotted in (a).

Figure 3

(a) Frequency shift $\Delta f$ of the cantilever oscillation frequency measured as a function of tip–sample voltage $V_{\mathrm{ts}}$. The spectrum was taken at 4.7 K with a sweep rate of 1 V/min on a position distant from topographic steps. The linear curve in the inset shows the quadratic dependence of $\Delta f$ on $V_{\mathrm{ts}}-V_{\Delta \phi }$. (b) Schematic band diagram of the interface and the tip. The contact potential difference $V_{\Delta \phi }$ corresponds to the difference of the work functions of interface ${\phi }_{\mathrm{s}}$ and tip ${\phi }_{\mathrm{t}}$. The nominal work function of the iridium tip is 5.27 eV[34] and we measure mV changes in $V_{\Delta \phi }$. The electrochemical potentials of sample and tip are labeled ${\mu }_{\mathrm{s}}$ and ${\mu }_{\mathrm{t}}$, respectively. In the case shown, the vacuum levels $E_{\mathrm{vac}}$ are balanced by a voltage $V_{\Delta \phi }$ applied between interface and tip.

Figure 4

(a) Contact potential difference $V_{\Delta \phi }$ measured as a function of $V_{\mathrm{G}}$. The measurements were performed at 4.7 K. Spectrum 2 was recorded directly after spectrum 1. $V_{\Delta \phi }$ was obtained through quadratic fits of the $\Delta f\left(V_{\mathrm{ts}}\right)$ spectra. (b) The inverse electronic compressibility $d{\mu }_{\mathrm{s}}/dn$ plotted as function of the change of the carrier density $\delta n$. The value of $\delta n$ was determined by integrating the capacitance between interface and back gate over the gate voltage.