In 2D electron systems (2DESs) the electrons are confined to quantum wells in which the size is comparable or smaller than the Fermi wavelength. The most studied 2DESs are based on conventional semiconductors (Si, GaAs, etc.). Interestingly, in the mid 2000’s it was discovered that transition metal oxides can also host 2DESs. The archetypal example is the LaAlO3/SrTiO3 interface. Compared to conventional semiconductors, oxide interface 2DESs are more confined spatially (on the ~ 1 nm scale) and are characterized by electrons that can exhibit strong correlations. At temperatures below about 200 mK, a superconductive transition is observed.
Which is the origin of the 2DES at the LaAlO3/SrTiO3 (001) interface? The polar catastrophe scenario
LaAlO3 has electrically charged atomic planes along the  direction, whereas the planes of SrTiO3 are neutral along the same direction. The stacking of LaAlO3 planes thus creates a divergent electrostatic potential that, above a critical thickness (approx. 4 unit cells or about 1.6 nm) is suppressed by a charge transfer to the interface, forming the 2DES.
(Upper) Schematic depiction of the charge transfer driven by polar discontinuity. The charge transfer generates the 2DES at the interface. (Lower) STEM-HAADF image of the (001)-oriented LaAlO3/SrTiO3 interface (from D. Pesquera et al., Phys. Rev. Lett. 113, 156802 (2014))
Recently, we have revealed by HRTEM and STEEM/EELS the off-centered ion displacements in the lattice caused by the internal electric field when the thicknes of LaAlO3 is less than 4 uc (< 1.6 nm). At thicknesses above the threshold value > 4 uc (< 1.6 nm), these polar distortions disappear gradually. This is firsthand evidence of the existence of a sizable internal electric field caused by the electrostatic divergence when the thickness of LaAlO3 is below the critical value. Our results have been published in
The balance between two competing order parameters can be controlled by quantum confinement to stabilize a perovskite compound into one of two possible phases.
Dependence of the 2DES physical properties on the crystal symmetry
Over the last years, our research hes been focused on the study of the effect of crystal symmetry on the electronic band structure of 2DEGs at the LaAlO3/SrTiO3 interface. For that purpose, we have pioneered the research of oxide interfaces along crystal orientations other than the conventional <001>. Indeed, we have demonstrated the existence of 2DES beyond the conventional (001) orientation. See our work in Herranz et al., Scientific Reports 2, 758 (2012) doi:10.1038/srep00758. The existence of 2DES in quantum wells along different crystal orientations paves the way to the modulation of the physical properties of the two-dimensional electron gases (see below for more information about our research on this topic).
(Upper) Schematic representation of the atomic planes in LaAlO3/SrTiO3 interfaces oriented along different orientations. (Lower) Sheet resistance, carrier density and mobility of (110) and (111) interfaces. From Herranz et al., Sci. Rep. 2, 758 (2012)
Modulation of the 2D-superconductivity and Rashba spin-orbit fields in LaAlO3/SrTiO3 quantum wells built along different crystals orientations.
We have shown that the crystal symmetry imposes distinctive 2DEG orbital hierarchies on (001)-and (110)-oriented quantum wells. This, in turn, enables the selective occupancy of states of different symmetry (Pesquera et al., PRL 113, 156802 (2014)). This orientational tuning expands the possibilities for electronic engineering of these 2DESs and opens up opportunities to understand the link between orbital symmetry and complex correlated states at LaAlO3/SrTiO3 quantum wells.
Indeed, taking advantage of crystal symmetry, we have demonstrated the feasibility of ad-hoc selection of orbital symmetry to study their impact on physical properties. In particular, by carrying out electrostatic gating experiments in LaAlO3/SrTiO3 wells of different crystal orientations, we have observed that the spatial extension and anisotropy of the 2D superconductivity and the Rashba spin–orbit field can be largely modulated by controlling the 2DEG sub-band filling (Herranz et al., Nature Communications, 6 6028 (2015)).
(a) and (b) show the gate modulation of the superconductive transition for interfaces along (001) and (110) orientations, respectively. (c) Gate modulated spin orbit field (BSO) for (001) and (110)-oriented interfaces. (d) Schematic depiction of the orbital energy hierarchy of (001)- and (110)-oriented interfaces. From Herranz et al., Nature Comms. 6, 6028 (2015).