Gate-Tunable Band Structure of the LaAlO3−SrTiO3 Interface

Abstract

The two-dimensional electron system at the interface between LaAlO 3 and SrTiO 3 has several unique properties that can be tuned by an externally applied gate voltage. In this work, we show that this gate tunability extends to the effective band structure of the system. We combine a magnetotransport study on top-gated Hall bars with self-consistent Schrödinger-Poisson calculations and observe a Lifshitz transition at a density of 2.9 × 10 13 cm −2 . Above the transition, the carrier density of one of the conducting bands decreases with increasing gate voltage. This surprising decrease is accurately reproduced in the calculations if electronic correlations are included. These results provide a clear, intuitive picture of the physics governing the electronic structure at complex-oxide interfaces. DOI: 10.1103/PhysRevLett.118.106401 The two-dimensional electron system (2DES) at the interface between the band insulators LaAlO 3 (LAO) and SrTiO 3 (STO) displays many intriguing phenomena, which may be harnessed for novel electronic devices [1][2][3][4][5]. The discovery of superconductivity [6], magnetic signatures [7][8][9][10], and their apparent coexistence [11] sparked growing interest in this material system. These properties can be tuned by varying parameters during growth [4,7], as well as by an externally applied electric field after growth [12]. Using this field effect, control of superconductivity [13][14][15][16][17], of spin-orbit coupling [17][18][19][20], and of carrier mobility [21,22] has been reported. Recent progress on local control of superconductivity [16] opened a route towards electrically controlled oxide Josephson junctions [23,24], providing new opportunities for superconducting electronic devices. Because these phenomena are related to the interfacial band structure, a fundamental understanding of the band structure is vital for the understanding of these phenomena and their exploitation in electronic devices.The interface band structure is formed by the conduction band of STO, which is bent down at the interface and crosses the Fermi level [25]. The origin of the band bending is still an open question [26][27][28]. This band bending creates a potential well, confining the carriers to a few nanometers in the out-of-plane direction [29][30][31][32]. In the well, the effective band structure is formed by the Ti t 2g orbitals. For interfaces grown along the [001] direction, the in-plane oriented d xy bands lie below the out-of-plane oriented d yz;xz bands in energy due to the confinement, as measured using x-ray absorption [33].By backgating the interface through the STO substrate, an additional conduction channel was observed to emerge above a carrier density of ð1.7 AE 0.1Þ × 10 13 cm −2 [34]. This observation was linked to tuning the Fermi level across the bottom of the d yz;xz bands, making additional electron pockets available for conduction. As a result, the Fermi surface topology changes, which is the characteristic feature of a Lifshitz transition [35].The model proposed by Joshua et...

Possible flexoelectric origin of the Lifshitz transition in LaAlO3/SrTiO3 interfaces

“…The effects of gating have not been reported; however, one may infer from Fig. 4(a) that if the strain were to relax with increasing n 2D , the slope above the transition would be negative, as found in some experiments [15][16][17]. Figure 4(e) shows that the inclusion of intra-atomic interactions has a small quantitative effect on n 1xy , but does not change qualitative features of the transition.…”

“…From the form ofĤ U [Eq. (15)], it is clear that minimization of the intra-orbital Coulomb energy favors a spreading-out of charge between orbitals if U 0 and J are large, and the collapse of charge into a single orbital type if U is large. Indeed, we find that our calculations favor occupation of d xy orbitals over d xz and d yz orbitals when J < U 0 /5, and favor occupation of multiple orbital types when J > U 0 /5.…”

“…While there is general agreement that the sensitivity to doping is connected to an observed Lifshitz transition [5, 14-17] between a single occupied band at low density and multiple occupied bands at high density [6,[17][18][19][20][21][22][23][24], the mechanism by which this transition happens is not established.Density functional theory (DFT), while instrumental in establishing fundamental interface properties [25][26][27][28], finds electron densities that are an order of magnitude larger than the Lifshitz transition density n L ∼ 0.02-0.05 electrons per 2D unit cell, and cannot easily be tuned through the transition. Schrödinger-Poisson calculations, for which n 2D can be continuously tuned, persistently find multiple occupied bands even for n 2D n L [5,15,[29][30][31]. Indeed, we showed previously that, because of STO is close to a ferroelectric (FE) quantum critical point [32], electrons become deconfined from an ideal interface as n 2D → 0, and form a dilute quasi-threedimensional (quasi-3D) gas extending far into the STO substrate [33].…”

Superconducting dome in doped 2D superconductors with broken inversion symmetry

“…According to our analysis one can formulate two conditions which have to be met in order to observe the characteristic domelike shape driven by the inter-subband pairing: (i) the lack of the inversion symmetry and (ii) the energetic proximity of the bands between which the pairing appears. Both requirements are met in the LaAlO 3 /SrTiO 3 interface: (i) the calculations for the conduction band at LaAlO 3 /SrTiO 3 interface based on the Poisson equation demonstrate that the confinement in the z-direction at the interface has a shape of the triangular quantum well 34,41,42 , which leads to the lack of the inversion symmetry; (ii) the tight-binding model for the LaAlO 3 /SrTiO 3 structure reveals the presence of three bands two of which (d XY /d Y Z and d Y Z /d XZ ) have relatively similar Fermi surfaces just above the Lifshitz transition what makes the intersubband pairing between them possible 30 . Nevertheless, this proposal still needs a detailed theoretical analysis in a more realistic model with all three d XY , d XZ , d Y Z orbitals, and the influence of the spin-orbit coupling, included.…”

Correlation between superconductivity, band filling, and electron confinement at the LaAlO3/SrTiO3 interface

“…This led to proposals to base the phase diagram on the sheet conductivity [24][25][26][27], which also does not provide a universal result. Almost all these experiments were done in a backgate geometry, whereas topgating has a different effect on carrier mobility [28][29][30] and on the band structure [31]. This difference is due to the opposite direction of the applied electric field, resulting in a disparate effect on the shape of the confining 2 potential well.…”