Oxide heterostructures are of great interest both for fundamental and applicative reasons. In particular the two-dimensional electron gas at the LaAlO3/SrTiO3 or LaTiO3/SrTiO3 interfaces displays many different physical properties and functionalities. However there are clear indications that the interface electronic state is strongly inhomogeneous and therefore it is crucially relevant to investigate possible intrinsic electronic mechanisms underlying this inhomogeneity. Here the electrostatic potential confining the electron gas at the interface is calculated self-consistently, finding that the electron confinement at the interface may induce phase separation, to avoid a thermodynamically unstable state with a negative compressibility. This provides a generic robust and intrinsic mechanism for the experimentally observed inhomogeneous character of these interfaces.PACS numbers: 73.43.Nq,73.21.Fg, The two-dimensional electron gas (2DEG) that forms at the interface of two insulating oxides, like LaAlO 3 /SrTiO 3 and LaTiO 3 /SrTiO 3 (hereafter generically referred to as LXO/STO) [1][2][3][4], exhibits a rich phenomenology, such as a gate-tunable metal-tosuperconductor transition [5][6][7][8], a magnetic-field-tuned quantum criticality [9], and inhomogeneous magnetic responses [10][11][12][13][14][15]. Tunneling [16,17] and SQUID magnetometry [18] provide clear evidence of an inhomogeneous interface on both micro-and nanoscopic scales. Transport measurements report further signs of inhomogeneity and a percolative metal-to-superconductor transition with a sizable fraction of the 2DEG never becoming superconducting down to the lowest accessible temperatures [19][20][21][22]. For both fundamental reasons and applicative purposes, like device design, it is crucial to identify possible intrinsic mechanisms that may render the 2DEG so strongly inhomogeneous via a phase separation (PS). This is precisely the focus of the present work.Here, we identify a very effective electron-driven mechanism leading to PS, based on the confinement of the 2DEG at the interface. From customary self-consistent calculations of the confining potential well in semiconductors, it is well known [23] that a finite lateral extension usually renders the 2DEG more compressible than its strictly 2D counterpart. This effect is much stronger in LXO/STO than in ordinary semiconductor interfaces, due to the huge dielectric constant of STO, allowing for much larger electron densities, with a strong amplification of the self-consistent adjustments of the confining potential. As a consequence, a non-rigid band structure arises, which varies with the local electron density: an increased electron density is accompanied by a corresponding increase of the positive countercharges (due to oxygen vacancies and/or polarity catastrophe [24][25][26][27][28][29]), from which the interfacial electrons are introduced and restoring the overall charge neutrality. For small-to-moderate increases of electron and countercharge densities the potential well deepens and the e...

It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that triggers sizeable Berry dipoles. We show indeed that uniaxially strained monolayer and bilayer graphene, with substrate-induced and gate-induced band gaps respectively, are characterized by Berry curvature dipoles comparable in strength to those observed in monolayer and bilayer transition metal dichalcogenides.

When the electron density of highly crystalline thin films is tuned by chemical doping or ionic liquid gating, interesting effects appear including unconventional superconductivity, sizeable spin-orbit coupling, competition with charge-density waves, and a debated low-temperature metallic state that seems to avoid the superconducting or insulating fate of standard two-dimensional electron systems. Some experiments also find a marked tendency to a negative electronic compressibility. We suggest that this indicates an inclination for electronic phase separation resulting in a nanoscopic inhomogeneity. Although the mild modulation of the inhomogeneous landscape is compatible with a high electron mobility in the metallic state, this intrinsically inhomogeneous character is highlighted by the peculiar behaviour of the metal-to-superconductor transition. Modelling the system with superconducting puddles embedded in a metallic matrix, we fit the peculiar resistance vs. temperature curves of systems like TiSe2, MoS2, and ZrNCl. In this framework also the low-temperature debated metallic state finds a natural explanation in terms of the pristine metallic background embedding non-percolating superconducting clusters. An intrinsically inhomogeneous character naturally raises the question of the formation mechanism(s). We propose a mechanism based on the interplay between electrons and the charges of the gating ionic liquid. arXiv:1706.01274v2 [cond-mat.mes-hall]

Several experiments reveal the inhomogeneous character of the superconducting state that occurs when the carrier density of the two-dimensional electron gas formed at the LaXO3/SrTiO3 (X=Al or Ti) interface is tuned above a threshold value by means of gating. Re-analyzing previous measurements, that highlight the presence of two kinds of carriers, with low and high mobility, we shall provide a description of multi-carrier magneto-transport in an inhomogeneous two-dimensional electron gas, gaining insight into the properties of the physics of the systems under investigation. We shall then show that the measured resistance, superfluid density, and tunneling spectra result from the percolative connection of superconducting "puddles" with randomly distributed critical temperatures, embedded in a weakly localizing metallic matrix. We shall also show that this scenario is consistent with the characteristics of the superconductor-to-metal transition driven by a magnetic field. A multi-carrier description of the superconducting state, within a weak-coupling BCS-like model, will be finally discussed.

We study one-dimensional structures that may be formed at the LaAlO 3 /SrTiO 3 oxide interface by suitable top gating. These structures are modeled via a single-band model with Rashba spin-orbit coupling, superconductivity and a magnetic field along the one-dimensional chain. We first discuss the conditions for the occurrence of a topological superconducting phase and the related formation of Majorana fermions at the chain endpoints, highlighting a close similarity between this model and the Kitaev model, which also reflects in a similar condition the formation of a topological phase. Solving the model in real space, we also study the spatial extension of the wave function of the Majorana fermions and how this increases with approaching the limit condition for the topological state. Using a scattering matrix formalism, we investigate the stability of the Majorana fermions in the presence of disorder and discuss the evolution of the topological phase with increasing disorder.