Tight-binding modeling and low-energy behavior of the semi-Dirac point

Anisotropic magnetoresistance and electronic features of the candidate topological compound praseodymium monobismuthide

PrBi, a sister member of the rare-earth monopnictide family, is an excellent candidate for studying extreme magnetoresistance and nontrivial topological electronic states. In this study, we perform angular magnetoresistance measurements as well as bulk and surface band structure calculations on this compound. PrBi's magnetoresistance is revealed to be significantly angle-dependent and shows a fourfold symmetry as always observed in the nonmagnetic isostructural counterparts, including LaSb, LaBi, and LuBi. Its angular magnetoresistance can be reproduced well using the semiclassical two-band model. The deduced parameters suggest that PrBi hosts an elongated electron pocket with a mobility anisotropy of ∼3.13 and is slightly uncompensated in its carrier concentration. Our bulk and surface band structure calculations confirm the anisotropic electronic features. Moreover, we reveal that a nodal-line-shaped surface state appears at the X̄ point, and is associated with the quadratic dispersion along the -X̄ direction, and the linear type-I Dirac dispersion along the X̄-M̄ direction. Owing to the type-I Dirac dispersion feature, PrBi could serve as a promising material platform for studying many unexpected physical properties, such as the highly anisotropic transport and valley polarization of electrons.

Dirac cones in bipartite square-octagon lattice: A theoretical approach

Dirac cones are difficult to achieve in a square lattice with full symmetry. Here, we have theoretically investigated a bipartite tetragonal lattice composed of tetragons and octagons using both Tight-Binding (TB) model and density functional theory (DFT) calculations. The TB model predicts that the system exhibits nodal line semi-metallic properties when the on-site energies of all atoms are identical. When the on-site energies differ, the formation of an elliptical Dirac cone is predicted. Its physical properties (anisotropy, tilting, merging, and emerging) can be regulated by the hopping energies. An exact analytical formula is derived to determine the position of the Dirac point by the TB parameters, and a criterion for the existence of Dirac cones is obtained. The "divide-and-coupling" method is applied to understand the origin of the Dirac cone, which involves dividing the bands into several groups and examining the couplings among inter-groups and intra-groups. Various practical systems computed by DFT methods, e.g., t-BN, t-Si, 4,12,2-graphyne, and t-SiC, are also examined, and they all possess nodal lines or Dirac cones as predicted by the TB model. The results provide theoretical foundation for designing novel Dirac materials with tetragonal symmetry.

Quantum quench of photoinduced semi-Dirac materials: Hall response

In this work, far from equilibrium Hall response of semi-Dirac materials is studied. This required preparing the system in non-equilibrium states through a quantum quench protocol. We show that in the non-equilibrium setting, there is non-zero Hall response even when instantaneous time reversal symmetry (TRS) is present and the Hall current persists for long times. This is in contrast to the equilibrium case where the system is required to break TRS for a Hall response. This highlights unique features of far from equilibrium response in semi-Dirac materials that are not present in the corresponding equilibrium state.

Non-Hermitian semi-Dirac semi-metals

Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points (EPs) originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems.

Topological phase transition induced by band structure modulation in a Chern insulator

We study a systematic evolution of the topological properties of a Chern insulator upon smooth variation of a hopping parameter (t₁) of the electrons among a pair of nearest neighbour sites on a honeycomb lattice, while keeping the other two hopping terms (t) fixed. In the absence of a Haldane flux, the tuning oft₁results in gradual shifting of the Dirac cones which eventually merge into one at theMpoint in the Brillouin zone (BZ) att₁= 2twith a gapless semi-Dirac dispersion at low energies. In the presence of a Haldane flux, the system becomes a Chern insulator fort₁< 2t, but turns gapless att₁= 2twith the semi-Dirac dispersion being transformed to an anisotropic Dirac one. The spectrum eventually gaps out and transforms into a trivial insulator fort₁> 2t. The Chern number phase diagram obtained via integrating the Berry curvature over the BZ shows a gradual shrinking of the 'topological' lobes, and vanishes just beyondt₁= 2t, where a small but a finite Berry curvature still exists. Thus, there is a phase transition from a topological phase to a trivial phase across the semi-Dirac point (t₁= 2t). The vanishing of the anomalous Hall conductivity plateau and the merger of the chiral edge states with the bulk bands near theMpoint provide robust support of the observed phase transition.

Effect of Interactions on the Quantization of the Chiral Photocurrent for Double-Weyl Semimetals

The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied AC electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear DC current as it is second order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of non-zero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On examining the effect of short-ranged Hubbard interactions up to first-order corrections, we find that this quantization is destroyed. This implies that unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in topological semimetals is not protected.

Pressure and electric field tuning of Schottky contacts in PdSe2/ZT-MoSe2 van der Waals heterostructure

A two-dimensional van der Waals (vdW) heterostructure (PdSe₂/ZT-MoSe₂) has been investigated through vdW corrected density functional theory. ZT-MoSe₂ acts as a Dirac material with an anisotropic Dirac cone and variable Fermi velocity (0.52-1.91 × 10⁵ ms^-1). The intrinsic Schottky barrier height can be effectively tuned by applying external pressure and an electric field to the heterostructure. The p-type Schottky barrier transforms into a p-type ohmic contact at pressure P ≈ 16 GPa. A positive electric field induces p-type ohmic contact while a negative electric field results in the transition from p-type Schottky contact to n-type Schottky contact, and finally to n-type ohmic contact at the higher values of the field. Moreover, the external positive (negative) electric field induces n-type (p-type) doping of ZT-MoSe₂ in the heterostructure and remarkably controls the charge carrier concentration. Our results demonstrate that controlling the external pressure and electric field in a PdSe₂/ZT-MoSe₂ heterostructure can result in an unprecedented opportunity for the design of high-performance nanodevices.

Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling

We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly (d_{L}) and (at most) quadratically (d_{Q}) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with d_{Q}>0. As a demonstrative example, we relate a two-dimensional anisotropic semimetal with d_{L}=d_{Q}=1, describing the topological transition between a Dirac semimetal and a normal insulator, and its three-dimensional counterparts with d_{L}=1, d_{Q}=2. We address the quantum critical phenomena and emergence of non-Fermi liquid states with unusual dynamical structures within the framework of an ε expansion, where ε=2-d_{Q}, when these systems reside at the brink of charge- or spin-density-wave orderings, or an s-wave pairing. Our results can be germane to two-dimensional uniaxially strained optical honeymcomb lattice, α-(BEDT-TTF)_{2}I_{3}.

Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals

Cooper instability (CI) associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead CI can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the CI at zero chemical potential, which in principle are harmful to CI although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the CI is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.

Tunable Dirac cones in two-dimensional acoustic metamaterials with matryoshka structure

Dirac cones of an acoustic system are the foundation of most topological phase transitions and topological states and have recently become a research hotspot. Although the Dirac cones, Dirac-like cones, double Dirac cones, and semi-Dirac points are all skillfully designed, it is still indispensable to realize a tunable Dirac cone in a novel acoustic structure. This paper proposes two-dimensional acoustic metamaterials with matryoshka structure to achieve tunable Dirac cones and topological spin states. Dirac points can be obtained on the dispersion curves owing to the high symmetry. The concentric circular scattering units of the matryoshka structure are arranged in honeycomb lattices. By a rotating-scatterer mechanism to break the symmetry, the Dirac cone at K (K^') is split and the topological spin states appear at the band valley. The existence of a topological transition with opposite Chern numbers as the rotating angle varies is also verified, and helical edge states are obtained along the interfaces separating the topologically opposite spin states insulators. Moreover, the frequency of the Dirac cone is tuned by rotating the inner structure in a double-layer matryoshka structure.

Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids

We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.

Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials

We study the effects of four-fermion interaction and impurity on the low-energy states of 2D semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of 2D semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transitions and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.

A maximally particle-hole asymmetric spectrum emanating from a semi-Dirac point

Tight binding models have proven an effective means of revealing Dirac (massless) dispersion, flat bands (infinite mass), and intermediate cases such as the semi-Dirac (sD) dispersion. This approach is extended to a three band model that yields, with chosen parameters in a two-band limit, a closed line with maximally asymmetric particle-hole dispersion: infinite mass holes, zero mass particles. The model retains the sD points for a general set of parameters. Adjacent to this limiting case, hole Fermi surfaces are tiny and needle-like. A pair of large electron Fermi surfaces at low doping merge and collapse at half filling to a flat (zero energy) closed contour with infinite mass along the contour and enclosing no carriers on either side, while the hole Fermi surface has shrunk to a point at zero energy, also containing no carriers. The tight binding model is used to study several characteristics of the dispersion and density of states. The model inspired generalization of sD dispersion to a general  ±[Formula: see text] form, for which analysis reveals that both n and m must be odd to provide a diabolical point with topological character. Evolution of the Hofstadter spectrum of this three band system with interband coupling strength is presented and discussed.

Quasilinear quantum magnetoresistance in pressure-induced nonsymmorphic superconductor chromium arsenide

In conventional metals, modification of electron trajectories under magnetic field gives rise to a magnetoresistance that varies quadratically at low field, followed by a saturation at high field for closed orbits on the Fermi surface. Deviations from the conventional behaviour, for example, the observation of a linear magnetoresistance, or a non-saturating magnetoresistance, have been attributed to exotic electron scattering mechanisms. Recently, linear magnetoresistance has been observed in many Dirac materials, in which the electron–electron correlation is relatively weak. The strongly correlated helimagnet CrAs undergoes a quantum phase transition to a nonmagnetic superconductor under pressure. Here we observe, near the magnetic instability, a large and non-saturating quasilinear magnetoresistance from the upper critical field to 14 T at low temperatures. We show that the quasilinear magnetoresistance may arise from an intricate interplay between a nontrivial band crossing protected by nonsymmorphic crystal symmetry and strong magnetic fluctuations.

The electronic structure of the helimagnet CrAs is unusual due to its nonsymmorphic crystal symmetry. Here, the authors observe quasilinear magnetoresistance close to a pressure-driven superconducting transition, which may arise from the interaction of the band structure and magnetic fluctuations.

Existence of semi-Dirac cones and symmetry of two-dimensional materials

There have been growing efforts to find new two-dimensional (2D) materials with anisotropic properties due to their potential applications in electronics. Although in such a search, a symmetry based analysis can be useful, it has not been reported so far. Using group theory we have found sufficient conditions for the existence of a linear dispersion in one direction and quadratic one in perpendicular direction, in the vicinity of points of symmetry in the Brillouin zone (BZ) of any non-magnetic, 2D material with negligible spin-orbit coupling. We have formulated a set of symmetry conditions that lead to the semi-Dirac dispersion and analyzed all possible symmetries of 2D materials. In four, out of all eighty symmetry groups, combined time-reversal and crystal symmetry leads, at given points in the BZ, to such dispersion. The result is valid irrespectively of strength of electronic correlations in the system, model used to calculate the band structure, or the actual crystal structure that realizes given groups. We have illustrated our findings using a tight-binding example.

Fregoso B, de Juan F, Coh S, Moore JE. Design principles for shift current photovoltaics

While the basic principles of conventional solar cells are well understood, little attention has gone towards maximizing the efficiency of photovoltaic devices based on shift currents. By analysing effective models, here we outline simple design principles for the optimization of shift currents for frequencies near the band gap. Our method allows us to express the band edge shift current in terms of a few model parameters and to show it depends explicitly on wavefunctions in addition to standard band structure. We use our approach to identify two classes of shift current photovoltaics, ferroelectric polymer films and single-layer orthorhombic monochalcogenides such as GeS, which display the largest band edge responsivities reported so far. Moreover, exploring the parameter space of the tight-binding models that describe them we find photoresponsivities that can exceed 100 mA W-1. Our results illustrate the great potential of shift current photovoltaics to compete with conventional solar cells.

Semi-Dirac semimetal in silicene oxide

Silicene upon covalent addition of group-VI elements and strain engineering could exhibit semi-Dirac cones at the Brillouin zone center.

Emergent Non-Fermi-Liquid at the Quantum Critical Point of a Topological Phase Transition in Two Dimensions

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.

Novel Quantum Criticality in Two Dimensional Topological Phase transitions

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO₂-VO₂ heterostructure to organic material α-(BEDT-TTF)₂I₃ under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.

Dirac directional emission in anisotropic zero refractive index photonic crystals

A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal.

Highly Anisotropic Dirac Fermions in Square Graphynes

We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.

The rare two-dimensional materials with Dirac cones

Inspired by the great development of graphene, more and more research has been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition-metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann–Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.

In situ atom scale visualization of domain wall dynamics in VO2 insulator-metal phase transition

A domain wall, as a device, can bring about a revolution in developing manipulation of semiconductor heterostructures devices at the atom scale. However, it is a challenge for these new devices to control domain wall motion through insulator-metal transition of correlated-electron materials. To fully understand and harness this motion, it requires visualization of domain wall dynamics in real space. Here, domain wall dynamics in VO₂ insulator-metal phase transition was observed directly by in situ TEM at atom scale. Experimental results depict atom scale evolution of domain morphologies and domain wall exact positions in (202) and (040) planes referring to rutile structure at 50°C. In addition, microscopic mechanism of domain wall dynamics and accurate lattice basis vector relationship of two domains were investigated with the assistance of X-ray diffraction, ab initio calculations and image simulations. This work offers a route to atom scale tunable heterostructure device application.

Strong anisotropy of Dirac cones in SrMnBi2 and CaMnBi2 revealed by angle-resolved photoemission spectroscopy

The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One particular interest is to generate Dirac cone anisotropy so that the electrons can propagate differently from one direction to the other, creating an additional tunability for new properties and applications. While various theoretical approaches have been proposed to make the isotropic Dirac cones of graphene into anisotropic ones, it has not yet been met with success. There are also some theoretical predictions and/or experimental indications of anisotropic Dirac cone in novel topological insulators and AMnBi2 (A = Sr and Ca) but more experimental investigations are needed. Here we report systematic high resolution angle-resolved photoemission measurements that have provided direct evidence on the existence of strongly anisotropic Dirac cones in SrMnBi2 and CaMnBi2. Distinct behaviors of the Dirac cones between SrMnBi2 and CaMnBi2 are also observed. These results have provided important information on the strong anisotropy of the Dirac cones in AMnBi2 system that can be governed by the spin-orbital coupling and the local environment surrounding the Bi square net.

A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.

Constructing a large variety of Dirac-cone materials in the Bi(1-x)Sb(x) thin film system

We theoretically predict that a large variety of Dirac-cone materials can be constructed in Bi(1-x)Sb(x) thin films and we here show how to construct single-, bi- and tri-Dirac-cone materials with various amounts of wave vector anisotropy. These different types of Dirac cones can be of special interest to electronic device design, quantum electrodynamics and other fields.

Spontaneous quantum Hall effect via a thermally induced quadratic Fermi point

Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas, most of these special band-crossing points are built in the electronic structure of the noninteracting lattice models, we show that a quadratic Fermi point characterized by a nonzero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against the onset of scalar spin chirality that opens a gap and induces a spontaneous quantum Hall insulator as the temperature tends to zero.

Electronic phenomena at complex oxide interfaces: insights from first principles

Oxide interfaces have attracted considerable attention in recent years due to the emerging novel behavior which does not exist in the corresponding bulk parent compounds. This opens possibilities for future applications in oxide-based electronics and spintronics devices. Among the different materials combinations, heterostructures containing the two simple band insulators LaAlO(3) and SrTiO(3) have advanced to a model system exhibiting unanticipated properties ranging from conductivity, to magnetism, even to superconductivity. Electronic structure calculations have contributed significantly towards understanding these phenomena and we review here the progress achieved in the past few years, also showing some future directions and perspectives. A central issue in understanding the novel behavior in these oxide heterostructures is to discover the way (or ways) that these heterostructures deal with the polar discontinuity at the interface. Despite analogies to polar semiconductor interfaces, transition metal oxides offer much richer possibilities to compensate the valence mismatch, including, for example, an electronic reconstruction. Moreover, electronic correlations can lead to additional complex behavior like charge disproportionation and order, magnetism and orbital order. We discuss in some detail the role of finite size effects in ultrathin polar films on a nonpolar substrate leading to another intriguing feature-the thickness-dependent insulator-to-metal transition in thin LaAlO(3) films on a SrTiO(3)(001) substrate, driven by the impending polar catastrophe. The strong and uniform lattice polarization that emerges as a response to the potential build-up enables the system to remain insulating up to a few layers. However, beyond a critical thickness there is a crossover from an ionic relaxation to an electronic reconstruction. At this point two bands of electron and hole character, separated both in real and in reciprocal space, have been shifted sufficiently by the internal field in LaAlO(3) to impose the closing of the bandgap. We discuss briefly further parameters that allow one to manipulate this behavior, e.g. via vacancies, adsorbates or an oxide capping layer.