Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.

We present a tight-binding calculation of a twisted bilayer graphene at magic angle θ ∼ 1.08 • , allowing for full, in-and out-of-plane, relaxation of the atomic positions. The resulting band structure displays as usual four narrow mini bands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the mini-bands Bloch functions reveals an emergent D6 symmetry, despite the lack of any manifest point group symmetry in the relaxed lattice. The Bloch functions at the Γ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C3z, i.e., transforming like one-dimensional, in-plane symmetric irreducible representation of an "emergent" D6 group. Out of plane, the lower doublet is even under C2x, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two s-like and two pz-like for each of the two supercell sublattices AB and BA are necessary, probably not sufficient, to describe the four mini bands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.

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The non-equilibrium approach to correlated electron systems is often based on the paradigm that different degrees of freedom interact on different timescales. In this context, photo-excitation is treated as an impulsive injection of electronic energy that is transferred to other degrees of freedom only at later times. Here, by studying the ultrafast dynamics of quasi-particles in an archetypal strongly correlated charge-transfer insulator (La 2 CuO 4 þ d ), we show that the interaction between electrons and bosons manifests itself directly in the photo-excitation processes of a correlated material. With the aid of a general theoretical framework (Hubbard-Holstein Hamiltonian), we reveal that sub-gap excitation pilots the formation of itinerant quasi-particles, which are suddenly dressed by an ultrafast reaction of the bosonic field.

We demonstrate that hexagonal graphene nanoflakes with zigzag edges display quantum interference (QI) patterns analogous to benzene molecular junctions. In contrast with graphene sheets, these nanoflakes also host magnetism. The cooperative effect of QI and magnetism enables spin-dependent quantum interference effects that result in a nearly complete spin polarization of the current and holds a huge potential for spintronic applications. We understand the origin of QI in terms of symmetry arguments, which show the robustness and generality of the effect. This also allows us to devise a concrete protocol for the electrostatic control of the spin polarization of the current by breaking the sublattice symmetry of graphene, by deposition on hexagonal boron nitride, paving the way to switchable spin filters. Such a system benefits from all of the extraordinary conduction properties of graphene, and at the same time, it does not require any external magnetic field to select the spin polarization, as magnetism emerges spontaneously at the edges of the nanoflake.

Strong correlations effects, which are often associated to the approach to a Mott insulating state, in some cases may be observed even far from half-filling. This typically happens whenever the inter-site Coulomb repulsion induces a tendency towards charge ordering, an effect that confines the electrons, and in turn favors local moment formation, i.e. Mott localization. A distinct intermediate regime then emerges as a precursor of such a Wigner-Mott transition, which is characterized by both charge and spin correlations, displaying large mass enhancements and strong renormalizations of other Fermi liquid parameters. Here we present a careful study of a quarter filled extended Hubbard model -a simple example where such physics can be studied in detail, and discuss its relevance for the understanding of the phenomenology of low-density two dimensional electron gases.

Mott insulators are "unsuccessful metals" in which Coulomb repulsion prevents charge conduction despite a metal-like concentration of conduction electrons. The possibility to unlock the frozen carriers with an electric field offers tantalizing prospects of realizing new Mott-based microelectronic devices. Here we unveil how such unlocking happens in a simple model that shows coexistence of a stable Mott insulator and a metastable metal. Considering a slab subject to a linear potential drop we find, by means of Dynamical Mean-Field Theory that the electric breakdown of the Mott insulator occurs via a first-order insulator-to-metal transition characterized by an abrupt gap-collapse in sharp contrast to the standard Zener breakdown. The switch-on of conduction is due to the field-driven stabilization of the metastable metallic phase. Outside the region of insulator-metal coexistence, the electric breakdown occurs through a more conventional quantum tunneling across the Hubbard bands tilted by the field. Our findings rationalize recent experimental observations and may offer a guideline for future technological research.

We solve the Periodic Anderson model in the Mott-Hubbard regime, using Dynamical Mean Field Theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metalinsulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the Periodic Anderson model, even in the Mott-Hubbard regime.PACS numbers: 71.30.+h,71.10.Fd,71.27.+a The metal-insulator transition in strongly correlated materials remains a central problem of modern condensed matter physics [1,2]. Great progress in its understanding was made possible by the development of new theoretical approaches such as the Dynamical Mean Field Theory [3], which is a method that becomes exact in the limit of large lattice connectivity [4]. The mean field equations can usually be tackled with a variety of numerical approaches which allow to obtain reliable solutions and insights. In this context, the Hubbard model, which is probably the simplest model that captures a correlation driven metal-insulator transition (MIT), called Mott-Hubbard transition, has received most of the attention in the past 15 years. As a result of intense investigation, our understanding of the metal-insulator transition in that model is now profound. The studies have unveiled a scenario where, at low temperatures and moderate interaction, the half-filled Mott insulator may be driven to a correlated metallic state through a first order transition [5]. The transition can occur as a function of correlation strength, temperature or doping. The first order line ends at finite temperature in a critical point and the critical region can be described by a GinzburgLandau theory [6]. This theoretical prediction was experimentally verified in experiments on V 2 O 3 [7]. The Hubbard model is often considered as a minimal model for the study of rather complicated compounds such as transition metal oxides and heavy fermion systems. This is supported by the implicit assumption that the Hubbard model is expected to be the effective low energy Hamiltonian for a wider class of more realistic multiband models for strongly correlated electron systems.On the other hand, a more realistic model which is also widely used in theoretical investigations of strongly interacting systems, though still schematic, is the Periodic Anderson model (PAM). In the context of correlated electron systems, this model permits to describe explicitly both, the localized orbitals, such as the d in transition metal oxides or the f in heavy fermion systems, and their hybridization to an itinerant electron band (such as that of p orbitals of oxygen in transition metal oxides). In fact, the PAM allows to investigate the various regimes where Mott insulating states occur, as characterized by the Zaanen-Sawatzky-Allen (ZSA) scheme...