Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models.

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of Sriram Ganeshan, J. H. Pixley, and S. Das Sarma [Phys. Rev. Lett. 114, 146601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.146601] and J. Biddle and S. Das Sarma [Phys. Rev. Lett. 104, 070601 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.070601]. The analytical treatment follows from recognizing these models as a novel type of fixed points of the renormalization group procedure recently proposed in Phys. Rev. B 108, L100201 (2023)10.1103/PhysRevB.108.L100201 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and nontrivial mobility edges in an undriven system without the need for the unbounded potentials required by previous proposals.

Disorder-Driven Multifractality Transition in Weyl Nodal Loops.

The effect of short-range disorder in nodal line semimetals is studied by numerically exact means. For arbitrary small disorder, a novel semimetallic phase is unveiled for which the momentum-space amplitude of the ground-state wave function is concentrated around the nodal line and follows a multifractal distribution. At a critical disorder strength, a semimetal to compressible metal transition occurs, coinciding with a multi- to single-fractality transition. The universality class of this critical point is characterized by the correlation length and dynamical exponents. At considerably higher disorder, an Anderson metal-insulator transition takes place. Our results show that the nature of the semimetallic phase in nonclean samples is fundamentally different from a clean nodal semimetal.

Temperature-Driven Gapless Topological Insulator.

We investigate the phase diagram of the Haldane-Falicov-Kimball model-a model combining topology, interactions, and spontaneous disorder at finite temperatures. Using an unbiased numerical method, we map out the phase diagram on the interaction-temperature plane. Along with known phases, we unveil an insulating charge ordered state with gapless excitations and a temperature-driven gapless topological insulating phase. Intrinsic-temperature-generated-disorder is the key ingredient explaining the unexpected behavior. Our findings support the possibility of having temperature-driven topological transitions into gapped and gapless topological insulating phases in mass unbalanced systems with two fermionic species.

Symmetry Breaking and Lattice Kirigami.

We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.

Chern band insulators in a magnetic field.

The effect of a magnetic field on a two-dimensional Chern band insulator is discussed. It is shown that, unlike the trivial insulator, an anomalous Hall insulator with Chern number C becomes a metal when a magnetic field is applied at constant particle density, for any C > 0. For a time-reversal invariant topological insulator with a spin Chern resolved number, C↑ = −C↓ = C, the magnetic field induces a spin polarized spin Hall insulator. We consider also the effect of a superlattice potential and extend previous results for the quantization of the Hall conductance of filled Hofstadter bands to this problem.

Topological Fermi liquids from Coulomb interactions in the doped honeycomb lattice.

We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple lattice models based on enlarging the unit cell. As an example we study the honeycomb lattice with nearest neighbor hopping and a local nearest neighbor Coulomb interaction V. We show that when the unit cell is enlarged to host six atoms that permits Kekulé distortions, self-consistent currents spontaneously form creating nontrivial magnetic configurations with total zero flux at high electron densities. A very rich phase diagram is obtained within a variational mean field approach that includes metallic phases with broken time reversal symmetry (T). The predominant (T) breaking configuration is an anomalous Hall phase, a realization of a topological Fermi liquid.

New type of vacancy-induced localized States in multilayer graphene.

We demonstrate the existence of a new type of zero energy state associated with vacancies in multilayer graphene that has a finite amplitude over the layer with a vacancy and adjacent layers, and the peculiarity of being quasilocalized in the former and totally delocalized in the adjacent ones. In a bilayer, when a gap is induced in the system by applying a perpendicular electric field, these states become truly localized with a normalizable wave function. A transition from a localized to an extended state can be tuned by the external gate for experimentally accessible values of parameters.

Limits on charge carrier mobility in suspended graphene due to flexural phonons.

The temperature dependence of the mobility in suspended graphene samples is investigated. In clean samples, flexural phonons become the leading scattering mechanism at temperature T≳10 K, and the resistivity increases quadratically with T. Flexural phonons limit the intrinsic mobility down to a few m(2)/V s at room T. Their effect can be eliminated by applying strain or placing graphene on a substrate.

Substitutional disorder and charge localization in manganites.

In the manganites RE(1 - x)AE(x)MnO(3) (RE and AE being rare-earth and alkaline-earth elements, respectively) the random distribution of RE(3 + ) and AE(2 + ) induces random, but correlated, shifts of site energies of charge carriers in the Mn sites. We consider a realistic model of this diagonal disorder, in addition to the double-exchange hopping disorder, and investigate the metal-insulator transition as a function of temperature, across the paramagnetic-ferromagnetic line, and as a function of doping  x. Contrary to previous results, we find that values of parameters, estimated from the electronic structure of the manganites, are not incompatible with the possibility of a disorder-induced metal to insulator transition accompanying the ferromagnetic to paramagnetic transition at intermediate doping (x ∼ 0.2-0.4). These findings indicate clearly that substitutional disorder has to be considered as an important effect when addressing the colossal magnetoresistance properties of manganites.

Electronic properties of a biased graphene bilayer.

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

Valley symmetry breaking in bilayer graphene: a test of the minimal model.

Physical properties reflecting the valley asymmetry of Landau levels in a biased bilayer graphene under a magnetic field are discussed. Within the 4-band continuum model with a Hartree-corrected self-consistent gap and finite damping factor we predict the appearance of anomalous steps in quantized Hall conductivity due to the degeneracy lifting of Landau levels. Moreover, the valley symmetry breaking effect appears as a nonsemiclassical de Haas-van Alphen effect where the reduction of the oscillation period to half cannot be accounted for through quasiclassical quantization of the orbits in reciprocal space.

Low-density ferromagnetism in biased bilayer graphene.

We compute the phase diagram of a biased graphene bilayer. The existence of a ferromagnetic phase is discussed with respect to both carrier density and temperature. We find that the ferromagnetic transition is first-order, lowering the value of U relatively to the usual Stoner criterion. We show that in the ferromagnetic phase the two planes have unequal magnetization and that the electronic density is holelike in one plane and electronlike in the other.

Localized states at zigzag edges of bilayer graphene.

We report the existence of zero-energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.

Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect.

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.

Algebraic solution of a graphene layer in transverse electric and perpendicular magnetic fields.

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigenvalues and the eigenfunctions of the graphene plane. It is shown that the eigenstates of the problem can be cast in terms of coherent states, which appears in a natural way from the formalism.

Double exchange model for magnetic hexaborides.

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu1-xCaxB6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature T(C) as a function of the plasma frequency omega(p).