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Smooth interfaces of topological systems are known to host massive surface states along with the topologically protected chiral one. We show that in Weyl semimetals these massive states, along with the chiral Fermi arc, strongly alter the form of the Fermi-arc plasmon, Most saliently, they yield further collective plasmonic modes that are absent in a conventional interfaces. The plasmon modes are completely anisotropic as a consequence of the underlying anisotropy in the surface model and expected to have a clear-cut experimental signature, e.g. in electron-energy loss spectroscopy., Maintext: 5 pages + 4 figures; Supp.: 9 pages + 1 figure

International audience; As a consequence of the approximate spin-valley symmetry in graphene, the ground state of electrons in graphene at charge neutrality is a particular SU(4) quantum Hall ferromagnet to minimize their exchange energy. If only the Coulomb interaction is taken into account, this ferromagnet can appeal either to the spin degree of freedom or equivalently to the valley pseudo-spin degree of freedom. This freedom in choice is then limited by subleading energy scales that explicitly break the SU(4) symmetry, the simplest of which is given by the Zeeman effect that orients the spin in the direction of the magnetic field. In addition, there are also valley symmetry-breaking terms that can arise from short-range interactions or electron-phonon couplings. Here, we build upon the phase diagram, which has been obtained by Kharitonov [M. Kharitonov, Phys. Rev. B 85, 155439 (2012)PRBMDO1098-012110.1103/PhysRevB.85.155439], in order to identify the different skyrmions that are compatible with these types of quantum Hall ferromagnets. Similarly to the ferromagnets, the skyrmions at charge neutrality are described by the Gr(2,4) Grassmannian at the center, which allows us to construct the skyrmion spinors. The different skyrmion types are then obtained by minimizing their energy within a variational approach, with respect to the remaining free parameters that are not fixed by the requirement that the skyrmion at large distances from their center must be compatible with the ferromagnetic background. We show that the different skyrmion types have a clear signature in the local, sublattice-resolved, spin magnetization, which is in principle accessible in scanning-tunneling microscopy and spectroscopy.

We study generalized spin waves in graphene under a strong magnetic field when the Landau-level filling factor is $\nu=\pm 1$. In this case, the ground state is a particular SU(4) quantum Hall ferromagnet, in which not only the physical spin is fully polarized but also the pseudo-spin associated with the valley degree of freedom. The nature of the ground state and the spin-valley polarization depend on explicit symmetry breaking terms that are also reflected in the generalised spin-wave spectrum. In addition to pure spin waves, one encounters valley-pseudo-spin waves as well as more exotic entanglement waves that have a mixed spin-valley character. Most saliently, the SU(4) symmetry-breaking terms do not only yield gaps in the spectra, but under certain circumstances, namely in the case of residual ground-state symmetries, render the originally quadratic (in the wave vector) spin-wave dispersion linear.

Landau-level spectroscopy, the optical analysis of electrons in materials subject to a strong magnetic field, is a versatile probe of the electronic band structure and has been successfully used in the identification of novel states of matter such as Dirac electrons, topological materials or Weyl semimetals. The latter arise from a complex interplay between crystal symmetry, spin-orbit interaction and inverse ordering of electronic bands. Here, we report on unusual Landau-level transitions in the monopnictide TaP that decrease in energy with increasing magnetic field. We show that these transitions arise naturally at intermediate energies in time-reversal-invariant Weyl semimetals where the Weyl nodes are formed by a partially gapped nodal-loop in the band structure. We propose a simple theoretical model for electronic bands in these Weyl materials that captures the collected magneto-optical data to great extent., Comment: 6 pages, 3 figures + supplementary materials, accepted in Phys. Rev. Lett

International audience; We study the neutral excitations of fractional quantum Hall states in electronic systems of finite width where an external anisotropy is introduced by tilting the magnetic field. As in the isotropic case, the neutral collective excitation can be worked out through the conserving method of composite fermions in the Hamiltonian theory because the interaction potential has a natural cutoff due to the quantum well width. We show how such a computation can be carried out perturbatively for an anisotropic interaction. We find that unlike the charge gap, the neutral collective gap is much more sensitive to the tilt and can thus, for certain fractional quantum Hall states, be easily destroyed by the parallel component of the magnetic field. We also discuss the convergence of the collective spectrum to the activation gap in the large-momentum limit.

A flat energy dispersion of electrons at the Fermi level of a material leads to instabilities in the electronic system and can drive phase transitions. Here we introduce a method to induce a flat band in two-dimensional (2D) materials. We show that the flat band can be achieved by sandwiching the 2D material by two cesium (Cs) layers. We apply this method to monolayer graphene and investigate the flat band by a combination of angle-resolved photoemission spectroscopy experiment and the calculation. Our work highlights that charge transfer, zone folding of graphene bands and the covalent bonding between C and Cs atoms are at the origin of the flat energy band formation. The presented approach is an alternative route for obtaining flat band materials to twisting bilayer graphene which yields thermodynamically stable flat band materials in large areas., 22 pages, 4 Figures

We investigate a quantum well that consists of a thin topological insulator sandwiched between two trivial insulators. More specifically, we consider smooth interfaces between these different types of materials such that the interfaces host not only the chiral interface states, whose existence is dictated by the bulk-edge correspondence, but also massive Volkov-Pankratov states. We investigate possible hybridization between these interface states as a function of the width of the topological material and of the characteristic interface size. Most saliently, we find a strong qualitative difference between an extremely weak effect on the chiral interface states and a more common hybridization of the massive Volkov-Pankratov states that can be easily understood in terms of quantum tunneling in the framework of the model of a (Dirac) quantum well we introduce here., accepted for publication in PRB (13 pages with appendix + 7 figures)

We study the in-gap states that appear at the boundaries of both 1D and 2D topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an s-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin-polarized on either side of the topological phase boundary. We also demonstrate that the spatial position, energy-level spacing, and spin polarization of the VP states can be modified by the introduction of in-plane electric fields., Comment: 10 pages, 8 figures

Weyl semimetals are known to host massless surface states called Fermi arcs. These Fermi arcs are the manifestation of the bulk-edge correspondence in topological matter and thus are analogous to the topological chiral surface states of topological insulators. It has been shown that the latter, depending on the smoothness of the surface, host massive Volkov-Pankratov(VP) states that coexist with the chiral ones. Here, we investigate these VP states in the framework of Weyl semimetals, namely their density of states and magneto-optical response. We find the selection rules corresponding to optical transitions which lead to anisotropic responses to external fields. In the presence of a magnetic field parallel to the interface, the selection rules and hence the poles of the response functions are mixed., 9 pages, 9 figures

In addition to the usual chiral surface states, massive surface states can arise at a smooth interface between a topological and a trivial bulk insulator. While not subject to topological protection as the chiral states, these massive states, theorized by Volkov and Pankratov in the 1980s, reflect nevertheless emergent Dirac physics at the interface. We study theoretically the magneto-optical response of these surface states, which is strikingly different from that of the bulk states. Most saliently, we show that these states can be identified clearly in the presence of a magnetic field and its orientation with respect to the interface., 5 pages with 2 figures, added references, fig.1a replaced

International audience; We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon increase of the tilt parameter $\eta$, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is $\sqrt{1-\eta^2}$ in the two-dimensional case where only the conductivity perpendicular to the tilt direction diverges for $\eta\rightarrow 1$, both conductivities diverge in three-dimensional Weyl semimetals, where $\eta=1$ separates a type-I (for $\eta1$)., Comment: 14 pages, 9 figures

International audience; We review measurements of angle and time resolved photoelectron spectroscopy on the surface states of the Bi(1 1 1) surface. The work covers several aspects of these surface states, discussing the topological properties, the strong anisotropy of the spin–orbit splitting and the dynamical relaxation of photoexcited electrons. Since time resolved experiments disentagle interaction processes in real time, the reported data offer a novel perspective on the motion of charge carriers in surface states and will serve as an unuseful reference for other systems with strong spin–orbit coupling.

Cadmium arsenide (Cd3As2) has recently became conspicuous in solid-state physics due to several reports proposing that it hosts a pair of symmetry-protected 3D Dirac cones. Despite vast investigations, a solid experimental insight into the band structure of this material is still missing. Here we fill one of the existing gaps in our understanding of Cd3As2, and based on our Landau level spectroscopy study, we provide an estimate for the energy scale of 3D Dirac electrons in this system. We find that the appearance of such charge carriers is limited - contrary to a widespread belief in the solid-state community - to a relatively small energy scale (below 40 meV)., Comment: to be published in Phys. Rev. B

We theoretically study the role of the Berry curvature on neutral and charged excitons in two-dimensional transition-metal dichalcogenides. The Berry curvature arises due to a strong coupling between the conduction and valence bands in these materials that can to great extent be described within the model of massive Dirac fermions. The Berry curvature lifts the degeneracy of exciton states with opposite angular momentum. Using an electronic interaction that accounts for non-local screening effects, we find a Berry-curvature induced splitting of $\sim 17$ meV between the 2$p_{-}$ and 2$p_{+}$ exciton states in WS$_2$, consistent with experimental findings. Furthermore, we calculate the trion binding energies in WS$_2$ and WSe$_2$ for a large variety of screening lenghts and different dielectric constants for the environment. Our approach indicates the prominent role played by the Berry curvature along with non-local electronic interactions in the understanding of the energy spectra of neutral and charged excitons in transition-metal dichalcogenides and in the the interpretation of their optical properties., Comment: 11 pages, 3 figures

Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter Landau-level (LL) Zener field, ratio of the Landau gap and cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large superpoissonian shot noise signals the breakdown via inter-LL scattering. The breakdown is ultimately limited by collective excitations in a regime where phonon and impurity scattering are quenched. The breakdown mechanism can be described by a Landau critical velocity as it bears strong similarities with the roton mechanism of superfluids., 13 pages, 3 figures

International audience; We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the z direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudopotentials. We find that the off-diagonal components of the pseudopotentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of p filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest and first Landau levels.

It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. In this article we report on a set of experimental observations indicating the existence of massive surface states. These states are confined at the interface and dominate equilibrium and transport properties at high energy and/or high electric field. By monitoring the AC admittance of HgTe topological insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energy and electric fields. The Dirac surface states are characterized by a compressibility minimum, a linear energy dependence and a high mobility persisting up to energies much larger than the transport bandgap of the bulk. New features are revealed at high energies with signatures such as conductance peaks, compressibility bumps, a strong charge metastability and a Hall resistance anomaly. These features point to the existence of excited massive surface states, responsible for a strong intersubband scattering with the Dirac states and the nucleation of metastable bulk carriers. The spectrum of excited states agrees with predictions of a phenomenological model of the topological-trivial semiconductor interface. The model accounts for the finite interface depth and the effect of electric fields. The existence of excited topological states is essential for the understanding of topological phases and opens a route for engineering and exploiting topological resources in quantum technology., Comment: 29 pages, 8 figures

We show that a smooth interface between two insulators of opposite topological Z2 indices possesses multiple surface states, both massless and massive. While the massless surface state is non-degenerate, chiral and insensitive to the interface potential, the massive surface states only appear for a sufficiently smooth heterojunction. The surface states are particle-hole symmetric and a voltage drop reveals their intrinsic relativistic nature, similarly to Landau bands of Dirac electrons in a magnetic field. We discuss the relevance of the massive Dirac surface states in recent ARPES and transport experiments., Comment: 5 pages, 3 figures; 6 pages of supplementary material incorporated; accepted for publication in Physical Review B as a Rapid Communication

We report on infrared transmission and reflectivity experiments performed on Cd 3 As 2 in a wide range of the photon energies and magnetic fields. The observed magneto-optical response unambiguously indicates the presence of 3D massless charge carriers. The detailed analysis of cyclotron resonances implies the presence of massless Kane electrons at a large energy scale, while the symmetry-protected 3D Dirac cones may appear at a small scale.

We consider finite-sized interfaces of a Weyl semi-metal and show that the corresponding confinement potential is similar to the application of a magnetic field. Among the numerous states, which can be labeled by indices n like in Landau levels, the n = 0 surface state describes the Weyl semimetal Fermi arc at a given chemical potential. Moreover, the analogy with a magnetic field shows that an external in-plane magnetic field can be used to distort the Fermi arc and would explain some features of magneto-transport in Weyl semimetals. We derive the Fermi arc for type-I and type-II Weyl semimetals where we deal with the tilt anisotropy by the use of Lorentz boosts. In the case of type-II Weyl semimetals, this leads to many additional topologically trivial surface states at low energy. Finally, we extend the Aharonov-Casher argument and demonstrate the stability of the Fermi arc over fluctuations of the surface potential., 16 pages, 11 figures; 3 pages of supplementary material incorporated ; accepted for publication in Physical Review B

Defect-free SrTiO3 (STO) is a band insulator but Angle Resolved Photoemission Spectroscopy (ARPES) experiments have demonstrated the existence of a nanometer thin two-dimensional electron liquid (2DEG) at the (001) oriented surface of this compound. The bulk is a trivial insulator, but our theoretical study reveals that the parity of electronic wavefunctions in this 2DEG is inverted in the vicinity of special points in reciprocal space where the low-energy dispersion consists of four gapped Dirac cones with a tilted and anisotropic shape. This gives rise to linearly dispersing topological edge states at the one-dimensional boundary. We propose to probe these modes by measuring the Josephson radiation from gapless bound Andreev states in STO based junctions, as it is predicted that they display distinctive signatures of topology., 10 pages, 6 figures

Topological condensed matter physics is a recent arrival among the disciplines of modern physics of a distinctive and substantive nature. Its roots reach far back, but much of its current importance derives from exciting developments in the last half-century. The field is advancing rapidly, growing explosively, and diversifying greatly. There is now a zoo of topological phenomena–the quantum spin Hall effect, topological insulators, Coulomb spin liquids, non-Abelian anyonic statistics and their potential application in topological quantum computing, to name but a few–as well as an increasingly sophisticated set of concepts and methods underpinning their understanding. The aim of this Les Houches Summer School was to present an overview of this field, along with a sense of its origins and its place on the map of advances in fundamental physics. The school comprised a set of basic lectures (Part I) aimed at a pedagogical introduction to the fundamental concepts, which was accompanied by more advanced lectures (Part II) covering individual topics at the forefront of today’s research in condensed matter physics.

This review aims at a theoretical discussion of Dirac points in twodimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in low-energy physics has spread beyond condensed matter to artificial graphene systems. In these alternative systems, a large versatility in the manipulation of the relevant band parameters can be achieved. This allows for a systematic study of the motion and different possible fusions of Dirac points, which are beyond the physical limits of graphene. We introduce the basic properties of Dirac fermions and the motion of Dirac points here and aim at a topological classification of these motions. The theoretical concepts are illustrated in particular model systems.

International audience; We report experimental measurements and theoretical analysis of Shubnikov-de Haas (SdH) oscillations in a Dirac cone system: the α-(BEDT-TTF)2I3 organic metal under hydrostatic pressure. The measured SdH oscillations reveal anomalies at high magnetic fields B where the 1/B oscillations periodicity is lost above 7 T. We interpret these unusual results within a theoretical model that takes into account intrinsic distortions of the α-(BEDT-TTF)2I3 Dirac cones such as a parabolic particle-hole asymmetric correction. Others possible causes, such as a cone tilting or a Zeeman effect, are carefully ruled out. The observations are consistent among α-(BEDT-TTF)2I3 samples with different Fermi levels.

We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the STM/STS imaging of spin-pseudospin textures in graphene monolayer in quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N=0 Landau level, we discuss two unusual types -- the "entanglement skyrmion" whose texture lies in the space of the entanglement of spin and pseudospin, as well as the "deflated pseudospin skyrmion" with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely the sample tilting, the substrate anisotropy and the valley pseudospin analogue of Zeeman coupling., Comment: 28 pages, 25 figures

We develop an analytically solvable model able to qualitatively explain nonhydrogenic exciton spectra observed recently in two-dimensional (2d) semiconducting transition metal dichalcogenides. Our exciton Hamiltonian explicitly includes additional angular momentum associated with the pseudospin degree of freedom unavoidable in 2d semiconducting materials with honeycomb structure. We claim that this is the key ingredient for understanding the nonhydrogenic exciton spectra that was missing so far., 4+ pages, 2 figures

We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt direction. Most saliently, the tilt can be described within the relativistic framework of Lorentz transformations that give rise to a rich spectrum, displaying new transitions beyond the usual dipolar ones in the optical conductivity. We identify particular features in the latter that allow one to distinguish between semimetals of different types., 5 pages, 3 figures; 3 pages of supplementary material incorporated; published version

We present a theory of quantum oscillations in insulators that are particle-hole symmetric and nontopological but with arbitrary band dispersion, at both zero and nonzero temperature. At temperatures $T$ less than or comparable to the gap, the dependence of oscillations on $T$ is markedly different from that in metals and depends crucially on the position of the chemical potential $\ensuremath{\mu}$ in the gap. If $\ensuremath{\mu}$ is in the middle of the gap, oscillations do not change with $T$; however, if $\ensuremath{\mu}$ is asymmetrically positioned in the gap, surprisingly, oscillations go to zero at a critical value of the inverse field determined by $T$ and $\ensuremath{\mu}$ and then change their phase by $\ensuremath{\pi}$ and grow again. Additionally, the temperature dependence is different for quantities derived from the grand canonical potential, such as magnetization and susceptibility, and those derived from the density of states, such as resistivity. However, the nontrivial features arising from asymmetric $\ensuremath{\mu}$ are present in both.

Le graphene est l’un des materiaux les plus prometteurs pour une technologie du futur. Il se distingue des autres materiaux par ses proprietes electroniques remarquables accompagnees a la fois d’une grande flexibilite mecanique, d’une grande robustesse, et d’une grande stabilite chimique. Aujourd’hui, le graphene sort des laboratoires de recherche fondamentale et fait son chemin vers l’industrie en raison de son grand potentiel pour des applications diverses. Ceci est notamment rendu possible par un grand progres dans la fabrication industrielle de graphene a grande echelle.

We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac cones from an insulating phase with a gap. We calculate the density of states and the specific heat. The spectrum in a magnetic field B is related to the resolution of a Schrodinger equation in a double well potential. They obey the general scaling law e_n \propto B^{2/3} f_n(Delta /B^{2/3}. They evolve continuously from a sqrt{n B} to a linear (n+1/2)B dependence, with a [(n+1/2)B]^{2/3} dependence at the transition. The spectrum in the vicinity of the topological transition is very well described by a semiclassical quantization rule. This model describes continuously the coupling between valleys associated with the two Dirac points, when approaching the transition. It is applied to the tight-binding model of graphene and its generalization when one hopping parameter is varied. It remarkably reproduces the low field part of the Rammal-Hofstadter spectrum for the honeycomb lattice.

We report on optical reflectivity experiments performed on Cd3As2 over a broad range of photon energies and magnetic fields. The observed response clearly indicates the presence of 3D massless charge carriers. The specific cyclotron resonance absorption in the quantum limit implies that we are probing massless Kane electrons rather than symmetry-protected 3D Dirac particles. The latter may appear at a smaller energy scale and are not directly observed in our infrared experiments.

We explore different skyrmion types in the lowest Landau level of graphene at a filling factor $\nu=\pm 1$. In addition to the formation of spin and valley pseudospin skyrmions, we show that another type of spin-valley entangled skyrmions can be stabilized in graphene due to an approximate SU(4) spin-valley symmetry that is affected by sublattice symmetry-breaking terms. These skyrmions have a clear signature in spin-resolved density measurements on the lattice scale, and we discuss the expected patterns for the different skyrmion types., Comment: 5 pages, 3 figures ; 6 pages of supplementary material included ; version accepted for publication in PRL

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at $1/4$-filling whose free-electron term is the $\ensuremath{\pi}$-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band ${\mathrm{Z}}_{2}$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [R. L. Doretto, A. O. Caldeira, and S. M. Girvin, Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor $\ensuremath{\nu}=1$. We show that, within the bosonization scheme, the topological Hubbard model is mapped to an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.

Massless Dirac fermions occur as low-energy modes in several quasi-two-dimensional condensed matter systems such as graphene, the surface of bulk topological insulators, and in layered organic semiconductors. When the rotational symmetry in such systems is reduced either by an in-plane electric field or an intrinsic tilt of the Dirac cones, the allowed dipolar optical transitions evolve from a few selected transitions into a wide fan of interband transitions. We show that the Lorentz covariance of the low-energy carriers allows for a concise analysis of the emerging magneto-optical properties. We predict that infrared absorption spectra yield quantitative information on the tilted Dirac cone structure in organic compounds such as $\ensuremath{\alpha}\ensuremath{-}{(\text{BEDT-TTF})}_{2}{\mathrm{I}}_{3}$.

On the basis of energy calculations, we investigate the competition between quantum-liquid and electron-solid phases in intermediate Landau levels as a function of their partial filling factor. An alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains an observed reentrance of the integral quantum Hall effect. The phase transitions are identified as first-order. Recent transport measurements under micro-wave irradiation reveal the crystalline origin of the reentrant points, and a mixed phase of a coexisting Wigner crystal and a 2-electron bubble phase is found in a Landau-level filling-factor range 4,15? ν? 4.26, as expected from our calculations.

International audience; We have observed the quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillations in highly disordered graphene at magnetic fields up to 65 T. Disorder was introduced by hydrogenation of graphene up to a ratio H/C approximate to 0.1%. The analysis of SdH oscillations and QHE indicates that the topological part of the Berry phase, proportional to the pseudospin winding number, is robust against introduction of disorder by hydrogenation in large-scale graphene.

We investigate numerically different phases that can occur at half filling in the lowest and the first excited Landau levels in wide-well twodimensional electron systems exposed to a perpendicular magnetic field. Within a twocomponent model that takes into account only the two lowest electronic subbands of the quantum well, we derive a phase diagram that compares favorably with an experimental one by Shabani et al. [Phys. Rev. B 88, 245413 (2013)]. In addition to the compressible composite-fermion Fermi liquid in narrow wells with a substantial subband gap and the incompressible twocomponent (331) Halperin state, we identify in the lowest Landau level a rectangular Wigner crystal occupying the second subband. This crystal may be the origin of the experimentally observed insulating phase in the limit of wide wells and high electronic densities. In the second Landau level, the incompressible Pfaffian state, which occurs in narrow wells and large subband gaps, is also separated by an intermediate region from a large-well limit in which a similar rectangular Wigner crystal in the excited subband is the ground state, as for the lowest Landau level. However, the intermediate region is characterized by an incompressible state that consists of two four-flux Pfaffians in each of the components., Comment: 18 pages, 18 figures; published version with new appendix (discussion of the role of wave function overlap in the crystalline phases), updated references

The physics of excitons, electron-hole pairs that are bound together by their mutual Coulomb attraction, can to great extent be understood in the framework of the quantum-mechanical hydrogen model. This model has recently been challenged by spectroscopic measurements on two-dimensional transition-metal dichalchogenides that unveil strong deviations from a hydrogenic spectrum. Here, we show that this deviation is due to the particular relativistic character of electrons in this class of materials. Indeed, their electrons are no longer described in terms of a Schroedinger but a massive Dirac equation that intimately links electrons to holes. Dirac excitons therefore inherit a relativistic quantum spin-1/2 that contributes to the angular momentum and thus the exciton spectrum. Most saliently, the level spacing is strongly reduced as compared to the hydrogen model, in agreement with spectroscopic measurements and ab-initio calculations., Comment: 3 pages, 1 figure, accepted for publication in the proceedings of ICPS 2016

We study the collective modes of a low-energy continuum model of the quasi-two-dimensional electron liquid in a layer of the organic compound $\ensuremath{\alpha}\ensuremath{-}{\mathrm{(BEDT-TTF)}}_{2}{\mathrm{I}}_{3}$ in a perpendicular magnetic field. As testified by zero magnetic field transport experiments and ab initio theory, this material hosts both massless and massive low-energy carriers, the former being described by two tilted and anisotropic Dirac cones. The polarizability of these cones is anisotropic, and two sets of magnetoplasmon modes occur between any two cyclotron resonances. We show that the tilt of the cones causes a unique intervalley damping effect: the upper hybrid mode of one cone is damped by the particle-hole continuum of the other cone in generic directions. We analyze how the presence of massive carriers affects the response of the system, and demonstrate how doping can tune $\ensuremath{\alpha}\ensuremath{-}{\mathrm{(BEDT-TTF)}}_{2}{\mathrm{I}}_{3}$ between regimes of isotropic and anisotropic screening.

We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the well. Within exact-diagonalization calculations in the spherical geometry, we find that the incompressible state is described in terms of a two-component wave function. Its overlap with the ground state can be optimized with the help of a rotation in the space of the pseudospin, which mimics the lowest two electronic subbands., 6 pages, 6 figures; modified version contains discussion of energy gaps and results for another value of the magnetic field; version accepted for publication in Phys. Rev. B

We investigate the behavior of low-energy electrons in two-dimensional molybdenum disulfide when submitted to an external magnetic field. Highly degenerate Landau levels form in the material, between which light-induced excitations are possible. The dependence of excitations on light polarization and energy is explicitly determined, and it is shown that it is possible to induce valley and spin polarization, i.e. to excite electrons of selected valley and spin. Whereas the effective low-energy model in terms of massive Dirac fermions yields dipole-type selection rules, higher-order band corrections allow for the observation of additional transitions. Furthermore, inter-Landau-level transitions involving the n=0 levels provide a reliable method for an experimental measurement of the gap and the spin-orbit gap of molybdenum disulfide., Comment: 8 pages, 6 figures; published version with minor modifications

We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to the Coulomb repulsion between electrons. We focus on fractional quantum Hall effect in asymmetric bilayer systems at filling factor nu=4/11 and show that an asymmetric Halperin-like trial wavefunction gives a valid description of the ground state of the system., 6 pages, 5 figures, HMF-20 proceedings

Transport measurements were performed on the organic layered compound \aI3 under hydrostatic pressure. The carrier types, densities and mobilities are determined from the magneto-conductance of \aI3 . While evidence of high-mobility massless Dirac carriers has already been given, we report here, their coexistence with low-mobility massive holes. This coexistence seems robust as it has been found up to the highest studied pressure. Our results are in agreement with recent DFT calculations of the band structure of this system under hydrostatic pressure. A comparison with graphene Dirac carriers has also been done.

International audience; We present infrared transmission spectroscopy study of the inter-Landau-level excitations in quasi-neutral epitaxial graphene nanoribbon arrays. We observed a substantial deviation in energy of the $L_{0(-1)}$$\to$$L_{1(0)}$ transition from the characteristic square root magnetic-field dependence of two-dimensional graphene. This deviation arises from the formation of upper-hybrid mode between the Landau level transition and the plasmon resonance. In the quantum regime the hybrid mode exhibits a distinct dispersion relation, markedly different from that expected for conventional two-dimensional systems and highly doped graphene.

El pdf del artículo es la versión pre-print: arXiv:1305.1448, The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order are also discussed. © 2013 Elsevier Ltd., R.R. acknowledges financial support from the Juan de la Cierva Program (MINECO,Spain). This work was partially funded by Triangle de la Physique.

We investigate the fine structure in the energy spectrum of bilayer graphene in the presence of various stacking defaults, such as a translational or rotational mismatch. This fine structure consists of four Dirac points that move away from their original positions as a consequence of the mismatch and eventually merge in various manners. The different types of merging are described in terms of topological invariants (winding numbers) that determine the Landau-level spectrum in the presence of a magnetic field as well as the degeneracy of the levels. The Landau-level spectrum is, within a wide parameter range, well described by a semiclassical treatment that makes use of topological winding numbers. However, the latter need to be redefined at zero energy in the high-magnetic-field limit as well as in the vicinity of saddle points in the zero-field dispersion relation., Comment: 17 pages, 16 figures; published version with enhanced discussion of experimental findings