arXiv subjects

J. -N. Fuchs

Publications and source records attributed to J. -N. Fuchs.

17 recordsLinked to original sources

arXiv2023

Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way

In two dimensions, topological phases of free Majorana fermions coupled to a $\mathbb{Z}_2$ gauge field are known to be classified according to the Chern number $ν\in \mathbb{Z}$. Its value mod 16 specifies the type of anyonic excitations. In this paper, we investigate triangular vortex configurations (and their dual) in the Kitaev honeycomb model and show that fourteen of these sixteen phases can be obtained by adding a time-reversal symmetry-breaking term. Missing phases are $ν=\pm 7$. More generally, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases.

cond-mat.str-el↗

arXiv2021

Orbital embedding and topology of one-dimensional two-band insulators

The topological invariants of band insulators are usually assumed to depend only on the connectivity between orbitals and not on their intra-cell position (orbital embedding), which is a separate piece of information in the tight-binding description. For example, in two dimensions, the orbital embedding is known to change the Berry curvature but not the Chern number. Here, we consider one-dimensional inversion-symmetric insulators classified by a $\mathbb{Z}_2$ topological invariant $\vartheta=0$ or $π$, related to the Zak phase, and show that $\vartheta$ crucially depends on orbital embedding. We study three two-band models with bond, site or mixed inversion: the Su-Schrieffer-Heeger model (SSH), the charge density wave model (CDW) and the Shockley model. The SSH (resp. CDW) model is found to have a unique phase with $\vartheta=0$ (resp. $π$). However, the Shockley model features a topological phase transition between $\vartheta=0$ and $π$. The key difference is whether the two orbitals per unit cell are at the same or different positions.

cond-mat.mes-hall↗

arXiv2021

Topological and geometrical aspects of band theory

This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to contributions in high-energy physics by Dirac. The review starts by a presentation of the Dirac magnetic monopole, goes on with the Berry phase in a two-level system and the geometrical/topological band theory for Bloch electrons in crystals. Next, specific examples of tight-binding models giving rise to lattice versions of the Dirac equation in various space dimension are presented: in 1D (Su-Schrieffer-Heeger and Rice-Mele models), 2D (graphene, boron nitride, Haldane model) and 3D (Weyl semi-metals). The focus is on topological insulators and topological semi-metals. The latter have a Fermi surface that is characterized as a topological defect. For topological insulators, the two alternative view points of twisted fiber bundles and of topological textures are developed. The minimal mathematical background in topology (essentially on homotopy groups and fiber bundles) is provided when needed. Topics rarely reviewed include: periodic versus canonical Bloch Hamiltonian (basis I/II issue), Zak versus Berry phase, the vanishing electric polarization of the Su-Schrieffer-Heeger model and Dirac insulators.

cond-mat.mes-hall↗

arXiv2021

Wegner-Wilson loops in string nets

We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey a modified area law, in agreement with a recent mean-field approach.

cond-mat.str-el↗

arXiv2019

Landau level broadening, hyperuniformity, and discrete scale invariance

We study the energy spectrum of a two-dimensional electron in the presence of both a perpendicular magnetic field and a potential. In the limit where the potential is small compared to the Landau level spacing, we show that the broadening of Landau levels is simply expressed in terms of the structure factor of the potential. For potentials that are either periodic or random, we recover known results. Interestingly, for potentials with a dense Fourier spectrum made of Bragg peaks (as found, e.g., in quasicrystals), we find an algebraic broadening with the magnetic field characterized by the hyperuniformity exponent of the potential. Furthermore, if the potential is self-similar such that its structure factor has a discrete scale invariance, the broadening displays log-periodic oscillations together with an algebraic envelope.

cond-mat.other↗

arXiv2013

Collisionless Hydrodynamics of Doped Graphene in a Magnetic Field

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 is also discussed.

cond-mat.mes-hall↗

arXiv2012

Manipulation of Dirac points in graphene-like crystals

We review different scenarios for the motion and merging of Dirac points in two dimensional crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels

cond-mat.mes-hall↗

arXiv2011

Theory of Bernstein Modes in Graphene

We present a theoretical description of Bernstein modes that arise as a result of the coupling between plasmon-like collective excitations (upper-hybrid mode) and inter-Landau-level excitations, in graphene in a perpendicular magnetic field. These modes, which are apparent as avoided level crossings in the spectral function obtained in the random-phase approximation, are described to great accuracy in a phenomenological model. Bernstein modes, which may be measured in inelastic light-scattering experiments or in photo-conductivity spectroscopy, are a manifestation of the Coulomb interaction between the electrons and may be used for a high-precision measurement of the upper-hybrid mode at small non-zero wave vectors.

cond-mat.mes-hall↗

arXiv2010

Spin-flip excitations, spin waves, and magneto-excitons in graphene Landau levels at integer filling factors

We study collective electronic excitations in graphene in the integer quantum Hall regime, concentrating mainly on excitations with spin reversal such as spin-flip and spin-wave excitations. We show that these excitations are correctly accounted for in the time-dependent Hartree-Fock and strong magnetic field approximations, in contrast to spin-conserving (magneto-exciton) modes which involve a strong Landau-level mixing at non-zero wave vectors. The collective excitations are discussed in view of prominent theorems, such as Kohn's and Larmor's. Whereas the latter remains valid in graphene and yields insight into the understanding of spin-dependent modes, Kohn's theorem does not apply to relativistic electrons in graphene. We finally calculate the exchange correction to the chemical potential in the weak magnetic field limit.

cond-mat.mes-hall↗

arXiv2009

The magnetic field particle-hole excitation spectrum in doped graphene and in a standard two-dimensional electron gas

The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electron interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.

cond-mat.mes-hall↗

arXiv2009

Merging of Dirac points in a two-dimensional crystal

We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological transition between a semi-metallic phase and a band insulator. We derive a universal Hamiltonian that describes the physical properties of the transition, which is controlled by a single parameter, and analyze the Landau-level spectrum in its vicinity. This merging may be observed in the organic salt alpha-(BEDT-TTF)_2 I_3 or in an optical lattice of cold atoms simulating deformed graphene.

cond-mat.mes-hall↗

arXiv2009

Filling-Factor-Dependent Magnetophonon Resonance in Graphene

We describe a peculiar fine structure acquired by the in-plane optical phonon at the Gamma-point in graphene when it is brought into resonance with one of the inter-Landau-level transitions in this material. The effect is most pronounced when this lattice mode (associated with the G-band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions 0 -> (+,1) and (-,1) -> 0, at a magnetic field B_0 ~ 30 T. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor dependence can be used experimentally to detect circularly polarized lattice modes.

cond-mat.mes-hall↗

arXiv2009

Collective modes of doped graphene and a standard 2DEG in a strong magnetic field: linear magneto-plasmons versus magneto-excitons

A doped graphene layer in the integer quantum Hall regime reveals a highly unusual particle-hole excitation spectrum, which is calculated from the dynamical polarizability in the random phase approximation. We find that the elementary neutral excitations in graphene in a magnetic field are unlike those of a standard two-dimensional electron gas (2DEG): in addition to the upper-hybrid mode, the particle-hole spectrum is reorganized in linear magneto-plasmons that disperse roughly parallel to $ω=v_F q$, instead of the usual horizontal (almost dispersionless) magneto-excitons. These modes could be detected in an inelastic light scattering experiment.

cond-mat.mes-hall↗

arXiv2009

A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal

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.

cond-mat.mes-hall↗

arXiv2009

Electric-field-induced lifting of the valley degeneracy in alpha-(BEDT-TTF)_2I_3 Dirac-like Landau levels

The relativistic Landau levels in the layered organic material alpha-(BEDT-TTF)_2I_3 [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] are sensitive to the tilt of the Dirac cones, which, as in the case of graphene, determine the low-energy electronic properties under appropriate pressure. We show that an applied inplane electric field, which happens to be in competition with the tilt of the cones, lifts the twofold valley degeneracy due to a different level spacing. The scenario may be tested in infrared transmission spectroscopy.

cond-mat.mes-hall↗

arXiv2008

Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3

We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a strong magnetic field, the relativistic form of which is reminiscent to that of graphene, with a renormalized Fermi velocity due to the tilt of the Dirac cones. These relativistic Landau levels, experimentally accessible via spectroscopy or even a quantum Hall effect measurement, may be used as a direct experimental verification of Dirac cones in alpha-(BEDT-TTF)_2I_3.

cond-mat.mes-hall↗

arXiv2008

High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.

cond-mat.mes-hall↗