26 research outputs found
Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides
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.Comment: 4+ pages, 2 figure
Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides
Using the quasiclassical concept of Berry curvature we demonstrate that a
Dirac exciton - a pair of Dirac quasiparticles bound by Coulomb interactions -
inevitably possesses an intrinsic angular momentum making the exciton
effectively self-rotating. The model is applied to excitons in two-dimensional
transition metal dichalcogenides, in which the charge carriers are known to be
described by a Dirac-like Hamiltonian. We show that the topological
self-rotation strongly modifies the exciton spectrum and, as a consequence,
resolves the puzzle of the overestimated two-dimensional polarizability
employed to fit earlier spectroscopic measurements.Comment: 4+ pages, 2 figures, suppl. mat. added (4 pages), the title changed
by PRL editor
Exciton spectrum in two-dimensional transition metal dichalcogenides: The role of Diracness
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 201
Dirac quantum well engineering on the surface of topological insulator
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.Comment: accepted for publication in PRB (13 pages with appendix + 7 figures
Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
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 [Phys. Rev. B \textbf{85},
155439 (2012)], 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
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
Non-trivial Surface-band Dispersion on Bi(111)
We performed angle-resolved photoelectron spectroscopy of the Bi(111) surface
to demonstrate that this surface support edge states of non-trivial topology.
Along the -direction of the surface Brillouin zone, a
surface-state band disperses from the projected bulk valence bands at
to the conduction bands at continuously, indicating
the non-trivial topological order of three-dimensional Bi bands. We ascribe
this finding to the absence of band inversion at the point of the bulk Bi
Brillouin zone. According to our analysis, a modification of tight-binding
parameters can account for the non-trivial band structure of Bi without any
other significant change on other physical properties.Comment: 13 pages, 4 figures. This manuscript has been accepted in New Journal
of Physic
Aspects topologiques des dérivés du graphène
Ces dernières années, la physique de la matière condensée a connu une profonde révolution de concepts par la découverte de nombreuses phases de la matière qui ne sont pas classifiables à la Landau, c est à dire par leur groupe de symétrie. Si les premiers travaux remontent à ceux des effets Hall quantiques (entier et fractionnaire), ce n est que récemment, avec l avènement du graphène et des isolants topologiques que les physiciens ont réalisé que ces phases de la matière ne nécessitent, dans l absolu, ni champ magnétique, ni basse température, par opposition aux effets Hall quantiques précédemment cités. Ces nouveaux états de la matière sont caractérisés non pas par la géométrie du problème mais plutôt par la topologie. Ici donc, la forme précise du spectre électronique n est pas importante, seules certaines caractéristiques, comme la présence ou l absence d un gap, le sont. De manière similaire à la classification de Landau des groupes de symétries, il est possible de classifier ces nouveaux systèmes par l intermédiaire de groupes topologiques. La branche mathématique invoquée est celle de la topologie algébrique. A travers les invariants qu elle génère, il est possible de classer les états topologiquement non-triviaux. De plus, les transitions entre des états à topologies distinctes sont aussi accessibles par cette théorie. Les travaux réalisés dans le cadre de cette thèse s intéressent aux effets topologiques dans la structure de bandes de matériaux bi-dimensionnels. Après une présentation du formalisme mathématique général, un premier chapitre s intéressera à la topologie locale, c est à dire pour une portion restreinte de la première zone de Brillouin, des points de croisements de bandes, dits points de Dirac. Un effort sera porté vers la classification de ces systèmes et des transitions associées. Le chapitre suivant mettra en lumière un moyen efficace de mesurer les effets de la topologie des électrons en deux dimensions. Il s agit de l étude des niveaux de Landau qui résultent de l application d un champ magnétique 5transverse au plan des électrons. Les points de Dirac se transmutent alors en niveaux à énergie nulle topologiquement stables, c est à dire peu ou pas influencés par les diverses perturbations. L étude des différents modèles justifiera la discrimination entre la physique à champ magnétique faible et celle à champ magnétique fort, faible ou fort étant très dépendant du système étudié. Enfin, dans un dernier chapitre plus prospectif on s intéressera à la topologie globale, c est à dire pour l ensemble de la première zone de Brillouin. Ce type d étude est surtout caractérisé par l existence d états de bords robustes. On en fera l expérience d une double manière. D abord par l étude un modèle à un électron, puis par celle d un système en forte interaction de N électrons. A travers les différents exemples étudiés, on s attachera à démontrer la puissance de l outil topologique pour les problèmes de la matière condensée, phénomène qui devrait s accentuer les prochaines années.During the last few decades, condensed matter physics has witnessed a deep refoundation of its paradigms, through the discovery of many systems that the usual symmety classification à la Landau cannot handle properly. Although the first major breaktroughs were realized at the time of discovery of integer and fractional quantum Hall effects, only recently physicists have agreed that these peculiar phases of matter require neither a magnetic field nor low temperature. Those new states of matter cannot be caracterized by the geometric aspects of the model but rather by topological ones. The precise shape of the electronic spectrum is no longer relevant, but only particular features are, such as the presence or the absence of a gap. Similarly to the Landau classification scheme, one can achieve a construction through extensive use of topological groups. This is the realm of algebraic topology. Related generated topological invariants can hold a classification of non-trivial topological states, as well as of the accompanying transitions. This thesis focusses on peculiar topological features of two-dimesnsional electronic band structures. After a technical introduction to the underlying formalism, the first chapter is devoted to local topology, that is for a restricted piece of the first Brillouin zone, of band crossing points, also known as Dirac points. Special care is taken to classify these points and related transitions. The next chapter sheds some light on a particularly efficent way of measuring topology for two-dimensional electrons. This is achieved through measurements of Landau levels that are generated by a magnetic field applied perpendicular to a plane. Dirac points then generate zero Landau levels that are topologically stable, i.e. almost not influenced by perturbations at all. Distinctions between low and high magnetic fields will prove to be relevant, although very system-dependant. Through the several models studied, we particularly stress out the importance of the topological tool for condensed matter physics, past present... and future.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF
Charge density waves and their transitions in anisotropic quantum Hall systems
In recent experiments, external anisotropy has been a useful tool to tune
different phases and study their competitions. In this paper, we look at the
quantum Hall charge density wave states in the Landau level. Without
anisotropy, there are two first-order phase transitions between the Wigner
crystal, the -electron bubble phase, and the stripe phase. By adding mass
anisotropy, our analytical and numerical studies show that the -electron
bubble phase disappears and the stripe phase significantly enlarges its domain
in the phase diagram. Meanwhile, a regime of stripe crystals that may be
observed experimentally is unveiled after the bubble phase gets out. Upon
increase of the anisotropy, the energy of the phases at the transitions becomes
progressively smooth as a function of the filling. We conclude that all
first-order phase transitions are replaced by continuous phase transitions,
providing a possible realisation of continuous quantum crystalline phase
transitions.Comment: 13+3 pages, 6 figure
Etude theorique des phases de densite inhomogene dans les systemes a effet Hall quantique
Thèse en cotutelle : Fribourg et Paris-Sud XIThe issue of this thesis is the study of the different electron-solid and quantum-liquid phases, which are found in two-dimensional electron systems under a perpendicular magnetic field. The formation of these phases is due to the strong Coulomb repulsion between the electrons of a partially filled Landau level. The energy calculations of the thesis allow one to understand recent experimental investigations, which have revealed a non-monotonic behaviour of the transverse (Hall) resistance. This effect is due to multiple first-order transitions between the competing phases. The derivation of a model of interacting composite fermions - the quasiparticles responsible for the fractional quantum Hall effect - furthermore allows for the study of new phases, which occur at high magnetic fields. Most saliently, a recently observed fractional quantum Hall effect at unusual values of the field has been identified as the manifestation of a second generation of composite fermions.L'objet de cette these est l'etude des differentes phases solides electroniques et liquides quantiques, que l'on trouve dans des systemes electroniques bi-dimensionnels exposes a un champ magnetique perpendiculaire. La formation de ces phases est due aà la repulsion coulombienne entre les electrons restreints a un niveau de Landau partiellement rempli. Les calculs d'energie de cette these permettent de comprendre des etudes experimentales recentes, qui ont mis en evidence un comportement non monotone de la resistance transverse (de Hall). Cet effet est du a des transitions multiples de premier ordre entre les phases en competition. La deduction d'un modele de fermions composites en interaction - les quasi-particules responsables de l'effet Hall quantique fractionnaire - permet de plus l'etude de nouvelles phases qui paraissent a fort champ magnetique. En particulier, un effet Hall quantique fractionnaire a des valeurs inhabituelles du champ a ete identifie comme la manifestation d'une deuxieme generation de fermions composites
Topological interface states - A possible path towards a Landau-level laser in the THz regime
Volkov-Pankratov surface bands arise in smooth topological interfaces, i.e. interfaces between a topological and a trivial insulator, in addition to the chiral surface state imposed by the bulk-surface correspondence of topological materials. These two-dimensional bands become Landau-quantized if a magnetic field is applied perpendicular to the interface. I show that the energy scales, which are typically in the 10-100 meV range, can be controlled both by the perpendicular magnetic field and the interface width. The latter can still be varied with the help of a magnetic-field component in the interface. The Landau levels of the different Volkov-Pankratov bands are optically coupled, and their arrangement may allow one to obtain population inversion by optical pumping. This could serve as the elementary brick of a multi-level laser based on Landau levels. Moreover, the photons are absorbed and emitted either parallel or perpendicular to the magnetic field, respectively in the Voigt and Faraday geometry, depending on the Volkov-Pankratov bands and Landau levels involved in the optical transitions