arXiv subjects

Frédéric Piéchon

Publications and source records attributed to Frédéric Piéchon.

26 records · Page 2Linked to original sources

arXiv2016

Fractal dimensions of the wavefunctions and local spectral measures on the Fibonacci chain

We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a new symmetry of wavefunctions under permutation of site and energy indices. We compute the wavefunction renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wavefunctions, as well as their global averages. The multifractality of wavefunctions is seen to appear at next-to-leading order in the ratio of the hopping amplitudes, $ρ$. Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of $ρ$ well outside the domain of applicability of perturbation theory.

cond-mat.mes-hall↗

arXiv2015

Plaquette chirality patterns for robust zero-gap states in $α$-type organic conductor

Dirac electrons with a zero-gap state (ZGS) in organic conductor $α$-(BEDT-TTF)$_2$I$_3$ result from a fine tuning of the seven nearest neighbors transfer integrals ($a_1, a_2, a_3, b_1, b_2, b_3, b_4$) between the four molecules of the unit cell. In this work we show that for given moduli $|a_1|,...|b_4|$, the possibility of having Dirac electron with a ZGS at $3/4$ (or $1/4$) filling strongly depends on the specific configurations of signs of the seven transfer integral. More precisely it is possible to classify the sign configurations into essentially four classes determined by $χ_{a}={\rm sign} (a_2a_3)$ and $χ_b={\rm sign} (b_1b_2b_3b_4)$. Using extended numerics, we show that for both weak and large inhomogeneity in the moduli, the class $(χ_a,χ_b)=(-,-)$ is the most favorable to find Dirac electrons with ZGS at $3/4$ (or $1/4$) filling. For the class $(χ_a,χ_b)=(+,+)$ in the opposite case, we never found any ZGS at either $1/4$ or $3/4$ filling. The last two classes \suzum{given by} $(χ_a,χ_b)=(+,-)$ and $(χ_a,χ_b)=(-,+)$ corresponding to an intermediate situation; they allow for ZGS at $3/4$ (resp. $1/4$) filling but are much less favorable than class $(χ_a,χ_b)=(-,-)$. As a matter of fact, all previous numerical studies of Dirac electrons and ZGS in $α$-(BEDT-TTF)$_2$I$_3$ correspond to class $(χ_a,χ_b)=(-,+)$.

cond-mat.str-el↗

arXiv2013

Spin- and valley-dependent magneto-optical properties of MoS2

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.

cond-mat.mes-hall↗

arXiv2013

Inversion Symmetry and Wave-Function-Nodal-Lines of Dirac Electrons in Organic Conductor alpha-(BEDT-TTF)_2I_3

By examining organic conductor alpha-(BEDT-TTF)_2I_3 which is described by a nearest neighbors tight-binding model it is shown that because of inversion symmetry, each component of a wave function (WF) exhibits nodal lines (NLs) in the Brillouin zone. In the absence of any band crossing, each NL connects two time reversal invariant momenta (TRIM) as partners. In the presence of a pair of Dirac points (band crossing), for each band that crosses and for each WF component there is a NL that connects the pair of Dirac points via a TRIM without partner. This second kind of NL leads to a discontinuous sign change for non vanishing components of the WF. Such a property is at the origin of the +/- pi Berry phase accumulated on a contour integral encircling one Dirac point. The results are examplified by numerical calculation of WFs components for the above conductor with a 3/4 filled band.

cond-mat.mes-hall↗

arXiv2013

Existence and merging of Dirac points in $α$-(BEDT-TTF)$_2$I$_3$ organic conductor

We reexamine the existence and stability conditions of Dirac points between valence and conduction bands of 3/4 filled $α$-(BEDT-TTF)$_2$I$_3$ conducting plane. We consider the usual nearest neigbhor tight binding model with the seven transfer energies that depend on the applied pressure. Owing to the four distinct molecules (A, A', B, C) per unit cell of the Bravais lattice, the corresponding Bloch Hamiltonian is a $4\times4$ matrix ${\cal H}({\bm k})$ for each wave vector $\mathbf{k}$ of the Brillouin zone. In most previous works the study of Dirac points was achieved through direct numerical diagonalization of matrix ${\cal H}({\bm k})$. In this work we develop a novel analytical approach which allows to analyze the existence and stability conditions of Dirac points from the knowledge of their merging properties at time reversal points. Within this approach we can discuss thoroughly the role of each transfer integrals and demonstrate that inversion symmetry is convenient but not necessary.

cond-mat.mes-hall↗

arXiv2013

Distant-Neighbor Hopping in Graphene and Haldane Models

Large Chern number phases in a Haldane model become possible if there is a multiplication of Dirac points in the underlying graphene model. This is realized by considering long-distance hopping integrals. Through variation of these integrals, it is possible to arrive at supermerging band touchings, which up to N7 graphene are unique in parameter space. They result from the synchronized motion of all supplementary Dirac points into the regular +/-K points of graphene. The energy dispersion power law is usually larger than the topological charge associated with them. Moreover, adding distant-neighbor hoppings in the Haldane mass allows one to sweep large Chern number phases in the topological insulator.

cond-mat.mes-hall↗

arXiv2010

Spin self-rephasing and very long coherence times in a trapped atomic ensemble

We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and susceptible to appear in other physical systems.

quant-ph↗

arXiv2001

Universal Scrambling Properties of Spectra and Wave functions in Disordered Interacting Systems

Recent experiments on quantum dots in the Coulomb Blockade regime have shown how adding successive electrons into a dot modifies the energy spectrum and the wave functions of the electrons already present in the dot. Using a microscopic model, we study the importance of electron-electron interaction on these ``scrambling'' effects. We compute the Hartree-Fock single particle properties as function of the number $p$ of added electrons. We define parametric correlation functions that characterize the scrambling properties of the Hartree-Fock wave functions and energy spectra. We find that each of these correlation functions exhibit a universal behavior in terms of the ratio $p/p^{\ast}$ where $p^{\ast}$ is a characteristic number that decreases with increasing either the interaction strength, the disorder strength or the system size

cond-mat.mes-hall↗