arXiv subjects

Gilles Montambaux

Publications and source records attributed to Gilles Montambaux.

At least 19 recordsLinked to original sources

arXiv2026

Lord Kelvin's Second Cloud

On April 27, 1900, William Thomson, better known as Lord Kelvin, delivered a visionary speech before the Royal Institution of Great Britain. In it, he presented two unresolved problems which, to him, appeared fundamental and unavoidable at the turn of the 20th century. He compared them to two clouds obscuring our understanding of physics. Dissipating these two clouds would eventually require the development of special relativity and quantum mechanics. This article revisits the second cloud which, contrary to what is often claimed in the literature, did not concern black-body radiation, but rather the specific heat of polyatomic molecules. To clarify this, the article aims to place Kelvin's speech within the historical context of the time and to situate it within the sequence of developments, from Kirchhoff to the first Solvay Conference in 1911, that marked the path of the extraordinary intellectual adventure that led to the birth of quantum mechanics. It will also be shown that Max Planck's initial motivation was not to solve the problem of the so-called "ultraviolet catastrophe."

physics.hist-ph↗

arXiv2025

Ramanujan, Landau and Casimir, divergent series: a physicist point of view

It is a popular paradoxical exercise to show that the infinite sum of positive integer numbers is equal to -1/12, sometimes called the Ramanujan sum. Here we propose a qualitative approach, much like that of a physicist, to show how the value -1/12 can make sense and, in fact, appears in certain physical quantities where this type of summation is involved. At the light of two physical examples, taken respectively from condensed matter -- the Landau diamagnetism -- and quantum electrodynamics -- the Casimir effect -- that illustrate this strange sum, we present a systematic way to extract this Ramanujan term from the infinity.

cond-mat.other↗

arXiv2020

Dirac points emerging from flat bands in Lieb-kagomé lattices

The energy spectra for the tight-binding models on the Lieb and kagomé lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagomé limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

cond-mat.mes-hall↗

arXiv2018

Artificial graphenes: Dirac matter beyond condensed matter

After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene. Among them are lattices of ultracold atoms, microwave or photonic lattices, "molecular graphene" or new compounds like phosphorene. The advantage of these structures is that they serve as new playgrounds for measuring and testing physical phenomena which may not be reachable in graphene, in particular: the possibility of controlling the existence of Dirac points (or Dirac cones) existing in the electronic spectrum of graphene, of performing interference experiments in reciprocal space, of probing geometrical properties of the wave functions, of manipulating edge states, etc. These cones, which describe the band structure in the vicinity of the two connected energy bands, are characterized by a topological "charge". They can be moved in reciprocal space by appropriate modification of external parameters (pressure, twist, sliding, stress, etc.). They can be manipulated, created or suppressed under the condition that the total topological charge be conserved. In this short review, I discuss several aspects of the scenarios of merging or emergence of Dirac points as well as the experimental investigations of these scenarios in condensed matter and beyond.

cond-mat.mes-hall↗

arXiv2018

Generalized Stefan-Boltzmann law

We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems {\it whose chemical potential vanishes}. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.

cond-mat.quant-gas↗

arXiv2018

Winding vector: how to annihilate two Dirac points with the same charge

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite ($+-$ scenario) or identical ($++$ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the {\it same} winding number emerge under appropriate distortion (interaction, etc), following the $++$ scenario. Under further distortion, these Dirac points merge following the $+-$ scenario, that is corresponding to {\it opposite} winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.

cond-mat.mes-hall↗

arXiv2016

Geometric orbital susceptibility: quantum metric without Berry curvature

The orbital magnetic susceptibility of an electron gas in a periodic potential depends not only on the zero field energy spectrum but also on the geometric structure of cell-periodic Bloch states which encodes interband effects. In addition to the Berry curvature, we explicitly relate the orbital susceptibility of two-band models to a quantum metric tensor defining a distance in Hilbert space. Within a simple tight-binding model allowing for a tunable Bloch geometry, we show that interband effects are essential even in the absence of Berry curvature. We also show that for a flat band model, the quantum metric gives rise to a very strong orbital paramagnetism.

cond-mat.mes-hall↗

arXiv2016

Chemical potential asymmetry and quantum oscillations in insulators

We present a theory of quantum oscillations in insulators that are particle-hole symmetric and non-topological but with arbitrary band dispersion, at both zero and non-zero 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 $μ$ in the gap. If $μ$ is in the middle of the gap, oscillations do not change with $T$; however, if $μ$ is asymmetrically positioned in the gap, surprisingly, oscillations go to zero at a critical value of the inverse field determined by $T$ and $μ$ and then change their phase by $π$ 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 non-trivial features arising from asymmetric $μ$ are present in both.

cond-mat.mes-hall↗

arXiv2016

Orbital edge states in a photonic honeycomb lattice

We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of $p$-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states that emerge not only in zigzag and bearded terminations, but also in armchair edges. The observations are reproduced by tight-binding and analytical calculations. Our work shows the potentiality of coupled micropillars in elucidating some of the electronic properties of emergent 2D materials with orbital bands.

cond-mat.mes-hall↗

arXiv2015

Geometry of Bloch states probed by Stückelberg interferometry

Inspired by recent experiments with cold atoms in optical lattices, we consider a Stückelberg interferometer for a particle performing Bloch oscillations in a tight-binding model on the honeycomb lattice. The interferometer is made of two avoided crossings at the saddle points of the band structure (i.e. at M points of the reciprocal space). This problem is reminiscent of the double Dirac cone Stückelberg interferometer that was recently studied in the continuum limit [Phys. Rev. Lett. 112, 155302 (2014)]. Although the two problems share similarities -- such as the appearance of a geometric phase shift -- lattice effects, not captured by the continuum limit, make them truly different. The particle dynamics in the presence of a force is described by the Bloch Hamiltonian $H(\boldsymbol{k})$ defined from the tight-binding Hamiltonian and the position operator. This leads to many interesting effects for the lattice Stückelberg interferometer: a twisting of the two Landau-Zener tunnelings, saturation of the inter-band transition probability in the sudden (infinite force) limit and extended periodicity or even non-periodicity beyond the first Brillouin zone. In particular, Stückelberg interferometry gives access to the overlap matrix of cell-periodic Bloch states thereby allowing to fully characterize the geometry of Bloch states, as e.g. to obtain the quantum metric tensor.

cond-mat.mes-hall↗

arXiv2015

Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations

We consider the electronic transport in multi-terminal mesoscopic networks of weakly disordered metallic wires. After a brief description of the classical transport, we analyze the weak localisation (WL) correction to the four-terminal resistances, which involves an integration of the Cooperon over the wires with proper weights. We provide an interpretation of these weights in terms of classical transport properties. We illustrate the formalism on examples and show that weak localisation to four-terminal conductances may become large in some situations. In a second part, we study the correlations of four-terminal resistances and show that integration of Diffuson and Cooperon inside the network involves the same weights as the WL. The formulae are applied to multiconnected wire geometries.

cond-mat.dis-nn↗

arXiv2014

Geometric phase in Stückelberg interferometry

We study the time evolution of a two-dimensional quantum particle exhibiting an energy spectrum, made of two bands, with two Dirac cones, as e.g. in the band structure of a honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated to each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wavefunctions.

cond-mat.mes-hall↗

arXiv2014

Manipulation of edge states in microwave artificial graphene

Edge states are one important ingredient to understand transport properties of graphene nanoribbons. We study experimentally the existence and the internal structure of edge states under uniaxial strain of the three main edges: zigzag, bearded, and armchair. The experiments are performed on artificial microwave graphene flakes, where the wavefunctions are obtained by direct imaging. We show that uniaxial strain can be used to manipulate the edge states: a single parameter controls their existence and their spatial extension into the ribbon. By combining tight-binding approach and topological arguments, we provide an accurate description of our experimental findings. A new type of zero-energy state appearing at the intersection of two edges, namely the corner state, is also observed and discussed.

cond-mat.mes-hall↗

arXiv2014

Dirac Fermions in condensed matter and beyond

This review aims at a theoretical discussion of Dirac points in two-dimensional 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 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.

cond-mat.mes-hall↗

arXiv2014

Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry

We show that a Stückelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum with two gapped cones, we propose several low-energy Hamiltonians differing by their eigenstates properties. The corresponding inter-band transition probability is affected by such differences in its interference fringes being shifted by a new phase of geometrical origin. This phase can be a useful bulk probe for topological band structures realized with artificial crystals.

cond-mat.quant-gas↗

arXiv2013

Tight-binding couplings in microwave artificial graphene

We experimentally study the propagation of microwaves in an artificial honeycomb lattice made of dielectric resonators. This evanescent propagation is well described by a tight-binding model, very much like the propagation of electrons in graphene. We measure the density of states, as well as the wave function associated with each eigenfrequency. By changing the distance between the resonators, it is possible to modulate the amplitude of next-(next-)nearest-neighbor hopping parameters and to study their effect on the density of states. The main effect is the density of states becoming dissymmetric and a shift of the energy of the Dirac points. We study the basic elements: An isolated resonator, a two-level system, and a square lattice. Our observations are in good agreement with analytical solutions for corresponding infinite lattice.

cond-mat.mes-hall↗

arXiv2013

Ergodic vs diffusive decoherence in mesoscopic devices

We report on the measurement of phase coherence length in a high mobility two-dimensional electron gas patterned in two different geometries, a wire and a ring. The phase coherence length is extracted both from the weak localization correction in long wires and from the amplitude of the Aharonov-Bohm oscillations in a single ring, in a low temperature regime when decoherence is dominated by electronic interactions. We show that these two measurements lead to different phase coherence lengths, namely $L_Φ^\mathrm{wire}\propto T^{-1/3}$ and $L_Φ^\mathrm{ring}\propto T^{-1/2}$. This difference reflects the fact that the electrons winding around the ring necessarily explore the whole sample (ergodic trajectories), while in a long wire the electrons lose their phase coherence before reaching the edges of the sample (diffusive regime).

cond-mat.mes-hall↗

arXiv2012

Topological transition of Dirac points in a microwave experiment

By means of a microwave tight-binding analogue experiment of a graphene-like lattice, we observe a topological transition between a phase with a point-like band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlled anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.

cond-mat.mes-hall↗