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The recent detection of the singular diamagnetism of Dirac electrons in a single graphene layer paved a new way of probing 2D quantum materials through the measurement of equilibrium orbital currents which cannot be accessed in usual transport experiments. Among the theoretical predictions is an intriguing orbital paramagnetism at saddle points of the dispersion relation. Here we present magnetisation measurements in graphene monolayers aligned on hexagonal boron nitride (hBN)crystals. Beside the sharp diamagnetic McClure response at the Dirac point, we detect extra diamagnetic singularities at the satellite Dirac points (sDP) of the moir\'e lattice. Surrounding these diamagnetic satellite peaks, we also observe paramagnetic peaks located at the chemical potential of the saddle points of the Graphene moir\'e band structure and relate them to the presence of van Hove logarithmic singularities in the density of states. These findings reveal the long ago predicted anomalous paramagnetic orbital response in 2D systems when the Fermi energy is tuned to the vicinity of saddle points., Comment: main paper 6 pages 5 figures and supplementaray materials 18 pages and 14 figures

The electronic properties of graphene have been intensively investigated over the last decade, and signatures of the remarkable features of its linear Dirac spectrum have been displayed using transport and spectroscopy experiments. In contrast, the orbital magnetism of graphene, which is one of the most fundamental signature of the characteristic Berry phase of graphene's electronic wave functions, has not yet been measured in a single flake. In particular, the striking prediction of a divergent diamagnetic response at zero doping calls for an experimental test. Using a highly sensitive Giant Magnetoresistance sensor (GMR) we have measured the gate voltage-dependent magnetization of a single graphene monolayer encapsulated between boron nitride crystals. The signal exhibits a diamagnetic peak at the Dirac point whose magnetic field and temperature dependences agree with theoretical predictions starting from the work of Mc Clure \cite{McClure1956}. Our measurements open a new field of investigation of orbital currents in graphene and 2D topological materials, offering a new means to monitor Berry phase singularities and explore correlated states generated by combined effects of Coulomb interactions, strain or moir\'e potentials., Comment: 6 pages 5 figures and supplemental material

Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancy-like defect in the lattice, we observe an anisotropically localized polariton distribution in a single sublattice, a consequence of the semi-Dirac dispersion. Our work opens up new horizons for the study of transport and localization in lattices with chiral symmetry and exotic Dirac dispersions., Comment: 6 pages, 3 figures

The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of intricate transport phenomena has been predicted, such as modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions. Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi-Dirac, tilted and, most interestingly, type-III Dirac cones that combine flat and linear dispersions. The tilted cones emerge from the touching of a flat and a parabolic band with a non-trivial topological charge. These results open the way to the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, to the study of topological and Dirac superfluids in photonic lattices., Comment: 10 pages + 10 pages supplementary information

A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu \cite{Gao}, that goes beyond the Onsager relation \cite{Onsager}. In addition to the integrated density of states, it formally involves magnetic response functions of all orders in the magnetic field. In particular, up to second order, it requires the knowledge of the spontaneous magnetization and the magnetic susceptibility, as was early anticipated by Roth \cite{Roth}. We study three applications of this relation focusing on two-dimensional electrons. First, we obtain magnetic response functions from Landau levels. Second we obtain Landau levels from response functions. Third we study magnetic oscillations in metals and propose a proper way to analyze Landau plots (i.e. the oscillation index $n$ as a function of the inverse magnetic field $1/B$) in order to extract quantities such as a zero-field phase-shift. Whereas the frequency of $1/B$-oscillations depends on the zero-field energy spectrum, the zero-field phase-shift depends on the geometry of the cell-periodic Bloch states via two contributions: the Berry phase and the average orbital magnetic moment on the Fermi surface. We also quantify deviations from linearity in Landau plots (i.e. aperiodic magnetic oscillations), as recently measured in surface states of three-dimensional topological insulators and emphasized by Wright and McKenzie \cite{Wright}., Comment: 31 pages, 8 figures; v2: SciPost style; v3: several references added, small corrections, typos fixed; v4: abstract changed, generalized quantization condition called Roth-Gao-Niu; v5: minor modifications, 2 references added

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy., Comment: 15 pages, 14 figures

We review the physics of magnetic quantum oscillations in quasi-one dimensional conductors with an open Fermi surface, in the presence of modulated order. We emphasize the difference between situations where a modulation couples states on the same side of the Fermi surface and a modulation couples states on opposite sides of the Fermi surface. We also consider cases where several modulations coexist, which may lead to a complex reorganization of the Fermi surface. The interplay between nesting effects and magnetic breakdown is discussed. The experimental situation is reviewed., Comment: 10 pages, 8 figures, Contribution to the memorial issue in honor of J. Friedel, C. R. Acad. Sci. Paris

We study the importance of interband effects on the orbital susceptibility of three bands $\alpha$-${\cal T}_3$ tight-binding models. The particularity of these models is that the coupling between the three energy bands (which is encoded in the wavefunctions properties) can be tuned (by a parameter $\alpha$) without any modification of the energy spectrum. Using the gauge-invariant perturbative formalism that we have recently developped, we obtain a generic formula of the orbital susceptibility of $\alpha$-${\cal T}_3$ tight-binding models. Considering then three characteristic examples that exhibit either Dirac, semi-Dirac or quadratic band touching, we show that by varying the parameter $\alpha$ and thus the wavefunctions interband couplings, it is possible to drive a transition from a diamagnetic to a paramagnetic peak of the orbital susceptibility at the band touching. In the presence of a gap separating the dispersive bands, we show that the susceptibility inside the gap exhibits a similar dia to paramagnetic transition., Comment: 15 pages,5 figs. Proceedings of the International Workshop on Dirac Electrons in Solids 2015Proceedings of the International Workshop on Dirac Electrons in Solids 2015

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called {\it modern theory of orbital magnetization} and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band -- either gapless or gapped -- systems. We point out some surprising features in the orbital susceptibility -- such as in-gap diamagnetism or parabolic band edge paramagnetism -- coming from interband coupling. From that we draw general conclusions on the orbital magnetism of itinerant electrons in multi-band tight-binding models., Comment: 18 pages, 9 figures

We analyze the low-energy properties of two-dimensional direct-gap semiconductors, such as for example the transition-metal dichalcogenides MoS$_2$, WS$_2$, and their diselenide analogues MoSe$_2$, WSe$_2$, etc., which are currently intensively investigated. In general, their electrons have a mixed character -- they can be massive Dirac fermions as well as simple Schr\"odinger particles. We propose a measure (Diracness) for the degree of mixing between the two characters and discuss how this quantity can in principle be extracted experimentally, within magneto-transport measurements, and numerically via ab initio calculations., Comment: 6 pages, 2 figures ; new version (with minor modifications) accepted for publication in EPL

We study the orbital susceptibility of coupled energy bands with a pair of Dirac points, as in graphene. We show that different systems having the same zero-field energy spectrum exhibit strong differences in their orbital magnetic response at zero energy, ranging from diamagnetism (graphene) to paramagnetism (dice lattice). A lattice model is introduced which interpolates continuously between these two limits. This striking behavior is related to a Berry phase varying continuously from pi to 0. These predictions could be tested with cold atoms in an optical lattice, Comment: 5 pages, 10 figures, supplementary material

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

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, Comment: 6 pages, 9 figures, Proceedings of ECRYS-2011, International School and Workshop on Electronic Crystals, Cargese (France)

We have measured the critical current dependence on the magnetic flux of two long SNS junctions differing by the normal wire geometry. The samples are made by a Au wire connected to W contacts, via Focused Ion Beam assisted deposition. We could tune the magnetic pattern from the monotonic gaussian-like decay of a quasi 1D normal wire to the Fraunhofer-like pattern of a square normal wire. We explain the monotonic limit with a semiclassical 1D model, and we fit both field dependences with numerical simulations of the 2D Usadel equation. Furthermore, we observe both integer and fractional Shapiro steps. The magnetic flux dependence of the integer steps reproduces as expected that of the critical current Ic, while fractional steps decay slower with the flux than Ic., Comment: 5 pages, 4 figures

We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, it confirms and generalizes the results of several previous works., Comment: 14 pages, 19 figures

We re-examine the band structure of the stripe charge ordered state of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure by using an extended Hubbard model within the Hartree mean-field theory. By increasing pressure, we find a topological transition from a conventional insulator with a single-minimum in the dispersion relation at the M-point in the Brillouin zone, towards a new phase which exhibits a double-minimum. This transition is characterized by the appearance of a pair of Dirac electrons with a finite mass. Using the Luttinger-Kohn representation at the M-point, it is shown that such a variation of the band structure can be described by an effective $2 \times 2$ low energy Hamiltonian with a single driving parameter. The topological nature of this transition is confirmed by the calculation of the Berry curvature which vanishes in the conventional phase and has a double peak structure with opposite signs in the new phase. We compare the structure of this transition with a simpler situation which occurs in two-component systems, like boron-nitride., Comment: 12 pages, 14 figures

We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of graphene and we derive a simplified effective low-energy Hamiltonian which captures the essential topological properties of twisted bilayer graphene. The corresponding Landau levels peculiarly reveal a degenerate zero-energy mode which cannot be lifted by strong magnetic fields., Comment: 5 pages, 3 figures; published version

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects -- such as Berry phase and Maslov index -- occurring at order $\hbar$ in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase -- which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands -- acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the "k-dependent Hamiltonian" H(k), where k is the Bloch wavevector., Comment: 15 pages, 6 figures, submitted to EPJB

The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair of Dirac points may merge into a single one, with a topological transition towards a gapped phase. At the transition, the spectrum is linear in one direction and quadratic in the other one (a spectrum recently named "hybrid" or "semi-Dirac"). This transition is studied in the framework of a general Hamiltonian describing the merging of Dirac points. The possibility of creating gauge fields for cold atoms in optical lattices may offer the first opportunity to observe this merging of Dirac points and the hybrid dispersion relation., Comment: 8 pages, 7 figures

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., Comment: 18 pages, 15 figures

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., Comment: 4 pages, 5 figures

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., Comment: 4 pages, 1 figure; version with minor corrections published in EPL

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., Comment: 11 pages, 5 figures; version accepted for publication in PRB, contains a more detailed discussion of the zero-energy Landau level in the presence of the tilt, technical parts shifted to the appendix

We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence, notably the low and high field dependence of the maximum switching current. In contrast with the well-known Fraunhoffer-type oscillations typical of short wide junctions, we find a monotonous gaussian extinction of the critical current at high field. As shown in [15], this monotonous dependence is typical of long and narrow diffusive junctions. We also find in some cases a puzzling reentrance at low field. In contrast, the temperature dependence of the critical current is well described by the proximity effect theory, as found by Dubos {\it et al.} [16] on SNS wires in the long junction limit. The switching current distributions and hysteretic IV curves also suggest interesting dynamics of long SNS junctions with an important role played by the diffusion time across the junction., Comment: 12 pages, 16 figures

We investigate weak localization in metallic networks etched in a two dimensional electron gas between $25\:$mK and $750\:$mK when electron-electron (e-e) interaction is the dominant phase breaking mechanism. We show that, at the highest temperatures, the contributions arising from trajectories that wind around the rings and trajectories that do not are governed by two different length scales. This is achieved by analyzing separately the envelope and the oscillating part of the magnetoconductance. For $T\gtrsim0.3\:$K we find $\Lphi^\mathrm{env}\propto{T}^{-1/3}$ for the envelope, and $\Lphi^\mathrm{osc}\propto{T}^{-1/2}$ for the oscillations, in agreement with the prediction for a single ring \cite{LudMir04,TexMon05}. This is the first experimental confirmation of the geometry dependence of decoherence due to e-e interaction., Comment: LaTeX, 5 pages, 4 eps figures

Although conservation of energy is fundamental in physics, its principles seem to be violated in the field of wave propagation in turbid media by the energy enhancement of the coherent backscattering cone. In this letter we present experimental data which show that the energy enhancement of the cone is balanced by an energy cutback at all scattering angles. Moreover, we give a complete theoretical description, which is in good agreement with these data. The additional terms needed to enforce energy conservation in this description result from an interference effect between incident and multiply scattered waves, which is reminiscent of the optical theorem in single scattering., Comment: 4 pages

Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases., Comment: published version, with a new figure and new section 5

We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory., Comment: 4 pages, 4 figures, added references

The stationnary Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction is revisited for arbitrarily large spin polarizations. The quasiclassical calculation of the supercurrent assumes that the Andreev reflection is complete for all channels. However, De Jong and Beenakker have shown that the Andreev reflection at a clean FS interface is incomplete, due to the exchange interaction in the ferromagnet. Taking into account this incomplete Andreev reflection, we investigate the quasiparticle spectrum, the Josephson current and the $0-\pi$ transition in a ballistic single channel SFS junction. We find that energy gaps open in the phase dependent spectrum. Although the spectrum is strongly modified when the exchange energy increases, the Josephson current and the $0-\pi$ transition are only weakly affected by the incomplete Andreev reflection, except when the exchange energy is close to the Fermi energy., Comment: 8 pages, 7 figures, added references, typos added

We investigate the ground state current of an isolated hybrid normal/superconducting ring (NS ring), threaded by an Aharonov-Bohm magnetic flux. We calculate the excitation spectrum of the ring for any values of the lengths of the normal metal and of the superconductor. We describe the nonlinear flux dependence of the energy levels above and below the gap edge. Using a harmonics expansion for the current, we isolate the contribution due to these nonlinearities and we show that it vanishes for large normal segment length. The remaining contribution is very easy to evaluate from the linearized low energy spectrum. This decomposition allows us to recover in a controlled way the current-flux relationships for SNS junctions and for NS rings. We also study the crossover from persistent current to Josephson current in a multichannel NS ring at finite temperature.

Aharonov-Bohm oscillations have been observed in a lattice formed by a two dimensional rhombus tiling. This observation is in good agreement with a recent theoretical calculation of the energy spectrum of this so-called T3 lattice. We have investigated the low temperature magnetotransport of the T3 lattice realized in the GaAlAs/GaAs system. Using an additional electrostatic gate, we have studied the influence of the channel number on the oscillations amplitude. Finally, the role of the disorder on the strength of the localization is theoretically discussed., Comment: 6 pages, 11 EPS figures

These notes contain a rapid overview of the methods and results obtained in the field of propagation of waves in disordered media. The case of Schr\"odinger and Helmholtz equations are considered that describe respectively electrons in metals and scalar electromagnetic waves. The assumptions on the nature of disorder are discussed and perturbation methods in the weak disorder limit are presented. A central quantity, namely the probability of quantum diffusion is defined and calculated in the same limit. It is then shown that several relevant physical quantities are related to the return probability. Examples are provided to substantiate this, which include the average electrical conductivity, its fluctuations, the average albedo and spectral correlations., Comment: 17 pages, no figure, proceedings of the Cargese advanced study institute on "Wave and Imaging through Random Media", Kluwer (2001)

We propose a simple formalism to calculate the conductance of any quantum network made of one-dimensional quantum wires. We apply this method to analyze, for two periodic systems, the modulation of this conductance with respect to the magnetic field. We also study the influence of an elastic disorder on the periodicity of the AB oscillations and we show that a recently proposed localization mechanism induced by the magnetic field resists to such a perturbation. Finally, we discuss the relevance of this approach for the understanding of a recent experiment on GaAs/GaAlAs networks., Comment: 4 pages, 5 EPS figures

Taking into account both Pauli and orbital effects of external magnetic field we compute the mean field phase diagram for charge density waves in quasi-one-dimensional electronic systems. The magnetic field can cause transitions to CDW states with two types of the shifts of wave vector from its zero-field value. It can also stabilize the field-induced charge density wave. Furthermore, the critical temperature shows peaks at a new kind of magic angles., Comment: 3 pages, 1 figure included

This is a comment to J. Konig, Y. Gefen and G. Schon, Phys. Rev. Lett. 81, 4468 (1998) who consider the coupling of two discrete levels of a dot to the continuum of states in reservoirs. We have generalized this work to the case of several discrete levels., Comment: 1 page, 1 figure

We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix which describes the topology of the graph. In certain limits, they are obtained by simple counting of the nodes and their connectivity. We relate the average current of a disordered graph with interactions and the non-interacting current of the same graph with clean 1D wires. A similar relation exists for orbital magnetism in general., Comment: 4 pages, 3 figures, to appear in Physical Review Letters

We have studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several particle-hole excitations. We have considered various couplings between two successive generations of this hierarchy and determined under which conditions this coupling can lead to Wigner-Dyson correlations. We have found that the cross-over from a Poisson to a Wigner distribution is characterized not only by the ratio $V/\Delta_c$, but also by the ratio $\Delta_c/\delta$. $V$ is the typical interaction matrix element, $\delta$ is the energy distance between {\it many-body} states and $\Delta_c$ is the distance between many-body states coupled by the interaction., Comment: proceedings of "Percolation, Interaction, Localization: Simulations of Transport in Disordered Systems", Berlin 98. 10 pages, 10 figures

In a recent letter, Yi et al. PRL 78, 3523 (1997), have considered the stability of a Charge Density Wave in a one-dimensional ring, in the presence of an Aharonov-Bohm flux. This comment shows that, in one dimension, the stability of the Charge Density Wave depends on the parity of the number of electrons in the ring. This effect is similar to the parity effect known for the persistent current in one-dimensional rings., Comment: Latex, 1 page, 2 figures

The theory and experiments showing Quantum Hall effect in the quasi-one-dimensional conductors of the Bechgaard salts family are briefly reviewed. The sign reversals observed under some experimental conditions are explained within the framework of the Quantized Nesting Model. The sequence of reversals is driven by slight modifications of the geometry of the Fermi surface. It is explained why only even phases can have sign reversals and why negative phases are less stable than positive ones., Comment: Proceedings of ICSM 1996, 6 pages, LateX, 7 figures

It is shown that the universal behavior of the spacing distribution of nearest energy levels at the metal--insulator Anderson transition is indeed dependent on the boundary conditions. The spectral rigidity $\Sigma^2(E)$ also depends on the boundary conditions but this dependence vanishes at high energy $E$. This implies that the multifractal exponent $D_2$ of the participation ratio of wave functions in the bulk is not affected by the boundary conditions., Comment: 4 pages of revtex, new figures, new abstract, the text has been changed: The large energy behavior of the number variance has been found to be independent of the boundary conditions

The Thouless conjecture states that the average conductance of a disordered metallic sample in the diffusive regime can be related to the sensitivity of the sample's spectrum to a change in the boundary conditions. Here we present results of a direct numerical study of the conjecture for the Anderson model. They were obtained by calculating the Landauer-B\"uttiker conductance $g_L$ for a sample connected to perfect leads and the distribution of level curvatures for the same sample in an isolated ring geometry, when the ring is pierced by an Aharonov-Bohm flux. In the diffusive regime ($L\gg l_e$) the average conductance $g_L$ is proportional to the mean absolute curvature $< |c| >$: $ g_L = \pi <| c | > / \Delta$, provided the system size $L$ is large enough, so that the contact resistance can be neglected. $l_e$ is the elastic mean free path, $\Delta$ is the mean level spacing. When approaching the ballistic regime, the limitation of the conductance due to the contact resistance becomes essential and expresses itself in a deviation from the above proportionality. However, in both regimes and for all system sizes the same proportionality is recovered when the contact resistance is subtracted from the inverse conductance, showing that the ``curvatures measure the conductance in the bulk''. In the localized regime, the mean logarithm of the absolute curvature and the mean logarithm of the Landauer-B\"uttiker conductance are proportional., Comment: 21 pages, Revtex, 8 PostScript figures included

The sign reversals of the Quantum Hall Effect observed in quasi-one-dimensional conductors of the Bechgaard salts family are explained within the framework of the quantized nesting model. The sequence of reversals is driven by slight modifications of the geometry of the Fermi surface. It is explained why only even phases can have signign reversals and why negative phases are less stable than positive ones., Comment: 4 LaTex pages, 3 Postscript figures

The influence of an external magnetic field on a quasi one-dimensional system with a charge density wave (CDW) instability is treated within the random phase approximation which includes both CDW and spin density wave correlations. We show that the CDW is sensitive to both orbital and Pauli effects of the field. In the case of perfect nesting, the critical temperature decreases monotonously with the field, and the wave vector of the instability starts to shift above some critical value of magnetic field. Depending on the ratio between the spin and charge coupling constants and on the direction of the applied magnetic field, the wave vector shift is either parallel ($CDW_x$ order) or perpendicular ($CDW_y$ order) to the most conducting direction. The $CDW_x$ order is a field dependent linear combination of the charge and spin density waves and is sensible only to the Pauli effect. The wave vector shift in $CDW_y$ depends on the interchain coupling, but the critical temperature does not. This order is affected by the confinement of the electronic orbits. By increasing the relative strength of the orbital effect with respect to the Pauli effect, one can destroy the $CDW_y$, establishing either a $CDW_x$, or a $CDW_0$ (corresponding to perfect nesting wave vector). We also show that by increasing the imperfect nesting parameter, one passes from the regime where the critical temperature decreases with the field to the regime where it is initially enhanced by the orbital effect and eventually suppressed by the Pauli effect. For a bad nesting, the quantized phases of the field-induced CDW appear., Comment: 30 pages (LaTeX) + 15 figures

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R(s,s')$. In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $<\delta n^2(s)>$ predicted by Al'tshuler and Shklovski\u{\i}. At the transition, at small energy scales, $R(s-s')$ starts linearly, with a slope larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-\gamma}$ with $c \sim 0.041$ and $\gamma \sim 0.83$, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $\tilde K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance contains two terms $<\delta n^2(s) >= B < n >^\gamma + 2 \pi \tilde K(0)< n > where $\tilde{K}(0)$ is the limit of the form factor for $t \to 0$., Comment: 7 RevTex-pages, 10 figures. Submitted to PRB

We calculate the persistent current of 1D rings of spinless fermions with short-range interactions on a lattice with up to 20 sites, and in the presence of disorder, for various band fillings. We find that {\it both} disorder and interactions always decrease the persistent current by localizing the electrons. Away from half-filling, the interaction has a much stronger influence in the presence of disorder than in the pure case., Comment: Latex file, 11 pages, 5 figures available on request, Report LPQTH-93/18