Thermodynamics and Transport in Mesoscopic Disordered Networks

We describe the effects of phase coherence on transport and thermodynamic properties of a disordered conducting network. In analogy with weak-localization correction, we calculate the phase coherence contribution to the magnetic response of mesoscopic metallic isolated networks. It is related to the return probability for a diffusive particle on the corresponding network. By solving the diffusion equation on various types of networks, including a ring with arms, an infinite square network or a chain of connected rings, we deduce the magnetic response. As it is the case for transport properties --weak-localization corrections or universal conductance fluctuations-- the magnetic response can be written in term of a single function S called spectral function which is related to the spatial average of the return probability on the network. We have found that the magnetization of an ensemble of CONNECTED rings is of the same order of magnitude as if the rings were disconnected.Comment: Proceedings of Minerva Workshop on Mesoscopics, Fractals and Neural Networks, Eilat, March 1997, 13 pages, RevTeX, 2 figure

Rapid magnetic oscillations and magnetic breakdown in quasi-1D conductors

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. Pari

Comment on "Peierls Gap in Mesoscopic Ring Threated by a Magnetic Flux"

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 figure

Pauli and orbital effects of magnetic field on charge density waves

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 include

Boundary conditions at the mobility edge

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 condition

Measure of Diracness in two-dimensional semiconductors

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 EP

Landau levels, response functions and magnetic oscillations from a generalized Onsager relation

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 adde