Landau diamagnetism revisited

Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter to distinguish different states of matter. Experiments in a number of correlated materials raise serious suspicions about the general validity of either notion. A growing body of theoretical work has confirmed these suspicions, and explored...

We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1-q)<<1, in terms of the factorization approach. Two methods agree under certain condit...

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero -- the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial, but s...

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.

Transport behavior characterized by a low-temperature electrical resistivity that displays a power-law behavior $\rho(T\to 0) \propto T^s$ with an exponent $s<2$, is commonly observed in magnetic materials in both the magnetic and nonmagnetic phases. We give a pedagogical overview of this phenomenon that summarizes both the experimental situation and the state of its theoretical understanding. We also put it in context by drawing parallels with unusual power-law transport beh...

The Landauer formula for quantum conductance, based on the modern paradigm: "conduction is transmission", is generalized to samples of macroscopic size. Two regimes of electrical conduction, namely diffusive and ballistic ones, are studied. In the former regime, Drude's formula for the electrical resistivity is recovered and it is found a maximum conductivity equal to $(e^2 m c)/(\pi \hbar^2)$, which is of the same order of magnitude as that of good metals at room temperature...

We report the observation of an acute sensitivity of the anisotropic longitudinal resistivity of two-dimensional electron systems in half-filled high Landau levels to the magnitude and orientation of an in-plane magnetic field. In the third and higher Landau levels, at filling fractions nu=9/2, 11/2, etc., the in-plane field can lead to a striking interchange of the "hard" and "easy" transport directions. In the second Landau level the normally isotropic resistivity and the w...

We perform a semiclassical calculation of the magnetoresistance of spinless two-dimensional fermions in a long-range correlated random magnetic field. In the regime relevant for the problem of the half filled Landau level the perturbative Born approximation fails and we develop a new method of solving the Boltzmann equation beyond the relaxation time approximation. In absence of interactions, electron density modulations, in-plane fields, and Fermi surface anisotropy we obtai...

In this paper, we revisit some quantum mechanical aspects related to the Quantum Hall Effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of Quantum Hall experiments. The resulting formalism is then used to compute explicitely the Hall conductivity from a Kubo formula.

Over the last century Bohr van Leuween theorem attracted the notice of physicists. The theorem states about the absence of magnetization in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years this topic has been investigated intensively and it is not free from controversy. We a have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpe...