Sub-Poissonian Shot Noise In A Diffusive Conductor

A review is given of the shot-noise properties of metallic, diffusive conductors. The shot noise is one third of the Poisson noise, due to the bimodal distribution of transmission eigenvalues. The same result can be obtained from a semiclassical calculation. Starting from Oseledec's theorem it is shown that the bimodal distribution is required by Ohm's law.Comment: 9 pages, LaTeX, including 2 figure

Photon shot noise

A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/I (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Buttiker's formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to 1 (as for a Poisson process). Absorption and amplification both increase the Fano factor above the Poisson value. For strong absorption P/I has the universal limit 1+3f/2 with f the Bose-Einstein function at the frequency of the incident radiation. This is the optical analogue of the one-third reduction factor of electronic shot noise in diffusive conductors. In the amplifying case the Fano factor diverges at the laser threshold, while the signal-to-noise ratio I^2/P reaches a finite, universal limit.Comment: 11 pages, 4 figures (caption to figure 3 corrected

Doubled Shot Noise In Disordered Normal-Metal-Superconductor Junctions

The low-frequency shot-noise power of a normal-metal-superconductor junction is studied for arbitrary normal region. Through a scattering approach, a formula is derived which expresses the shot-noise power in terms of the transmission eigenvalues of the normal region. The noise power divided by the current is enhanced by a factor two with respect to its normal-state value, due to Cooper-pair transport in the superconductor. For a disordered normal region, it is still smaller than the Poisson noise, as a consequence of noiseless open scattering channels.Comment: 4 pages, RevTeX v3.0, including 1 figure, Submitted to Physical Review

Excess noise for coherent radiation propagating through amplifying random media

A general theory is presented for the photodetection statistics of coherent radiation that has been amplified by a disordered medium. The beating of the coherent radiation with the spontaneous emission increases the noise above the shot-noise level. The excess noise is expressed in terms of the transmission and reflection matrices of the medium, and evaluated using the methods of random-matrix theory. Inter-mode scattering between $N$ propagating modes increases the noise figure by up to a factor of $N$, as one approaches the laser threshold. Results are contrasted with those for an absorbing medium.Comment: 8 pages, 6 figure

Reentrance effect in a graphene n-p-n junction coupled to a superconductor

We study the interplay of Klein tunneling (= interband tunneling) between n-doped and p-doped regions in graphene and Andreev reflection (= electron-hole conversion) at a superconducting electrode. The tunneling conductance of an n-p-n junction initially increases upon lowering the temperature, while the coherence time of the electron-hole pairs is still less than their lifetime, but then drops back again when the coherence time exceeds the lifetime. This reentrance effect, known from diffusive conductors and ballistic quantum dots, provides a method to detect phase coherent Klein tunneling of electron-hole pairs.Comment: 4 pages, 3 figure

Long-range correlation of thermal radiation

A general theory is presented for the spatial correlations in the intensity of the radiation emitted by a random medium in thermal equilibrium. We find that a non-zero correlation persists over distances large compared to the transverse coherence length of the thermal radiation. This long-range correlation vanishes in the limit of an ideal black body. We analyze two types of systems (a disordered waveguide and an optical cavity with chaotic scattering) where it should be observable.Comment: 4 pages, 3 figure

Effective mass and tricritical point for lattice fermions localized by a random mass

This is a numerical study of quasiparticle localization in symmetry class \textit{BD} (realized, for example, in chiral \textit{p}-wave superconductors), by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average (thermal) conductivity $\sigma$ is well described by an effective mass $M_{\rm eff}$, dependent on the first two moments of the random mass $M(\bm{r})$. The effective mass vanishes linearly when the average mass $\bar{M}\to 0$, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity $\sigma_{c}=1/\pi$ and critical exponent $\nu=1$. For strong disorder a transition to a metallic phase appears, with larger $\sigma_{c}$ but the same $\nu$. The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a \textit{repulsive} tricritical point.Comment: 6 pages, 9 figure

Anomalously large conductance fluctuations in weakly disordered graphene

We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W large compared to length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approaches the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the potential varies on the atomic scale, indicating that the absence of backscattering on the honeycomb lattice is at the origin of the anomalously large fluctuations.Comment: 5 pages, 8 figure

A hierarchy of models related to nanoflows and surface diffusion

In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis

Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum Hall phase connectivity

The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moir\'e super- lattice of graphene on an hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly misaligning the substrate, producing a hierarchy of conical singularities (Dirac points) in the band structure at rational values Phi = (p/q)(h/e) of the magnetic flux per supercell. Each Dirac point signals a switch of the topological quantum number in the connected component of the quantum Hall phase diagram. Model calculations reveal the scale invariant conductivity sigma = 2qe^2 / pi h and Klein tunneling associated with massless Dirac fermions at these connectivity switches.Comment: 4 pages, 6 figures + appendix (3 pages, 1 figure