Resonant Josephson current through a quantum dot

We calculate the DC Josephson current through a semiconducting quantum dot which is weakly coupled by tunnel barriers to two superconducting reservoirs. A Breit-Wigner resonance in the conductance corresponds to a resonance in the critical current, but with a different (non-lorentzian) lineshape.Comment: 5 pages including 1 figure; this paper was published in the proceedings of SQUID'91; it is archived here because of its relevance to cond-mat/011148

Photon statistics of a random laser

A general relationship is presented between the statistics of thermal radiation from a random medium and its scattering matrix S. Familiar results for black-body radiation are recovered in the limit S to 0. The mean photocount is proportional to the trace of 1-SS^dagger, in accordance with Kirchhoff's law relating emissivity and absorptivity. Higher moments of the photocount distribution are related to traces of powers of 1-SS^dagger, a generalization of Kirchhoff's law. The theory can be applied to a random amplifying medium (or "random laser") below the laser threshold, by evaluating the Bose-Einstein function at a negative temperature. Anomalously large fluctuations are predicted in the photocount upon approaching the laser threshold, as a consequence of overlapping cavity modes with a broad distribution of spectral widths.Comment: 26 pages, including 9 figure

Why does a metal-superconductor junction have a resistance?

This is a tutorial article based on a lecture delivered in June 1999 at the NATO Advanced Study Institute in Ankara. The phenomenon of Andreev reflection is introduced as the electronic analogue of optical phase-conjugation. In the optical problem, a disordered medium backed by a phase-conjugating mirror can become completely transparent. Yet, a disordered metal connected to a superconductor has the same resistance as in the normal state. The resolution of this paradox teaches us a fundamental difference between phase conjugation of light and electrons.Comment: 12 pages, 5 postscript figures [v2: all figures inline

Three "universal" mesoscopic Josephson effects

1. Introduction 2. Supercurrent from Excitation Spectrum 3. Excitation Spectrum from Scattering Matrix 4. Short-Junction Limit 5. Universal Josephson Effects 5.1 Quantum Point Contact 5.2 Quantum Dot 5.3 Disordered Point Contact (Average supercurrent, Supercurrent fluctuations)Comment: 21 pages, 2 figures; legacy revie

Dynamics of localization in a waveguide

This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption.Comment: 18 pages including 8 figures; minor correction

Full Counting Statistics of Superconductor--Normal-Metal Heterostructures

The article develops a powerful theoretical tool to obtain the full counting statistics. By a slight extension of the standard Keldysh method we can access immediately all correlation functions of the current operator. Embedded in a quantum generalization of the circuit theory of electronic transport, we are able to study the full counting statistics of a large class of two-terminal contacts and multi-terminal structures, containing superconductors and normal metals as elements. The practical use of the method is demonstrated in many examples.Comment: 35 pages, contribution to "Quantum Noise", ed. by Yu.V. Nazarov and Ya.M. Blanter, minor changes in text, references adde

Quantum Point Contacts and Coherent Electron Focusing

I. Introduction II. Electrons at the Fermi level III. Conductance quantization of a quantum point contact IV. Optical analogue of the conductance quantization V. Classical electron focusing VI. Electron focusing as a transmission problem VII. Coherent electron focusing (Experiment, Skipping orbits and magnetic edge states, Mode-interference and coherent electron focusing) VIII. Other mode-interference phenomenaComment: #3 of a series of 4 legacy reviews on QPC'

Gate-controlled Guiding of Electrons in Graphene

Ballistic semiconductor structures have allowed the realization of optics-like phenomena in electronics, including magnetic focusing and lensing. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogs of optical devices having both positive and negative indices of refraction. Here, we use gate-controlled density with both p and n carrier types to demonstrate the analog of the fiber-optic guiding in graphene. Two basic effects are investigated: (1) bipolar p-n junction guiding, based on the principle of angle-selective transmission though the graphene p-n interface, and (2) unipolar fiber-optic guiding, using total internal reflection controlled by carrier density. Modulation of guiding efficiency through gating is demonstrated and compared to numerical simulations, which indicates that interface roughness limits guiding performance, with few-nanometer effective roughness extracted. The development of p-n and fiber-optic guiding in graphene may lead to electrically reconfigurable wiring in high-mobility devices.Comment: supplementary materal at http://marcuslab.harvard.edu/papers/OG_SI.pd

Designing disorder

This is the author accepted manuscript. The final version is available from Springer Nature via the DOI in this recordMetasurfaces can in principle provide a versatile platform for optical functionalities, but in practice designing and fabricating them to specifications can be difficult. Now, the realization of metasurfaces with engineered disorder allows for versatile optical components that combine the best features of periodic and random systems

Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions

The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this article, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with two Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically-protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook towards more advanced microwave spectroscopy experiments, currently under development.Comment: Lectures given at the San Sebastian Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer