Random Walk to Graphene (Nobel Lecture)

The authors review conductance effects in small samples at low temperatures where quantum confinement and quantum interference are significant perturbations on the classical Drude conductance. In disordered materials, the elastic scattering of the carriers from impurities leads to random conductance fluctuations or resistance fluctuations. The fluctuations arise because of interference among the scattered waves, and they are random and sample specific because the impurity potential is. The fluctuations appear in response to changes in many extrinsic parameters such as the carrier density, the applied measuring current, external electric fields and external fields. The interface fluctuations have consequences for much larger samples, particularly in flicker noise, even though quantum coherence is obtained only over regions much smaller than the sample size, in completely phase coherent conductors a number of purely quantum effects are observed, including non-local response and Aharonov-Bohm effects. Other 'applications' of the quantum fluctuations include studies of reciprocity (which is related to time-reversal symmetry) and of the effects of the measurement probes on a quantum system. Interestingly, these are two areas where disagreements remain with theoretical calculations. The size and correlation scale of the fluctuations, however, are mainly in agreement with theoretical calculations of the same quantities, although one or two other small disagreements of detail remain. In very clean semiconductor heterostructures, the mean free path length between scattering events is large enough to allow for studies of ballistic transport that reveal a variety of conductance anomalies that result from device shape (as opposed to fortuitous placement of impurities as in the metals). These ballistic effects are reviewed briefly and connection is made to the effects of disorder in ballistic systems, and experiments on disordered metal samples are reviewed in detail.

https://iopscience.iop.org/article/10.1088/0034-4885/55/8/004/pdf

Quantum transport in small disordered samples from the diffusive to the ballistic regime

If one wants to understand the beautiful physics of graphene, they will be spoiled for choice with so many reviews and popular science articles now available. I hope that the reader will excuse me if on this occasion I recommend my own writings [1–3]. Instead of repeating myself here, I have chosen to describe my twisty scientific road that eventually led to the Nobel Prize. Most parts of this story are not described anywhere else, and its timeline covers the period from my PhD in 1987 to the moment when our 2004 paper, recognised by the Nobel Committee, was accepted for publication. The story naturally gets denser in events and explanations towards the end. Also, it provides a detailed review of pre-2004 literature and, with the benefit of hindsight, attempts to analyse why graphene has attracted so much interest. I have tried my best to make this article not only informative but also easy to read, even for non-physicists.

Random walk to graphene

In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits.

Coupled Langmuir oscillations in 2-dimensional quantum plasmas

Random Walk to Graphene

A new type of nonlocal oscillatory magnetoresistance effect is observed in heavily doped ${\mathit{n}}^{+}$-GaAs wires over a limited range of temperature (10\ensuremath{\le}T\ensuremath{\le}50 K) and at magnetic fields sufficiently large to give rise to Landau quantization. The effect is observed when quantum ballistic transport along the edges coexists with diffusive and dissipative conduction in the bulk.

P. Steda

Papers

New nonlocal magnetoresistance effect at the crossover between the classical and quantum transport regimes