Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

The electronic properties of graphene

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

/pdf/spintronics-fundamentals-and-applications-2dx38n6phu.pdf

Spintronics: Fundamentals and applications

Nanocrystals (NCs) discussed in this Review are tiny crystals of metals, semiconductors, and magnetic material consisting of hundreds to a few thousand atoms each. Their size ranges from 2-3 to about 20 nm. What is special about this size regime that placed NCs among the hottest research topics of the last decades? The quantum mechanical coupling * To whom correspondence should be addressed. E-mail: dvtalapin@uchicago.edu. † The University of Chicago. ‡ Argonne National Lab. Chem. Rev. 2010, 110, 389–458 389

/pdf/prospects-of-colloidal-nanocrystals-for-electronic-and-3dxpyhl3r7.pdf

Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications

This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

https://arxiv.org/pdf/cond-mat/0506047.pdf

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

1. Introduction 2. Supermathematics 3. Diffusion modes 4. Nonlinear supermatrix sigma- model 5. Perturbation theory and renormalization group 6. Energy level statistics 7. Quantum size effects in small metal particles 8. Persistent currents in mesoscopic rings 9. Transport through mesoscopic devices 10. Universal parametric correlations 11. Localization in systems with one-dimensional geometry 12. Anderson metal-insulator transition 13. Disorder in two dimensions 14. Afterword.

http://ipht.cea.fr/Docspht//articles/t12/020/public/2012_Efetov_lecture1+2_by_Ribault.pdf

Supersymmetry in Disorder and Chaos

Theoretical studies of the motion of an electron in a disordered system have led to a number of remarkable results especially those concerned with localization and with the importance of dimensionality. The theoretical approaches previously used run into some severe technical difficulties. This article sets out the bases of the recently introduced supersymmetry method which has already, as the article shows, provided unified derivations of the major results in this subject, free of the technical problems. The method reduces the systems it treats to field-theoretical models involving both bosons and fermions.

Supersymmetry and theory of disordered metals

We analyze the proximity effect in a superconductor/ferromagnet (S/F) structure with a local inhomogeneity of the magnetization in the ferromagnet near the S/F interface. We demonstrate that not only the singlet but also the triplet component of the superconducting condensate is induced in the ferromagnet due to the proximity effect. The singlet component penetrates into the ferromagnet over a short length xi(h) = sqrt[D/h] ( h is the exchange field and D the diffusion coefficient), whereas the triplet component penetrates over a long length sqrt[D/epsilon] and leads to a significant increase of the ferromagnet conductance below the superconducting critical temperature Tc.

https://arxiv.org/pdf/cond-mat/0011425.pdf

Long-range proximity effects in superconductor-ferromagnet structures.

Granular metals are arrays of metallic particles of a size ranging usually from a few to hundreds of nanometers embedded into an insulating matrix. Metallic granules are often viewed as artificial atoms. Accordingly, granular arrays can be treated as artificial solids with programmable electronic properties. The ease of adjusting electronic properties of granular metals assures them an important role for nanotechnological applications and makes them most suitable for fundamental studies of disordered solids. This review discusses recent theoretical advances in the study of granular metals, emphasizing the interplay of disorder, quantum effects, fluctuations, and effects of confinement. These key elements are quantified by the tunneling conductance between granules $g$, the charging energy of a single granule ${E}_{c}$, the mean level spacing within a granule $\ensuremath{\delta}$, and the mean electronic lifetime within the granule $\ensuremath{\hbar}∕g\ensuremath{\delta}$. By tuning the coupling between granules the system can be made either a good metal for $gg{g}_{c}=(1∕2\ensuremath{\pi}d)\mathrm{ln}({E}_{c}∕\ensuremath{\delta})$ ($d$ is the system dimensionality), or an insulator for $gl{g}_{c}$. The metallic phase in its turn is governed by the characteristic energy $\ensuremath{\Gamma}=g\ensuremath{\delta}$: at high temperatures $Tg\ensuremath{\Gamma}$ the resistivity exhibits universal logarithmic temperature behavior specific to granular materials, while at $Tl\ensuremath{\Gamma}$ the transport properties are those generic for all disordered metals. In the insulator phase the transport exhibits a variety of activation behaviors including the long-puzzling $\ensuremath{\sigma}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}({T}_{0}∕T{)}^{1∕2}]$ hopping conductivity. Superconductivity adds to the richness of the observed phases via one more energy parameter $\ensuremath{\Delta}$. Using a wide range of recently developed theoretical approaches, it is possible to obtain a detailed understanding of the electronic transport and thermodynamic properties of granular materials, as is required for their applications.

https://arxiv.org/pdf/cond-mat/0603522.pdf

Konstantin B. Efetov

Papers

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

Supersymmetry in Disorder and Chaos

Supersymmetry and theory of disordered metals

Long-range proximity effects in superconductor-ferromagnet structures.

Granular electronic systems