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

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Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5cpnozn547.pdf

New directions in the pursuit of Majorana fermions in solid state systems.

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.

Parity–time-symmetric whispering-gallery microcavities

The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic `topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to `engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5afwb64kak.pdf

New directions in the pursuit of Majorana fermions in solid state systems

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

Granular electronic systems

Scanning tunneling spectroscopy at very low temperatures on homogeneously disordered superconducting titanium nitride thin films reveals strong spatial inhomogeneities of the superconducting gap $\ensuremath{\Delta}$ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature ${T}_{c}$ towards zero, enhancement of spatial fluctuations in $\ensuremath{\Delta}$, and growth of the $\ensuremath{\Delta}/{T}_{c}$ ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.

Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition.

The melting transition in twinned and untwinned single crystals is measured resistively in fields up to 8 T as a function of the angle between the c axis and the a-b plane. The angular dependence follows the Lindemann criterion with ${\mathit{c}}_{\mathit{L}}$=0.15. The suppression of melting by strong pinning by twin boundaries is demonstrated.

Vortex lattice melting in untwinned and twinned single crystals of YBa2Cu3O7- delta.

The theory of pinning of a vortex liquid by weak disorder is developed. Two different vortex-liquid dissipative regimes are shown to exist: the flux flow above some crossover temperature ${\mathit{T}}_{\mathit{k}}$, where the vortex liquid is unpinned, and the thermally assisted flux flow below ${\mathit{T}}_{\mathit{k}}$. The activation barriers in the latter regime are those associated with the plastic motion of the vortices in the liquid.

Resistivity of high-Tc superconductors in a vortex-liquid state.

The long-time asymptotics of the current (magnetization) relaxation in high-temperature superconductors is studied within the framework of collective creep theory. The inverse normalized relaxation rate {ital S}{sup {minus}1} depends linearly on {ital T}ln({ital t}/{tau}{sub 0}). The attempt time {tau}{sub 0} is shown to be much longer than a microscopic'' time scale and is strongly size and {ital j}{sub {ital c}} dependent.

V. M. Vinokur

Papers

Granular electronic systems

Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition.

Vortex lattice melting in untwinned and twinned single crystals of YBa2Cu3O7- delta.

Resistivity of high-Tc superconductors in a vortex-liquid state.

Flux creep and current relaxation in high-Tc superconductors.