Current research into semiconductor clusters is focused on the properties of quantum dots-fragments of semiconductor consisting of hundreds to many thousands of atoms-with the bulk bonding geometry and with surface states eliminated by enclosure in a material that has a larger band gap. Quantum dots exhibit strongly size-dependent optical and electrical properties. The ability to join the dots into complex assemblies creates many opportunities for scientific discovery.

Semiconductor Clusters, Nanocrystals, and Quantum Dots

Fabrication techniques developed for graphene research allow the disassembly of many layered crystals (so-called van der Waals materials) into individual atomic planes and their reassembly into designer heterostructures, which reveal new properties and phenomena. Andre Geim and Irina Grigorieva offer a forward-looking review of the potential of layering two-dimensional materials into novel heterostructures held together by weak van der Waals interactions. Dozens of these one-atom- or one-molecule-thick crystals are known. Graphene has already been well studied but others, such as monolayers of hexagonal boron nitride, MoS2, WSe2, graphane, fluorographene, mica and silicene are attracting increasing interest. There are many other monolayers yet to be examined of course, and the possibility of combining graphene with other crystals adds even further options, offering exciting new opportunities for scientific exploration and technological innovation. Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as ‘van der Waals’) have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene’s springboard, van der Waals heterostructures should develop into a large field of their own.

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Van der Waals heterostructures

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

REVIEW Semiconductor devices generally take advantage of the charge of electrons, whereas magnetic materials are used for recording information involving electron spin. To make use of both charge and spin of electrons in semiconductors, a high concentration of magnetic elements can be introduced in nonmagnetic III-V semiconductors currently in use for devices. Low solubility of magnetic elements was overcome by low-temperature nonequilibrium molecular beam epitaxial growth, and ferromagnetic (Ga,Mn)As was realized. Magnetotransport measurements revealed that the magnetic transition temperature can be as high as 110 kelvin. The origin of the ferromagnetic interaction is discussed. Multilayer heterostructures including resonant tunneling diodes (RTDs) have also successfully been fabricated. The magnetic coupling between two ferromagnetic (Ga,Mn)As films separated by a nonmagnetic layer indicated the critical role of the holes in the magnetic coupling. The magnetic coupling in all semiconductor ferromagnetic/nonmagnetic layered structures, together with the possibility of spin filtering in RTDs, shows the potential of the present material system for exploring new physics and for developing new functionality toward future electronics.

https://science.sciencemag.org/content/sci/281/5379/951.full.pdf

Making Nonmagnetic Semiconductors Ferromagnetic

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

A variety of novel lithographic techniques have been used' to create quasi-onedimensional (Q1D) inversion layers in Si MOSFETs to study how their conductance depends on carrier density. It is remarkable that, despite the differences in the structure of the devices, the results are qualitatively similar: one observes random, but timeindependent, fluctuations in the conductance G as a function of electron density, which are exponentially large at small G and of order e2/h at large G. The latter are the universal conductance fluctuations2 seen in Q1 D metals as well,3 and the former result from one dimensional variable-range hopping.4 Among the inversion layers studied to date, those with smaller width w generally5 had lower mobility ( y 3000cm2/V-s is typical for w 40 nm). In Phys. Rev. Letters 62:583 (1989), we reported studies of narrower inversion layers ( w 25 nm) with higher y (15000 cm 2/V's) than previously reported that revealed qualitatively new behavior. The variations in G are still exponentially large at small electron density and very small at high density, but the variations are periodic in the density of electrons in the inversion layer, even in the absence of a magnetic field.

Ultralow Temperature Studies of Nanometer Size Semiconductor Devices

Quasi‐Elastic and Inelastic Neutron‐Scattering Studies of Superconducting Lanthanum Strontium Copper Oxide (La2‐xSrxCuO4)

Periodic conductance resonances in one-dimensional GaAs channels with nanoconstrictions

Optical absorption spectra are presented for four undoped single-crystal copper oxides: La2CuO4, Nd2CuO4, Pr2CuO4 and Sr2CuO2Cl2. Common absorption features are observed near 0.5 eV, which are shown from polarization measurements to be weakly electric-dipole allowed excitations of the CuO2 layers. The detailed polarization and spectral dependencies are consistent with normally forbidden valence-conserving crystal-field transitions with multi-magnon and phonon sidebands. Such transitions provide a natural origin for the mid-infrared band observed in doped copper oxides.

Mid-infrared excitations in undoped layered copper oxides

Theoretical work has suggested that monolayer MoS2 doped with Mn should behave as a two-dimensional dilute magnetic semiconductor, which would open up possibilities for spintronic applications, device physics, and novel ground states. The magnetic properties on Mn dopants in MoS2 are dependent on the mid-gap impurity states of said dopants as well as the sites of dopant incorporation and dopant concentration. In this work we use STM/STS to characterize multiple impurity types associated with Mn dopants in MoS2, and use ring features that appear in spectral maps due to tip-induced band bending to investigate the nature of the mid-gap impurity states. The doublet nature of the rings and comparison to DFT calculations show that the Mn states exhibit strong spin splitting which can be quantified. We used scanned MOKE experiments to extend these magnetization measurements from atomic scale to mm scales, and detect the spin susceptibility signal which increases with Mn concentration. These experiments show that single Mn atoms in MoS2 function as active unscreened magnetic moments in the TMD monolayer, and can be harnessed for spin physics applications and science.

Marc Kastner

Papers

Ultralow Temperature Studies of Nanometer Size Semiconductor Devices

Quasi‐Elastic and Inelastic Neutron‐Scattering Studies of Superconducting Lanthanum Strontium Copper Oxide (La2‐xSrxCuO4)

Periodic conductance resonances in one-dimensional GaAs channels with nanoconstrictions

Mid-infrared excitations in undoped layered copper oxides

Quantum Imaging of Single-Atom Spin-Splitting in a Monolayer Semiconductor