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

The Cu{sub 3}O{sub 4} layer in Sr{sub 2}Cu{sub 3}O{sub 4}Cl{sub 2} is a variant of the square CuO{sub 2} lattice of the high-temperature superconductors, in which the center of every second plaquette contains an extra Cu{sup 2+} ion. The ions that make up the conventional CuO{sub 2} network, called CuI, have CuI-CuI exchange energy {approx}130thinspmeV, and order antiferromagnetically at about 380 K; the CuII-CuII exchange is only {approx}10thinspmeV, and the CuII{close_quote}s order at {approx}40thinspK. A study is reported here of the dependence of the magnetization on field, temperature, and crystallographic orientation for this interesting system. We show that the small permanent ferromagnetic moment, that appears when the CuI spins order, and the unusual spin rotation transitions seen most clearly for one particular direction of the magnetic field, are the result of several small bond-dependent anisotropic terms in the spin Hamiltonian that are revealed because of the frustration of the isotropic Heisenberg interaction between CuI and CuII spins. These include a term which favors collinearity of the CuI and CuII spins, which originates from quantum fluctuations, and also the pseudodipolar interaction. Some of these small interactions also come into play in other lamellar cuprates, connected with the high-T{sub c} superconductivity materials,more » and in many spin-chain and spin-ladder compounds. {copyright} {ital 1999} {ital The American Physical Society}« less

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Field-Dependent Antiferromagnetism and Ferromagnetism of the Two Copper Sublattices in Sr 2 Cu 3 O 4 Cl 2

Results are presented of a detailed study of optical transitions from the excited states of the photoluminescence (PL) centres in c-As2Se3, including the first observation of photo-induced optical absorption (PA) arising from these states. It is inferred from observations of the decay rates and polarization dependences of the PL and PA that the lowest excited state of the PL centre is a triplet exciton state, and that the singlet-triplet splitting is 4 × 10−3 eV. The PA in the spectral range measured (0·4–2 eV) appears to probe transitions from the excttcd PL centres to states in the continuum. Also observed for the first time is PA from the excited states of the PL centres in a-As2Se3. The properties of the PL centres in a-As2Se3 and c-As2Se3 are compared.

Recombination and excited-state absorption at photoluminescence centres in crystalline and amorphous arsenic triselenide

We measure the relaxation rate $W \equiv T_{1}^{-1}$ of a single electron spin in a quantum dot at magnetic fields from 7 T down to 1.75 T, much lower than previously measured. At 1.75 T we find that $T_{1}$ is 170 ms. We find good agreement between our measurements and theoretical predictions of the relaxation rate caused by the spin-orbit interaction, demonstrating that spin-orbit coupling can account for spin relaxation in quantum dots.

https://arxiv.org/pdf/cond-mat/0607110.pdf

Measurements of the spin relaxation rate at low magnetic fields in a quantum dot

Neutron scattering experiments have been performed to study the dynamic spin properties of La 1.98 Sr 0.02 CuO 4 , a crystal with just enough Sr to destroy three-dimensional long range magnetic order and induce spin-glass behavior at low temperatures. The q -integrated susceptibility $\int \,{\rm d}^{2}q_{\rm 2D}\,{\rm Im}\,\chi _{\rm 2D}(q_{\rm 2D},\,\omega )$ follows the scaling function of ω/ T suggested by Keimer et al. Below 3 meV, however, clear deviation from the scaling function is observed at low temperatures. This probably originates from a gap in the spin-wave-like excitations due to the out-of-plane anisotropy.

Dynamic Spin Properties of La1.98Sr0.02CuO4

Photoluminescence (PL) originating from intrinsic defects in neutron-irradiated crystalline (x-)SiO2 is observed and compared with that from amorphous (a-)SiO2. The PL and photoluminescence excitation (PLE) spectra of x-SiO2 are qualitatively similar to those of a-SiO2. This suggests that PL centers, similar to those found in amorphous systems, are present in ordered systems. In addition, the PL and PLE spectra of a-SiO2 and a-As2S3 scale with energy band gap, suggesting that the radiative processes in a-SiO2 and semiconducting chalcogenide glasses are alike. The similarity of the PL from x-SiO2 to that from a-SiO2 and the scaling of the PL from a-SiO2 and a-As2S3 with energy band gap strongly suggest that PL centers are unique bonding configurations which primarily depend on the chemistry of the system rather than on the degree of long range order.

Marc Kastner

Papers

Field-Dependent Antiferromagnetism and Ferromagnetism of the Two Copper Sublattices in Sr 2 Cu 3 O 4 Cl 2

Recombination and excited-state absorption at photoluminescence centres in crystalline and amorphous arsenic triselenide

Measurements of the spin relaxation rate at low magnetic fields in a quantum dot

Dynamic Spin Properties of La1.98Sr0.02CuO4

Intrinsic-defect photoluminescence in amorphous and crystalline SiO2