Ballistic pomt contacts, defined in the two-dimensional electron gas of a GaAs-AlGaAs heterostructure, have been studied in zero magnetic field The conductance changes in quantized Steps of e 2 /nh when the width, controlled by a gate on top of the heterojunction, is vaned Up to sixteen Steps are observed when the pomt contact is widened from 0 to 360 nm An explanation is proposed, which assumes quantized transverse momentum in the pomt-contact region As a result of the high mobihty attamable in the twodimensional electron gas (2DEG) in GaAs-AlGaAs heterostructures it is now becoming feasible to study ballistic transport in small devices '" 6 In metals ideal tools for such studies are constnctions havng a width W and length L much smaller than the mean free path l e These are known äs Sharvin pomt contacts 7 Because of the ballistic transport through these constnctions, the resistance is determmed by the pomt-contact geometry only Point contacts have been used extensively for the study of elastic and melastic electron scattermg With use of biased pomt contacts, electrons can be mjected mto metals at energies above the Fermi level This allows the study of the energy dependence of the scattermg mechamsms 8 With the use of a geometry containmg two pomt contacts, with Separation smaller than l e , electrons mjected by a pomt contact can be focused mto the other contact, by the application of a magnetic field This technique (transverse electron focusmg) has been applied to the detailed study of Fermi surfaces 9 In this Letter we report the first expenmental study of the resistance of ballistic pomt contacts m the 2DEG of high-mobihty GaAs-AlGaAs heterostructures The smgle-pomt contacts discussed m this paper are part of a double-pomt-contact device The results of transverse electron focusmg m these devices will be published elsewhere '° The pomt contacts are dehned by electrostatic depletion of the 2DEG underneath a gate This method, which has been used by several authors for the study of l D conduction,' 1 offers the possibility to control the width of the pomt contact by the gate voltage Control of the width is not feasible in metal pomt contacts The classical expression for the conductance of a pomt contact m two dimensions (see below) is G=(e 2 /nh)k Y W/n(1) in which kf is the Fermi wave vector and W is the width of the contact This expression is vahd if l e » W and the Fermi wavelength λρ<ίί W The first condition is satisfied in our devices, which have a maximum width W mm «= 250 nm and l e =8 5 μηι The second condition should also hold when the devices have the maximum width We expect quantum effects to become important when the width becomes comparable to λρ, which is 42 nm m our devices In this way we are able to study the transition from classical to quantum ballistic transport through the pomt contactThe pomt contacts are made on high-mobility molecular-beam-epitaxy-grown GaAs-AlGaAs heterostructures The electron density of the matenal is 3 56xl0 15 /m 2 and the mobihty 85 m 2 /V s (at 0 6 K) These values ...

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Transverse electron focusing in a two-dimensional electron gas is mvestigated expenmentally and theoretically for the flrst time. A split Schottky gate on top of a GaAs-Al x Ga,_^As heterostructure defines two point contacts of variable width, which are used äs mjector and collector of ballistic electrons As evidenced by their quantized conductance, these are quantum point contacts with a width comparable to the Fermi wavelength At low magnetic flelds, skipping orbits at the electrongas boundary are directly observed, thereby establishing that boundary scattenng is highly specular Large additional oscillatory structure in the focusing spectra is observed at low temperatures and for small pomt-contact size This new phenomenon is mterpreted in terms of mterference of coherently excited magnetic edge states m a two-dimensional electron gas A theory for this effect is given, and the relation with nonlocal resistance measurements in quantum ballistic transport is discussed It is pomted out, and expenmentally demonstrated, that four-termmal transport measurements m the electron-focusmg geometry constitute a determmation of either a generalized longitudmal resistance or a Hall resistance At high magnetic fields the electron-focusmg peaks are suppressed, and a transition is observed to the quantum Hall regime The anomalous quantum Hall effect m this geometry is discussed m light of a four-termmal resistance formula

The group III nitrides (AlN, GaN and InN) represent an important trio of semiconductors because of their direct band gaps which span the range 1.95-6.2 eV, including the whole of the visible region and extending well out into the ultraviolet (UV) range. They form a complete series of ternary alloys which, in principle, makes available any band gap within this range and the fact that they also generate efficient luminescence has been the main driving force for their recent technological development. High brightness visible light-emitting diodes (LEDs) are now commercially available, a development which has transformed the market for LED-based full colour displays and which has opened the way to many other applications, such as in traffic lights and efficient low voltage, flat panel white light sources. Continuously operating UV laser diodes have also been demonstrated in the laboratory, exciting tremendous interest for high-density optical storage systems, UV lithography and projection displays. In a remarkably short space of time, the nitrides have therefore caught up with and, in some ways, surpassed the wide band gap II-VI compounds (ZnCdSSe) as materials for short wavelength optoelectronic devices. The purpose of this paper is to review these developments and to provide essential background material in the form of the structural, electronic and optical properties of the nitrides, relevant to these applications. We have been guided by the fact that the devices so far available are based on the binary compound GaN (which is relatively well developed at the present time), together with the ternary alloys AlGaN and InGaN, containing modest amounts of Al or In. We therefore concentrate, to a considerable extent, on the properties of GaN, then introduce those of the alloys as appropriate, emphasizing their use in the formation of the heterostructures employed in devices. The nitrides crystallize preferentially in the hexagonal wurtzite structure and devices have so far been based on this material so the majority of our paper is concerned with it, however, the cubic, zinc blende form is known for all three compounds, and cubic GaN has been the subject of sufficient work to merit a brief account in its own right. There is significant interest based on possible technological advantages, such as easier doping, easier cleaving (for laser facets) and easier contacting.

We show that by annealing Ga 1-x Mn x As thin films at temperatures significantly lower than in previous studies, and monitoring the resistivity during growth, an unprecedented high Curie temperature T C and conductivity can be obtained. T C is unambiguously determined to be 118 K for Mn concentration x=0.05, 140 K for x=0.06, and 120 K for x=0.08. We also identify a clear correlation between T C and the room temperature conductivity. The results indicate that Curie temperatures significantly in excess of the current values are achievable with improvements in growth and post-growth annealing conditions.

Hexagonal boron nitride is a large band-gap insulating material which complements the electronic and optical properties of graphene and the transition metal dichalcogenides. However, the intrinsic optical properties of monolayer boron nitride remain largely unexplored. In particular, the theoretically expected crossover to a direct-gap in the limit of the single monolayer is presently not confirmed experimentally. Here, in contrast to the technique of exfoliating few-layer 2D hexagonal boron nitride, we exploit the scalable approach of high-temperature molecular beam epitaxy to grow high-quality monolayer boron nitride on graphite substrates. We combine deep-ultraviolet photoluminescence and reflectance spectroscopy with atomic force microscopy to reveal the presence of a direct gap of energy 6.1 eV in the single atomic layers, thus confirming a crossover to direct gap in the monolayer limit.

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