Photon
The smallest possible amount of light – one indivisible packet of it. The packets of a given colour all carry the same energy, and blue ones carry more than red: that is why ultraviolet light gives you sunburn and red light, however bright, does not. A semiconductor absorbs only photons with enough energy to cross its band gap and gives light back at about the gap’s energy – which is why LEDs of different colours are made from different semiconductors.
The quantum of the electromagnetic field, with energy E = hν and momentum h/λ but no mass or charge. Visible photons carry about 1.7–3.1 eV, comparable to the band gaps of semiconducting TMDCs, but a momentum far smaller than the crystal momenta across the Brillouin zone, so optical transitions are vertical and an indirect gap needs a phonon to make up the difference. Single-photon emission is established by antibunching in photon-correlation measurements.
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Two-dimensional (2D) material
A crystal so thin that it is only one or a few atoms thick – a sheet rather than a lump. Graphene, a single layer of carbon atoms, is the best-known example: about 300,000 of its layers stacked up would be as thick as one sheet of paper. At that thickness a material can conduct, glow or respond to magnetism quite differently from the same substance in bulk.
A crystalline material whose thickness is one or a few unit cells, so that electrons, phonons and other excitations are confined in one direction. Most are obtained from layered bulk crystals in which strong in-plane bonds coexist with weak van der Waals bonding between layers.
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Field-effect transistor (FET)
The electronic switch at the heart of every chip. It works like a tap: a voltage on one terminal, the gate, opens or closes a channel through which current flows. Researchers test new 2D materials by making them into the channel of such a switch.
A three-terminal device in which a gate voltage modulates the carrier density of a semiconductor channel between source and drain through a thin dielectric. For 2D channels the key figures of merit are on/off ratio, subthreshold swing, mobility, contact resistance, hysteresis and threshold-voltage variability. A channel that conducts electrons at one gate polarity and holes at the other is ambipolar, as WSe2 often is, and whether a 2D transistor behaves as n-type, p-type or ambipolar depends as much on its contacts as on the channel.
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Silicon photonics
Guiding light instead of electricity through tiny channels on a silicon chip, made with the same factories and tools as ordinary computer chips. Light carries data faster and with less loss over distance, so such chips already connect the servers in data centres. Silicon itself is poor at a few jobs: it hardly emits light, cannot detect the infrared light used in fibre networks, and switches light only weakly. 2D materials laid on top of the light channels are one way to add the missing functions.
Photonic integrated circuits in silicon-on-insulator, in which submicron silicon waveguides, with their high index contrast to the buried oxide, route light at telecom wavelengths through splitters, rings and gratings made with CMOS tools; germanium detectors and silicon carrier-depletion modulators are standard, and lasers are bonded or grown from III–V semiconductors. 2D materials couple to the evanescent field of the waveguide: graphene gives broadband, fast modulators and photodetectors that can be integrated at wafer scale, thin MoTe2 and black phosphorus emit and detect in the near infrared, and low-loss phase-change Sb2 S3 and Sb2 Se3 give non-volatile switches and tuning. The obstacles are wafer-scale transfer or growth, contacts, optical loss and reproducibility to foundry standards.
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Band gap
The energy an electron needs to jump from a full band, where it is stuck, into an empty one where it can move and carry current. It is like a car in a packed car park, which can only drive off once it is lifted to the empty deck above. Metals have no gap and always conduct; insulators have a large gap and hardly conduct; semiconductors sit in between, which is what makes them switchable.
The energy range between the valence-band maximum and the conduction-band minimum in which a crystal has no electronic states. It is direct when both extrema lie at the same crystal momentum and indirect otherwise; monolayer MoS2 is direct while bulk MoS2 is indirect. In 2D the quasiparticle and optical gaps differ strongly because excitons are tightly bound.
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Pump–probe spectroscopy
A way to film events that last a millionth of a millionth of a second. A first, strong flash of laser light – the pump – disturbs the sample; a second, weaker flash – the probe – arrives a precisely set moment later and measures how the sample looks then. Repeating this with the delay changed step by step builds up a slow-motion film of how the electrons and atoms settle back. The delay is set by sending one flash along a longer path: a tenth of a millimetre more makes it a third of a picosecond later.
A stroboscopic measurement in which an ultrashort pump pulse excites the sample and a delayed probe pulse records the change, as a function of a delay set by an optical delay line, with a time resolution limited by the pulse durations – tens of femtoseconds routinely, a few with dedicated sources. The probe can be optical reflectivity or transmission, terahertz conductivity, photoemission (time-resolved ARPES), or X-ray or electron diffraction, giving access to carrier thermalisation and cooling, exciton formation, interlayer charge transfer, coherent phonons, and the melting, recovery or switching of ordered phases such as charge density waves and excitonic insulators. Its power lies in separating processes by timescale: electrons respond within femtoseconds, the lattice within picoseconds.
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Semiconductor
A material whose ability to carry electricity can be switched on and off, for example by an applied voltage. That switching is what every transistor in a computer chip relies on. Silicon is the classic example; several 2D materials, such as MoS2 , are semiconductors too.
A material with a band gap of a few electronvolts or less, whose conductivity can be tuned over many orders of magnitude by doping, gating, temperature or light. 2D semiconductors attract interest because their sub-nanometre thickness preserves electrostatic gate control in very short channels.
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Charge carrier mobility
How easily electrons, or the gaps they leave behind (holes), move through a material when pushed by a voltage. Higher mobility means faster, more efficient electronics – but it is easily ruined by dirt, defects and a poor substrate.
Drift velocity per unit electric field, usually quoted in cm2 /V·s. In 2D materials it is limited intrinsically by phonon scattering and extrinsically by charged impurities, roughness, remote phonons and disorder; field-effect values extracted from two-terminal devices can be distorted by contact resistance.
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Hall effect
Send a current along a strip in a magnetic field and the moving charges are pushed towards one edge, so a small voltage appears across the strip. Its size tells how many charge carriers there are, and its sign whether they are electrons or holes, which makes it the standard way to count them. In a magnetic material a sideways voltage appears even without an outside field – the anomalous Hall effect, a handy way to see whether a tiny flake is magnetic.
The transverse voltage that the Lorentz force produces when a current flows in a perpendicular magnetic field. For one type of carrier in a 2D sheet the Hall resistance is B/ne, independent of thickness, so its slope gives the sheet density n and its sign the carrier type; combined with the sheet resistance it gives the Hall mobility. Two carrier types make the Hall resistance non-linear in B and call for a two-band fit. In magnetic conductors an extra term that follows the magnetisation – the anomalous Hall effect – comes from the Berry curvature of the bands (intrinsic) or from skew and side-jump scattering (extrinsic); quantised, it becomes the quantum anomalous Hall effect.
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Wafer and wafer-scale growth
A wafer is the thin, round slice of ultra-pure silicon – today 300 millimetres across – on which computer chips are made, hundreds at a time. Wafer-scale growth means making a 2D material evenly over a whole wafer rather than as scattered flakes, which is what any factory needs. For the best 2D materials that is still hard: a sheet one atom thick has to have the same thickness, quality and orientation from one edge of a dinner-plate-sized disc to the other.
The substrate format of the semiconductor industry – 200 and 300 mm silicon wafers, with sapphire, SiC and glass for particular processes – and the scale at which a material must be grown, transferred and processed to enter manufacturing. Wafer-scale growth of 2D materials uses CVD and MOCVD of TMDCs, CVD of graphene and hBN, and MBE, with targets of uniform layer number, low defect and grain-boundary density and, increasingly, a single orientation on vicinal sapphire or Cu(111). The obstacles are the growth temperature against the thermal budget of a finished wafer (growth on the back end of line needs to stay below about 400 to 450 °C), the transfer from growth substrate to device wafer, and metrology that confirms thickness and quality across the wafer at production speed.
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Exciton
An electron paired with the ‘hole’ it left behind – the empty place, which acts like a positive charge. The two attract each other and form something like a tiny atom. In very thin materials these pairs hold together unusually strongly, so they dominate how the material absorbs and emits light – even at room temperature.
A bound state of a conduction-band electron and a valence-band hole. In 2D semiconductors reduced dielectric screening raises binding energies to hundreds of meV in freestanding TMDC monolayers, so excitons dominate optical spectra at room temperature and follow a non-hydrogenic Rydberg series.
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Gating
Changing a material by putting a voltage on a nearby electrode – a gate – separated from it by an insulator. The voltage pulls electrons into the material or pushes them out, as in every transistor. Because a 2D material is so thin, the gate reaches all of it, so the number of electrons can be dialled up and down continuously. A single device can be turned from insulator to metal, its magnetism strengthened, or superconductivity switched on. Two gates, above and below, can also apply an electric field across the layer.
Electrostatic control of carrier density and electric field through a gate coupled capacitively across a dielectric: the induced density equals the gate capacitance times the voltage beyond threshold, divided by the electron charge, reaching a few 1013 cm−2 with oxide or hBN gates before breakdown. Dual gating sets density and perpendicular displacement field independently, opening the gap of bilayer graphene and tuning moiré flat bands. Ionic-liquid and solid-electrolyte gating form an electric double layer about a nanometre thick and reach 1014 –1015 cm−2 , enough to induce superconductivity in MoS2 or raise the Curie temperature of Fe3 GeTe2 , but can intercalate or react electrochemically and work only while the ions are mobile. Hysteresis from traps, contact effects and quantum capacitance are the usual caveats.
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Polariton
A wave that is part light and part motion in a material – electrons or atoms swinging back and forth – travelling as one. In thin crystals such waves can be squeezed to wavelengths many times shorter than the light that made them, so they can guide and focus infrared light into spaces far smaller than light normally allows.
A hybrid mode of photons with a polarisation excitation: free-carrier plasma oscillations (plasmon polaritons), optical phonons (phonon polaritons) or excitons (exciton polaritons). In van der Waals crystals they confine light to wavelengths tens to hundreds of times below that in free space. hBN supports hyperbolic phonon polaritons in its two Reststrahlen bands, α-MoO3 in-plane anisotropic ones and graphene gate-tunable plasmons; TMDC monolayers in optical cavities form exciton polaritons. They are imaged in real space by scattering-type near-field microscopy (s-SNOM), which launches them from a sharp tip and maps their interference fringes.
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Spintronics
Electronics that uses the magnetic direction of an electron – its spin – as well as its charge. Writing information as a spin direction rather than as a pocket of charge can store it without power and switch it with less energy.
Device physics built on injecting, transporting, manipulating and detecting electron spin. Two-dimensional materials contribute long spin lifetimes and gate-tunable transport in graphene, spin–orbit coupling and exchange induced by proximity to an adjacent layer, spin–valley locking in TMDC monolayers, and van der Waals magnets that serve as tunnel barriers and free layers in an all-2D stack.
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Spin
A built-in property of every electron that makes it a tiny magnet. Measure it along any direction and you only ever find one of two answers, ‘up’ or ‘down’. Despite the name, nothing is actually spinning – the word stuck from an early picture – but the magnetism is real: countless electron spins lined up are what make a fridge magnet stick. Spintronics tries to carry information in spin rather than in charge.
The intrinsic angular momentum of the electron, ħ/2, with a magnetic moment of almost exactly one Bohr magneton; a measurement along any axis yields one of two values. In solids spin couples to orbital motion through spin–orbit coupling and to other spins through exchange; in 2D materials it sets magnetic order, spin–valley locking and how long a spin survives as a carrier of information.
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Ferromagnet and antiferromagnet
In a ferromagnet the tiny magnets of the atoms all point the same way, as in a fridge magnet. In an antiferromagnet neighbours point in opposite directions and cancel out. Both kinds of order have been found in sheets only one layer thick.
Magnetically ordered states with parallel (ferromagnetic) or antiparallel (antiferromagnetic) alignment of neighbouring moments. Long-range order in 2D requires magnetic anisotropy to evade the Mermin–Wagner theorem; CrI3 monolayers are Ising-like ferromagnets that couple antiferromagnetically between layers, and the MPS3 compounds are antiferromagnets.
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Monolayer
One single layer of a layered material. Two stacked layers are a bilayer; a handful are called few-layer. Many properties change between one, two and several layers, so the exact count matters.
A single structural layer of a layered crystal – one atom thick for graphene and hBN, three atomic planes for a TMDC such as MoS2 . Band structure, screening and symmetry depend on layer number (monolayer 2H-MoS2 lacks the inversion symmetry of the bilayer), so monolayer, bilayer and few-layer samples are distinct systems.
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Doping
Adding a small amount of extra electrons to a material, or taking some away to leave ‘holes’ that act as positive charges, to change how well it conducts. In silicon this is done by mixing in foreign atoms; in 2D materials it can also be done with a nearby voltage, molecules on the surface, or the material underneath.
Control of carrier type and density by substitutional impurities, surface charge transfer, electrostatic gating or the dielectric environment. Stable, spatially localised substitutional doping remains difficult in 2D semiconductors, and surface-transfer doping is often unstable in air.
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Interlayer coupling
How strongly neighbouring sheets in a stack affect one another. The pull holding them together is weak, but electrons can still hop from one sheet to the next and whole sheets can vibrate against each other. That is why one, two and many layers of the same crystal behave differently, and why twisting or sliding one sheet changes the whole stack.
The electronic hybridisation, mechanical force constants and electrostatic interaction between adjacent layers of a van der Waals crystal. Electronically it is hopping between orbitals that reach out of the plane, a few tenths of an electronvolt in graphite, which splits and shifts bands and makes the band structure depend on thickness, stacking and twist. Mechanically it sets the interlayer shear and breathing modes, whose Raman frequencies of a few tens of cm−1 measure it directly. Far weaker than in-plane bonding, it still decides the direct–indirect gap crossover of TMDCs, the flat bands of twisted bilayers and interlayer magnetic order.
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Superconductivity
A state in which a material carries electric current with zero resistance, usually only when very cold. It is what lets the magnets of hospital MRI scanners carry huge currents without heating up. Some 2D materials become superconductors, and in twisted graphene the effect can be switched on and off with a voltage.
A macroscopic quantum state of paired electrons with zero DC resistance and magnetic-flux expulsion below a critical temperature. 2D examples include gate-tunable superconductivity in magic-angle graphene and Ising superconductivity in monolayer NbSe2 and gated MoS2 ; in the 2D limit the transition is of Berezinskii–Kosterlitz–Thouless type.
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Magnon
A ripple of tilted spins – the atoms’ tiny magnets – travelling through a magnet, like a stadium wave in which each spectator only stands up and sits down yet the wave runs all the way round. Because the ripple carries information without moving any electrons, it is one route to lower-power devices.
A quantised spin-wave excitation of a magnetically ordered state. Its dispersion is set by exchange, anisotropy and dipolar terms, and in a 2D magnet the anisotropy gap at zero wavevector is what holds order against thermal fluctuations – so the magnon spectrum measures the same anisotropy that lets the material evade the Mermin–Wagner theorem.
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Photovoltaic effect
Light absorbed in a material frees electrons, and a built-in asymmetry – usually a junction between two different layers – pushes them one way rather than the other, producing a voltage. That is how a solar cell works.
Separation of photogenerated carriers by a built-in field at a p–n junction, a Schottky contact or a type-II van der Waals interface. Monolayers absorb roughly an order of magnitude more sunlight per unit thickness than GaAs or Si, so a stack a few nanometres thick reaches useful power per unit mass even though its absolute absorption stays small; in a gate-tunable heterojunction the alignment, and with it the sign and size of the photoresponse, can be switched electrically.
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Electron hole
Usually just called a hole: the empty place an electron leaves behind in an otherwise full band. It behaves like a particle of its own with a positive charge. When a neighbouring electron steps into the gap, the gap moves the other way – like the empty space in a queue of cars, which travels backwards as each car edges forward. Many materials conduct mainly with holes, and chips need both kinds of carrier.
An unoccupied state in an otherwise filled band, usually near the valence-band maximum, treated as a quasiparticle with positive charge and a positive effective mass set by the band curvature. Holes carry the current in p-type semiconductors and give a positive Hall coefficient. In 2D semiconductors good p-type transport is harder to obtain than n-type, largely because metal contacts pin the Fermi level nearer the conduction band.
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