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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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 – 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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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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Interlayer exciton
An electron in one layer bound to a hole in the layer next door. Because the two sit in different sheets, the pair lives far longer than an ordinary exciton and can be pushed around with an electric field.
An exciton whose electron and hole sit in adjacent layers of a type-II heterostructure. The spatial separation gives lifetimes orders of magnitude longer than intralayer excitons and a permanent out-of-plane dipole that makes the energy gate-tunable; in a twisted bilayer the moiré potential traps them on a regular grid, turning a heterobilayer into an array of nearly identical emitters.
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Photodetector
A device that turns light into an electrical signal. A single layer absorbs only a few percent of the light that hits it, but it responds quickly, can be tuned by a gate voltage and can be placed on surfaces an ordinary detector cannot reach, such as a flexible sheet or an optical chip.
A device converting incident photons into current or voltage. A 2D channel trades absorption per pass for gate tunability, short transit times and transfer onto arbitrary substrates or waveguides; the response may be photoconductive with gain, photovoltaic at a junction, or bolometric. Responsivity alone says little – it is only comparable alongside the mechanism, the bandwidth and the illuminated area.
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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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Epitaxy
Growing a crystal on top of another so that its atoms line up with the ones underneath and carry on the pattern of the crystal below. It is how most semiconductor chips, lasers and LEDs are built, and it works cleanly only when the two crystals’ atomic spacings match closely – a restriction that layered 2D materials largely escape.
Growth of a crystalline film whose orientation is fixed by a single-crystal substrate: homoepitaxy on the same material, heteroepitaxy on a different one. A covalently bonded film strains to the substrate’s lattice until, beyond a critical thickness that falls steeply with mismatch, misfit dislocations relax it, so mismatches above a few percent permit only very thin coherent films. In van der Waals epitaxy the film is aligned but not bonded and mismatch is largely irrelevant; in remote epitaxy the substrate’s potential aligns the film through a graphene interlayer.
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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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Chemical bond
The glue that holds atoms together. In a covalent bond two atoms share electrons, as within a sheet of graphene; in an ionic bond one atom hands electrons to another and the resulting charges attract, as in table salt; in a metal the outer electrons are shared by all the atoms at once. Much weaker van der Waals forces hold molecules and the layers of a layered crystal together. A 2D material is a crystal with strong bonds within its layers and only weak ones between them – which is why it can be peeled.
The attractive interactions that hold atoms in molecules and solids, classified by how electrons are shared: covalent bonds, from overlapping orbitals holding shared electron pairs, strong and directional (sp2 carbon, Mo–S in TMDCs); ionic bonds, from electron transfer and electrostatic attraction (halides, oxides); metallic bonding, with electrons delocalised in a partly filled band; and the weak, non-directional van der Waals interaction from correlated charge fluctuations, besides hydrogen bonds. Real bonds are mixtures, characterised by electronegativity differences and charge analyses. Layered crystals combine in-plane bonds of several electronvolts with interlayer binding of only about 20 meV per Å2 (some 0.3 J/m2 ), the criterion high-throughput screens use to identify exfoliable compounds.
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Strain
Stretching or squeezing a material. Because 2D materials can be stretched much further than ordinary crystals before breaking, strain can be used as a knob to change their colour, conductivity or band gap.
Relative deformation of a lattice. 2D crystals sustain elastic strains of several percent, with graphene exceeding 10 % in nanoindentation, and strain shifts band edges, Raman modes and exciton energies. Unintended strain from substrates, bubbles and transfer is a common confounder in measurements.
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Van der Waals force
A weak attraction between neighbouring atoms and molecules – strong enough, added up over millions of tiny hairs, to let a gecko walk up a pane of glass. In layered crystals it is what holds the layers together, and it is weak enough that a single layer can be peeled off, which is how many 2D materials are made from ordinary crystals.
The weak, non-directional attraction arising from correlated charge fluctuations (dispersion) and related dipolar terms. In layered crystals it binds adjacent layers with energies of tens of meV per atom, roughly two orders of magnitude below in-plane covalent bonds, which enables exfoliation and the free stacking of dissimilar layers.
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Charge transfer
Electrons moving from one material to its neighbour simply because they are more comfortable there. It is how a layer gets doped without adding a single impurity atom to it – the charge comes from the molecule, substrate or layer next door.
Equilibration of electrochemical potential across an interface, moving electrons to whichever side has the deeper states and leaving a dipole and band bending behind. It dopes 2D layers without substitutional disorder, from adsorbed molecules and substrate surface states to the partner layer in a type-II stack, where photoexcited carriers separate in tens of femtoseconds – faster than they recombine, which is what makes such stacks useful for light harvesting and detection.
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Dielectric
An electrical insulator used for what it does in an electric field rather than for carrying current – the thin layer inside a capacitor, or the insulator that separates a transistor’s gate from its channel. A good dielectric blocks current completely, withstands a strong field without breaking down and, for gates, has a high permittivity, so that a voltage on the gate pulls many charges into the channel. For 2D transistors the dielectric is as hard to get right as the 2D layer itself.
An insulator characterised by its permittivity κ, band gap and band offsets to the channel, breakdown field, leakage, and density of fixed charge and traps at the interface and in the bulk (border traps). Silicon technology moved from SiO2 (κ ≈ 3.9) to hafnium-based high-κ oxides (κ ≈ 20–25) to keep gate control at sub-nanometre equivalent oxide thickness. For 2D channels, hBN gives clean, trap-poor interfaces but a low κ of about 3–4 and is hard to grow at wafer scale; ALD oxides nucleate poorly on basal planes; alternatives include crystalline CaF2 , native oxides such as Bi2 SeO5 on Bi2 O2 Se, and molecular crystals. Reliability – hysteresis, bias-temperature instability and time-dependent breakdown – is the yardstick for any dielectric meant for products.
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Magic angle
Stack two sheets of graphene and turn one very slightly. At about 1.1 degrees the pattern they make together slows the electrons almost to a standstill, so they start acting collectively – and the pair can even become a superconductor.
The twist angle (about 1.1° for bilayer graphene) at which interlayer tunnelling makes the lowest moiré bands nearly flat.
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Angle-resolved photoemission spectroscopy (ARPES)
A measurement that shines light on a crystal, catches the electrons it knocks out and records the direction and energy of each one. From that it reconstructs how the electrons were moving inside – the closest thing there is to a photograph of a material’s electronic structure.
Photoemission with energy and momentum resolution, giving the occupied band structure, Fermi surface and self-energy directly. It needs a clean, flat, conducting surface in ultrahigh vacuum; focused micro- and nano-ARPES beamlines bring the spot down to the size of an exfoliated flake, which is what makes single-domain twisted and few-layer samples measurable at all.
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Scanning tunnelling microscopy (STM)
A needle sharpened to a single atom is brought so close to a surface that electrons tunnel across the gap – a quantum effect by which they pass through a barrier they could never climb over. The current maps the surface atom by atom, and how it changes with voltage tells you which energies electrons are allowed to have at that exact spot.
Tunnelling between a sharp tip and a conducting surface, giving atomic-resolution topography and, in spectroscopy mode, the local density of states against energy. On 2D materials it resolves defect levels, moiré potentials, edge modes and quasiparticle gaps site by site. The sample has to be clean and conducting, so it is run on epitaxial films or on flakes placed on graphite, in vacuum and often at cryogenic temperature.
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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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Substrate
The base a thin film or flake sits on – often a polished slice of silicon, glass or sapphire. For a crystal one atom thick, the substrate is not just a table: its bumps, stray charges and vibrations reach right into the sheet and change how it conducts and glows. That is why the same material can behave differently on two substrates, and why the flattest, cleanest one – boron nitride – gives the best results.
The material beneath a 2D layer. It acts on the layer through surface roughness, charged impurities, surface optical phonons, dielectric screening, strain and charge transfer, and during growth it sets orientation through epitaxy. Replacing SiO2 with hexagonal boron nitride, which is atomically flat and nearly free of dangling bonds and charge traps, improved the mobility and charge homogeneity of graphene by close to an order of magnitude.
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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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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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Dielectric screening
The way a material weakens the pull between two charges inside it: its own electrons shift slightly and partly cancel the field between them. A sheet one atom thick has almost nothing around it to do this, so charges in it attract each other far more strongly than in a thick crystal – which is why light makes tightly bound pairs in 2D materials, and why whatever a sheet rests on changes its properties.
The reduction of the Coulomb interaction by the polarisation of bound electrons and ions and, in metals and doped layers, by free carriers, described by a dielectric function ε(q, ω). In a monolayer the field lines between distant charges run through the surroundings, so ε(q) approaches 1 as q → 0 and the screening is non-local and set by the environment. Exciton binding energies reach hundreds of meV, and a change of substrate or encapsulation shifts the quasiparticle gap by 100 meV or more while the optical gap barely moves.
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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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