Point defect
A flaw in a crystal that involves a single atomic site: an atom missing (a vacancy), an atom of the wrong kind in a site (a substitution, or an antisite when the crystal’s own two kinds of atom swap places), or an extra atom squeezed in between (an interstitial). Every real crystal has some. In a sheet a few atoms thick each one sits at the surface, so a handful of them can change how the material conducts, glows or reacts far more than in a thick crystal.
A defect confined to one or a few lattice sites – vacancy, interstitial, substitutional impurity, antisite or adatom – or a small complex of them. What it does is set by the levels it introduces: shallow levels dope, deep levels trap carriers and act as non-radiative recombination centres, and an isolated deep level in a wide gap can emit single photons. Formation energies and charge states depend on the chemical conditions of growth and on the Fermi level. In 2D materials every defect is a surface defect, less screened and more exposed to the environment, and densities of 1012 to 1013 per cm2 are typical of TMDC monolayers.
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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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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.
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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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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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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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Fermi-level pinning
When the junction between a metal and a semiconductor behaves the same whichever metal is used. The choice of metal ought to set the height of the energy step electrons must climb to get into the semiconductor, but stray electron states at the interface take up charge and hold the step at much the same height every time. It makes low-resistance contacts hard to engineer.
The fixing of the Fermi level at a metal–semiconductor interface by interface states, so the Schottky barrier barely depends on the metal work function.
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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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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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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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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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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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Quasiparticle
An electron moving through a crystal is never alone: it pushes and pulls on all the other electrons and atoms around it, and drags a little cloud of disturbance along. Physicists treat the electron together with its cloud as a new particle – a quasiparticle – with its own mass and lifetime. The idea goes further: holes, excitons, vibrations of the lattice and waves of spins also behave like particles, and describing a solid as a gas of such quasiparticles is how most of its properties are understood.
An elementary excitation of an interacting many-body system that behaves like a particle with a defined energy–momentum relation, charge or spin, and a finite lifetime, as in Landau’s Fermi-liquid theory. Dressed electrons and holes (renormalised by screening, phonons or correlations, with effective masses that can reach hundreds of free-electron masses in heavy-fermion systems), excitons, trions and polarons, and bosonic collective modes such as phonons, magnons, plasmons and polaritons are all quasiparticles. Their energies are poles of the Green’s function; the GW approximation computes quasiparticle band structures, which in 2D semiconductors are strongly renormalised by the reduced screening, so that the quasiparticle gap exceeds the optical gap by the large exciton binding energy.
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Effective mass
How heavy an electron seems as it moves through a crystal. Pushed by an electric field, it speeds up as if its mass were different from a free electron’s – lighter in some materials, heavier in others, and in graphene as if it had no mass at all. Light carriers generally make for faster devices.
The mass m* with which a carrier near a band edge responds to forces as if it were free, set by the band curvature: 1/m* = (1/ħ2 ) d2 E/dk2 . It enters the mobility (μ = eτ/m*), the density of states, confinement energies and tunnelling rates, and in anisotropic crystals it is a tensor – in black phosphorus the armchair and zigzag masses differ several-fold. Graphene’s linear bands have no curvature, and its carriers are described as massless Dirac fermions; their cyclotron mass, the Fermi energy divided by the square of the Fermi velocity, grows with the square root of the carrier density.
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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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Fermi level
Roughly, the energy up to which a material’s electron states are filled – like the water line in a partly filled glass. Where it sits relative to the band gap decides how many charges can move and whether they are electrons or holes, the empty places electrons leave behind. A gate voltage raises and lowers it, like pouring water in or out.
The electrochemical potential of electrons: the energy at which a state has 50 % occupation in thermal equilibrium. Its position relative to the band edges sets carrier density and type; at metal–semiconductor contacts, interface states can pin it and fix the Schottky barrier.
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