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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Chalcogen vacancy
A spot in a TMDC crystal where a sulfur, selenium or tellurium atom is missing. It is the most commonly reported flaw in these materials, and it is easily confused with an oxygen atom sitting in its place.
A missing S, Se or Te atom – the most commonly reported point defect in TMDCs, often confused with substitutional oxygen.
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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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Chemical vapour deposition (CVD)
A way of growing thin films from gases. The ingredients arrive as vapour, react on a hot surface and leave a solid layer behind. It is how large sheets of graphene and other 2D materials are made for industry.
Growth of films from gas-phase precursors that react or decompose on a heated substrate. For 2D materials this includes graphene on copper foil, powder-source CVD of TMDCs from metal oxides and chalcogens, and metal-organic CVD (MOCVD) for wafer-scale TMDC films; grain size, nucleation density and residues are the usual quality limits.
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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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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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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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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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Photoluminescence (PL)
Light given off by a material after it has absorbed light – what a highlighter pen does under a black light. In 2D semiconductors the colour and brightness of that glow report how many layers there are, how clean the sample is and whether it is carrying extra charge.
Radiative recombination following optical excitation. In monolayer TMDCs the spectrum is dominated by excitons and trions rather than free carriers, so peak energy, linewidth and quantum yield track layer number, strain, dielectric environment, doping and defect density. The indirect-to-direct crossover makes the monolayer far brighter than the bilayer, and chemical treatment of defects can bring the yield close to unity.
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Hysteresis
When a device gives different readings depending on whether a voltage is swept up or down, because charges are trapped and released along the way. It is a sign of an unclean or unstable device.
Different transfer curves for forward and reverse gate sweeps, caused by charge trapping in adsorbates, dielectrics or defects.
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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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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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Photocatalysis and electrocatalysis
Using light, or an applied voltage, to drive a chemical reaction at a surface – most often splitting water to make hydrogen. Thin materials are natural candidates because nearly every atom is a surface atom, and because their edges are usually far more active than their flat faces.
Surface reactions driven by photons (photocatalysis) or by electrode potential (electrocatalysis), judged by overpotential, Tafel slope and turnover per site rather than by raw current. In MoS2 the basal plane is close to inert while the edge sites carry the hydrogen-evolution activity – the result that made layered chalcogenides catalyst candidates – so activity scales with edge length, defect density and phase, and any comparison needs an active-site count rather than a geometric area.
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Memristor and neuromorphic computing
A memristor is a device whose resistance remembers the voltage it has seen, so the same spot both stores a number and multiplies by it. Chips built from arrays of them work more like a brain than like a processor with memory bolted on the side – which is what neuromorphic means.
Non-volatile resistive switching used as memory and as an analogue synaptic weight, so that a crossbar performs multiply–accumulate where the data already sits. Two-dimensional materials contribute switching layers under a nanometre thick – vacancy or metal-atom migration in a monolayer TMDC gives non-volatile switching – along with gate-tunable synaptic transistors and back-end-compatible integration above logic.
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Transmission electron microscopy (TEM)
Electrons are fired through a sample thin enough to be transparent to them, forming an image that can show individual atoms and which element each one is. A 2D crystal is the ideal specimen, because it is already thin enough.
Imaging with transmitted electrons, either parallel-beam (TEM) or scanned-probe (STEM), where annular dark-field contrast scales roughly with Z2 and identifies single atoms chemically. It resolves point defects, grain boundaries, stacking and moiré patterns directly, at the cost of knock-on damage – which is why 2D samples are imaged at 60–80 kV – and of a clean, suspended specimen.
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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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Atomic force microscopy (AFM)
A tip on a tiny springy arm is moved across a surface and its bending is measured, mapping height point by point – much as a fingertip reads Braille. It works on anything, conducting or not, which is why it is the routine way to check how thick a flake is.
Force microscopy in contact, tapping or non-contact mode, used for thickness, roughness, bubbles and polymer residue, with variants for surface potential (KPFM) and local conductivity (c-AFM). Apparent height is not the crystallographic thickness: the tip interacts differently with flake and substrate, so a monolayer commonly reads between 0.4 and 1 nm. Quote the mode, and calibrate against a step of known height.
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Raman spectroscopy
Shining a laser on a material and measuring the tiny fraction of light that comes back at slightly different colours. The shifts reveal how the atoms vibrate, which tells researchers how many layers a flake has and whether it is strained or damaged.
Inelastic light scattering that measures phonon energies. In 2D materials peak positions, widths and intensity ratios – graphene’s G and 2D bands, or the E′ and A′1 modes of TMDCs – report layer number, strain, doping and defect density; laser heating and substrate interference must be controlled.
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G and 2D bands
The two main peaks in the Raman spectrum of graphene. Their shape, position and relative height reveal how many layers there are and whether the graphene is stretched or electrically doped.
Graphene’s first-order in-plane Raman mode and its second-order double-resonant overtone, which together report layer number, strain and doping.
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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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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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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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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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