Monolayer

Also called single layer

Everyday term

In plain words

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.

Going deeper

A monolayer, bilayer and few-layer stack of a MoS₂-type crystal, seen from the side. One “layer” here is three planes of atoms. Going from one layer to two changes the band gap from direct to indirect and restores a centre of inversion – which is why the layer count is part of a sample’s identity rather than a detail.

What counts as one layer

A monolayer is one repeat unit of a layered crystal, the thinnest slice that keeps its chemistry – and that means different things in different families. In graphene or hBN it is a single sheet of atoms. In MoS₂ and the other it is a sandwich of three atomic planes, a metal plane between two planes, about 0.65 nm thick. In Bi₂Se₃ it is a five-plane quintuple layer about 1 nm thick, and in MnBi₂Te₄ a seven-plane septuple layer. “Monolayer” always refers to that repeat unit, never to a single plane of atoms taken out of it.

Why the exact number matters

Properties can change abruptly between one layer and two. MoS₂ is the textbook case: the monolayer has a and glows brightly, while the bilayer has an indirect gap and barely emits. Symmetry changes too. A monolayer has no centre of inversion, so it is and produces strong light; a bilayer stacked in the natural way has one, and both effects vanish. Bilayer graphene, unlike the monolayer, can have a band gap opened by an electric field across it.

Because of this, monolayer, bilayer and few-layer samples are best treated as different materials that share a name, and a measurement without a layer count is hard to interpret.

How layers are counted

The first estimate comes from under a microscope, which changes step by step with thickness on a suitable oxide . It is then confirmed spectroscopically. In MoS₂ the two main peaks move apart as layers are added, from about 19 cm⁻¹ in the monolayer to about 25 cm⁻¹ in the bulk; graphene’s 2D Raman band changes shape with layer number; and brightens sharply for a monolayer of a TMDC. measures height, but the apparent step can differ from the true layer thickness by a few tenths of a nanometre, so it is best used together with the optical methods.

For specialists

A single structural layer of a layered crystal – one atom thick for graphene and hBN, three atomic planes for a TMDC such as MoS₂. , screening and symmetry depend on layer number (monolayer 2H-MoS₂ lacks the of the bilayer), so monolayer, bilayer and few-layer samples are distinct systems.

Where this comes from

Emerging photoluminescence in monolayer MoS₂ Splendiani et al. · Nano Letters 10, 1271 (2010) cited by 9,520
Anomalous lattice vibrations of single- and few-layer MoS₂ Lee et al. · ACS Nano 4, 2695 (2010) cited by 4,882

Chalcogenide, halide and pnictide

Family names for compounds, taken from the element in them that carries the negative charge. Chalcogenides contain sulfur, selenium or tellurium; halides contain fluorine, chlorine, bromine or iodine; pnictides contain phosphorus, arsenic, antimony or bismuth. Most layered crystals belong to one of these families, and the catalogue groups many of them that way.

Compounds named for their most electronegative constituent: chalcogenides of group 16 (S, Se, Te; oxides are conventionally counted apart), halides of group 17 (F, Cl, Br, I) and pnictides of group 15 (P, As, Sb, Bi; nitrides usually keep their own name). Down each group the anion grows larger and less electronegative, so bonding turns more covalent, gaps shrink and spin–orbit coupling grows. Chalcogenides give the MX₂ semiconductors and metals, halides mostly ionic, often magnetic insulators built from edge-sharing octahedra, and pnictides many metals, semimetals and the parents of the iron-based superconductors; mixed-anion compounds such as oxychalcogenides and chalcohalides combine two.

Full explanation

Second-harmonic generation (SHG)

Shine intense light on a crystal and a little of it comes back at exactly twice the frequency – half the wavelength, which is how a green laser pointer turns invisible infrared into green light. It happens only if the crystal has no centre of symmetry, which makes it a quick, contactless test of symmetry, layer number and crystal orientation.

A second-order nonlinear response, forbidden in centrosymmetric media, so in 2H TMDCs it appears for odd layer numbers and vanishes for even ones. The polarisation dependence gives crystal orientation, and so the twist angle in a stack; the intensity follows layer number and strain; and it detects broken inversion symmetry in ferroelectric and magnetic layers where no other quick probe exists.

Full explanation

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.

Full explanation

Band structure

The map of the energies an electron may have in a crystal. The allowed energies come in ranges called bands, with forbidden gaps between them – like the decks of a multi-storey car park, where a car can stand on a deck but never between two. Whether a material conducts, gives off light or lets its electrons move easily can all be read from it, and in a layered material the map changes with the number of layers.

The electron energies E(k) of a periodic crystal as functions of crystal momentum, one branch per band, usually plotted along high-symmetry lines of the Brillouin zone. Band edges, slopes and curvatures give the gap, group velocities and effective masses; crossings and inversions give the topology. In layered crystals interlayer hybridisation makes it depend on thickness: the valence-band maximum of MoS₂ moves from Γ in the bulk to K in the monolayer, turning an indirect gap into a direct one.

Full explanation