Xene

Also called elemental 2D material

Everyday term

In plain words

The name for single-element modelled on graphene: silicene from silicon, germanene from germanium, phosphorene from phosphorus and so on. Most of them are far less stable in air than graphene.

Going deeper

The Xenes are single-element sheets named after graphene. Most are not flat: heavier elements prefer bonding that pulls alternate atoms out of the plane, which changes their electronic structure and, in most cases, leaves them far more reactive than graphene.

Why most of them buckle

Carbon is happy with flat sp² bonding, which is why graphene is a plane. Silicon, germanium and tin favour sp³-like bonding with angles, so their sheets corrugate: alternate atoms sit above and below the mean plane, by about 0.4 Å in silicene. Phosphorene goes further, with a puckered structure that also makes its two in-plane directions inequivalent.

Buckling is not merely cosmetic. It mixes orbitals that stay separate in a flat sheet, brings in the much stronger of heavier elements, and makes the sheet respond to an electric field applied across it – the basis for predictions that stanene and germanene could be with usable gaps.

Made on a surface, not peeled off one

Graphene comes from graphite, and phosphorene from black phosphorus, because those bulk parents are layered. Silicon and germanium have no layered allotrope, so silicene and germanene must be grown, usually by depositing atoms onto a metal surface in ultrahigh vacuum. The 2012 report of silicene on Ag(111) combined tunnelling microscopy, and calculations to argue that a buckled honeycomb of silicon had formed.

Growing on a metal has a cost: the hybridises with the sheet, so the free-standing is altered, and claims of in supported silicene have been contested on exactly those grounds. Moving such a sheet onto an without destroying it remains the hard part; directly after growth is one route that has been tried.

Stability, and what they are good for

Air is the main enemy. Phosphorene degrades within hours to days unless capped, silicene and germanene oxidise almost immediately off their growth substrate, and only a few – antimonene and bismuthene among them – are comparatively robust. This is why almost all device results for these materials involve immediate encapsulation, and why reported properties should be read together with how long the sample had been exposed.

What they offer in exchange is variety that graphene lacks: a real in phosphorene and antimonene, strong spin–orbit coupling in the heavier members, in-plane in phosphorene and tellurene, and predicted . Tellurene is the odd member, built from helical chains rather than a honeycomb.

For specialists

Monoelemental 2D crystals named by analogy with graphene – borophene, silicene, germanene, stanene, phosphorene, antimonene, bismuthene and tellurene. Unlike graphene most are buckled or puckered, many exist only on supporting substrates, and is a major constraint.

Where this comes from

Silicene: compelling experimental evidence for graphenelike two-dimensional silicon Vogt et al. · Physical Review Letters 108, 155501 (2012) cited by 3,914

Coordination polyhedron

The small shape traced by the atoms that surround a metal atom in a crystal. In many layered materials each metal sits inside an octahedron – six neighbours, three above and three below, turned against each other – or a trigonal prism, where the upper three sit right above the lower three. That one turn can make the same compound a semiconductor or a metal.

The polyhedron formed by an atom’s nearest neighbours; their number is its coordination number. In MX₂ layers the metal is either trigonal prismatic (D3h, as in 2H-MoS₂) or octahedral (D3d, as in 1T-TaS₂, and distorted in 1T′-WTe₂), and the ligand-field splitting of the d levels in each geometry, together with the d-electron count, decides whether the layer is a semiconductor or a metal. Halides and many oxides build layers from MX₆ octahedra sharing edges (CrI₃, RuCl₃) or corners (layered perovskites), and that connectivity sets the lattice – honeycomb, triangular or square – that the metal ions form.

Full explanation

Honeycomb lattice

A flat net of hexagons, like a beehive, with an atom at every corner. Graphene is the famous example, but the same pattern gives boron nitride its band gap, gives graphene its massless electrons, and gives some magnets interactions that cannot all be satisfied at once.

A triangular Bravais lattice with a two-site basis, so every site has three nearest neighbours on the other sublattice. Equivalent sublattices with nearest-neighbour hopping give Dirac cones at K and K′ (graphene); inequivalent ones open a gap with valley-contrasting Berry curvature (hBN, TMDC monolayers seen from above); buckling mixes in spin–orbit coupling (the Xenes); and bond-dependent exchange on the same geometry gives the exactly solvable Kitaev model behind the α-RuCl₃ spin-liquid programme.

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

Metal, semimetal and insulator

The three basic ways a solid treats electricity, set by how its electrons fill the energies open to them. In a metal they fill a band of energies only partly, so the smallest push sets them moving, and it conducts at any temperature. In an insulator they fill a band completely and a wide gap separates it from the next, so nothing can move. A semimetal sits in between: two bands just touch or overlap a little, leaving a small number of mobile electrons and holes. NbSe₂ is a metal, graphene a semimetal, hBN an insulator.

A classification by where the Fermi level falls in the band structure. In a metal it crosses a partly filled band, leaving a Fermi surface, a carrier density of order one per atom (about 10²² cm⁻³) and a resistivity that falls on cooling. In a band insulator it lies in a gap of several electronvolts; a semiconductor is an insulator whose gap is small enough to be doped or gated. A semimetal has a slight overlap between conduction and valence bands (graphite, bismuth, bulk WTe₂) or bands that touch at isolated points (graphene), giving low and nearly equal densities of electrons and holes. Interactions can open gaps that band theory does not predict: Mott insulators from half-filled bands, excitonic insulators from semimetals.

Full explanation

Topological phase

A state of matter told apart not by how its atoms are arranged but by a whole number that describes how its electrons’ waves twist across the crystal – the way a doughnut differs from a ball by its one hole. A whole number cannot change a little, so what it guarantees, such as current running along an edge without loss, survives defects and dirt until the band gap itself closes.

A gapped phase characterised by a topological invariant of its occupied bands – a Chern number, a Z₂ index, a winding number – that cannot change under deformations that keep the gap open and any protecting symmetry intact. Where regions with different invariants meet, the gap must close, which forces boundary states: chiral edge channels in Chern insulators, helical ones in quantum spin Hall insulators, Fermi arcs in Weyl semimetals, Majorana modes in topological superconductors. Topological order in the strict sense – the long-range entanglement of fractional quantum Hall states and spin liquids – is a distinct, stronger notion.

Full explanation