Superconductivity

Everyday term

In plain words

A state in which a material carries electric current with zero resistance, usually only when very cold. It is what lets the magnets of hospital MRI scanners carry huge currents without heating up. Some become superconductors, and in twisted graphene the effect can be switched on and off with a voltage.

Going deeper

Superconductivity in thin and in tunable form. In a single layer, fluctuations smear the drop in resistance and push zero resistance to a lower temperature. In magic-angle graphene, superconducting domes flank a correlated insulating state, and one device moves between them when the gate voltage changes.

Pairs that move as one

In a conventional superconductor, an attraction mediated by lattice vibrations binds electrons of opposite momentum and into Cooper pairs – the mechanism of the 1957 theory by Bardeen, Cooper and Schrieffer. The pairs condense into a single quantum state with an , so small disturbances can no longer scatter them and resistance vanishes. The same state expels magnetic fields, the Meissner effect.

Three limits bound it: the , the critical magnetic field and the critical current density. NbSe₂, the best-known layered superconductor, becomes superconducting at about 7 K in bulk and at roughly 3 K as a . In the pairing mechanism is still debated.

What changes in two dimensions

In a single layer, fluctuations of the superconducting phase are strong enough to destroy true long-range order at any finite temperature. Superconductivity survives in a weaker form, and the transition follows the scenario: below the transition, vortices and antivortices are bound in pairs; above it they unbind and move freely, and their motion causes resistance. Zero resistance therefore appears below the temperature at which pairs form, and the resistive transition is broadened.

Monolayers without a centre of inversion add another twist. In NbSe₂ and gated MoS₂, pins the electron spins perpendicular to the layer, in opposite directions in the two . An in-plane magnetic field then struggles to break the pairs, and this survives fields several times the usual paramagnetic limit.

Switchable superconductivity, and how to prove it

Because a 2D layer can be filled with carriers by a gate, superconductivity can be turned on electrically. induces it in MoS₂, and in graphene near 1.1° a small gate voltage moves a single device between a and a superconductor with a critical temperature of about 1.7 K.

A drop in resistance is not proof on its own. Convincing evidence combines resistance that is zero within the resolution of a measurement, a critical field and critical current that behave as expected, and ideally independent signatures such as diamagnetism or . In small the magnetic measurements are hard, and superconducting contacts or filamentary paths can imitate a transition that the layer itself does not have.

For specialists

A macroscopic quantum state of paired electrons with zero DC resistance and magnetic-flux expulsion below a critical temperature. 2D examples include gate-tunable superconductivity in magic-angle graphene and Ising superconductivity in monolayer NbSe₂ and gated MoS₂; in the 2D limit the transition is of Berezinskii–Kosterlitz–Thouless type.

Where this comes from

Theory of superconductivity Bardeen et al. · Physical Review 108, 1175 (1957) cited by 13,210
Ising pairing in superconducting NbSe₂ atomic layers Xi et al. · Nature Physics 12, 139 (2016) cited by 1,231
Unconventional superconductivity in magic-angle graphene superlattices Cao et al. · Nature 556, 43 (2018) cited by 8,397

Spin

A built-in property of every electron that makes it a tiny magnet. Measure it along any direction and you only ever find one of two answers, ‘up’ or ‘down’. Despite the name, nothing is actually spinning – the word stuck from an early picture – but the magnetism is real: countless electron spins lined up are what make a fridge magnet stick. Spintronics tries to carry information in spin rather than in charge.

The intrinsic angular momentum of the electron, ħ/2, with a magnetic moment of almost exactly one Bohr magneton; a measurement along any axis yields one of two values. In solids spin couples to orbital motion through spin–orbit coupling and to other spins through exchange; in 2D materials it sets magnetic order, spin–valley locking and how long a spin survives as a carrier of information.

Full explanation

Phase transition

A sudden change in the state of a material when temperature, pressure or another control is varied – ice melting into water, a magnet losing its magnetism when heated, a metal becoming a superconductor when cooled. Each happens at a definite transition temperature. In quantum materials, transitions mark where new kinds of order appear: charge density waves, magnetism, superconductivity, ferroelectricity. A map of which state appears where, against temperature and a second knob such as doping or pressure, is a phase diagram.

A non-analytic change of thermodynamic state at a transition point, described by an order parameter that vanishes in the disordered phase and is finite in the ordered one – magnetisation, polarisation, charge-density-wave amplitude, superconducting gap. First-order transitions show latent heat, phase coexistence and hysteresis; continuous ones show a diverging correlation length and susceptibility and universal critical exponents set by dimension and symmetry (Landau theory, the renormalisation group). In two dimensions fluctuations are stronger: the Mermin–Wagner theorem forbids breaking a continuous symmetry at finite temperature, leaving anisotropic, Ising-like order or Berezinskii–Kosterlitz–Thouless quasi-order. Transition temperatures change with layer number, gating, strain and twist, which makes 2D materials tunable platforms for phase diagrams, including quantum phase transitions driven at zero temperature by non-thermal parameters.

Full explanation

Berezinskii–Kosterlitz–Thouless transition

How a flat, two-dimensional system that cannot have perfect order can still switch between an almost-ordered state and a disordered one. At low temperature, tiny whirlpools in the pattern of its spins – or of a superconductor – exist only in tightly bound pairs; above a critical temperature they break free and scramble the order.

A phase transition without a local order parameter in two-dimensional systems with a continuous planar symmetry – XY magnets, superfluid and superconducting films – driven by the unbinding of vortex–antivortex pairs. Below T_BKT correlations decay as a power of distance (quasi-long-range order), above it exponentially. The superfluid stiffness jumps to zero from the universal value 2k_BT_BKT/π, and in superconducting films the current–voltage curve follows V ∝ I³ at T_BKT. It evades the Mermin–Wagner theorem, which forbids true long-range order but not this.

Full explanation

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 Fe₃GeTe₂, 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.

Full explanation

Strong electron correlation

What happens when electrons in a material repel each other so strongly that they can no longer be treated as moving independently. Each electron’s motion then depends on where all the others are, and the result can be an insulator where simple theory predicts a metal, or magnetism, superconductivity and other collective states.

The regime in which the Coulomb repulsion U between electrons is comparable to or larger than their kinetic energy, set by the bandwidth W, so single-particle band theory fails. At half filling with U well above W the Hubbard model gives a Mott insulator with local moments and antiferromagnetic exchange of order t²/U; doping or tuning U/W gives correlated metals, heavy-fermion behaviour and unconventional superconductivity. In 2D, weak screening keeps U large and moiré superlattices shrink W, so twisted bilayers make U/W tunable by gate and twist. Semi-local DFT misses the physics; DFT+U, DMFT, exact diagonalisation and quantum Monte Carlo are the usual tools.

Full explanation

Resistivity and sheet resistance

Two ways to put a number on how strongly a material resists a current. Resistivity belongs to the material itself, whatever the size of the piece: copper’s is tiny, glass’s enormous. For a sheet so thin that its thickness is hard to pin down, the sheet resistance is used instead: the resistance of a square of it, measured from one edge to the opposite one, which comes out the same for a square of any size. It is quoted in ohms per square.

Resistivity ρ relates electric field to current density, in Ω·m or Ω·cm, so that a bar of length L and cross-section A has resistance ρL/A. For a film of thickness t the sheet resistance is ρ/t, quoted in Ω per square, and a strip L long and W wide has the sheet resistance times L/W. For an atomically thin layer it is the natural quantity, since the thickness is a convention, and it equals 1/neμ for sheet density n and mobility μ. Both are measured with four probes – a Hall bar, a collinear four-point probe or the van der Pauw method for arbitrary shapes – so that the voltage is sensed away from the current contacts and the contact resistance drops out.

Full explanation

Josephson effect

A current that flows between two superconductors through a thin barrier with no voltage at all, carried by pairs of electrons tunnelling across – slipping through a barrier that everyday physics says they cannot pass. How large that current is, and how it reacts to a magnetic field, is one of the sharpest ways to find out what kind of superconductor you are holding.

Phase-coherent tunnelling of Cooper pairs across a weak link, giving a supercurrent I = I_c·sin Δφ and, under a voltage, an oscillation at 2eV/h. In van der Waals stacks the weak link can be a graphene channel, a semiconducting monolayer or a twisted interface, and the current–phase relation, the Fraunhofer pattern and the temperature dependence of the critical current report on ballistic transport, edge modes and pairing symmetry.

Full explanation