Pair density wave

In plain words

A whose strength rises and falls in a repeating pattern across the crystal. In an ordinary superconductor electrons pair up evenly everywhere. In a pair density wave the pairs carry momentum, and the superconductivity varies periodically in space, like a made of pairs. It is hard to see, because it averages out in most measurements; can map it, and such as CsV₃Sb₅ are among the places it has been reported.

As the site uses it

The superconducting state is the second puzzle: pairing on top of a reconstructed Fermi surface, with pair density wave modulations reported in tunnelling.

CsV₃Sb₅, KV₃Sb₅ · Kagome metals AV₃Sb₅

Going deeper

In an ordinary superconductor pairs form evenly everywhere. If the pairs carry momentum, the pairing oscillates in space – a pair density wave. Because it averages out in most measurements, it is found by mapping the superconducting gap atom by atom, as in CsV₃Sb₅.

Pairs on the move

In a superconductor electrons bind into Cooper pairs, and in the usual case each pair has zero total momentum, so the pairing is the same everywhere. If the pairs carry a finite momentum instead, the superconducting order oscillates in space: its strength rises and falls with a fixed period, a pair density wave. Weak-coupling versions, the Fulde–Ferrell–Larkin–Ovchinnikov states, were proposed in the 1960s for superconductors in a magnetic field and are now sought in cold atoms, unconventional superconductors and crystals without .

A pair density wave drags other orders along: it induces a charge-density wave, and if it partly melts it can leave behind orders that outlive it. That is why it is discussed wherever superconductivity and charge order appear intertwined – in the copper oxides, where whether it is a parent order or a competitor is still argued (Agterberg and colleagues, 2020).

Seen in a kagome metal

Because a pair density wave averages to nothing in most bulk measurements, the evidence comes from imaging. In CsV₃Sb₅, scanning tunnelling spectroscopy found a V-shaped superconducting gap of about 0.5 meV, large for its (2Δ/k_BT_c ≈ 5, a sign of strong coupling), coexisting with charge order of 2a₀ × 2a₀ and 4a₀ periods. The gap, the height of its coherence peaks and its depth all varied across the surface with a period of 4a₀/3 in two directions, seen with both ordinary and Josephson tunnelling spectroscopy (Chen and colleagues, 2021).

The authors called it a roton pair density wave, tied it to an underlying lattice of and antivortices, and, probing it around field-induced vortices, in fields that suppress superconductivity and above the transition, argued that it underlies an emergent pseudogap. Other studies of the same family report conventional, nodeless superconductivity with several gaps, and which picture holds is one of the open questions about these metals.

Hard to pin down

The signatures of a pair density wave are subtle. A modulated superconducting gap can also reflect the charge order beneath an otherwise ordinary superconductor, and charge order at related periods is expected either way. Telling them apart needs the gap mapped atom by atom, ideally with a superconducting tip that responds to the pairs themselves, and comparisons across samples and probes – the work that keeps the kagome metals’ superconductivity under debate.

For specialists

A superconducting state whose order parameter is modulated at a finite wavevector – Cooper pairs with nonzero centre-of-mass momentum – rather than uniform. It induces charge-density-wave order of its own and, partly melted, can leave vestigial orders; its weak-coupling relatives are the Fulde–Ferrell–Larkin–Ovchinnikov states, and whether it is a parent or a competitor of the other orders in the copper oxides is debated. In CsV₃Sb₅, a strong-coupling superconductor (2Δ/k_BT_c ≈ 5) with 2a₀ × 2a₀ and 4a₀ charge order, scanning and Josephson spectroscopy found the gap, its coherence peaks and its depth modulated in two directions with a 4a₀/3 period – reported as a roton pair density wave underlying a pseudogap.

Where this comes from

The physics of pair-density waves: cuprate superconductors and beyond Agterberg et al. · Annual Review of Condensed Matter Physics 11, 231 (2020)
Roton pair density wave in a strong-coupling kagome superconductor Chen et al. · Nature 599, 222 (2021) cited by 620

In the news

The newest items in the site’s news feed that use the term, one from each source.

Preprintnot yet peer reviewed 24 Sep 2026 arXiv

Repulsion-Driven p - i p Superconductivity in a Single Valley Revealed by DMRG

We demonstrate repulsion-driven of a single species of , motivated by -polarized phases observed in two-dimensional materials such as graphene. Using density-matrix renormalization group calculations on the Qi-Wu-Zhang lattice model on cylinders of width up…

TheoryTwisted graphene Graphene

Preprintnot yet peer reviewed 23 Sep 2026 arXiv

Weak-Coupling Pair-Density-Wave from Momentum-Space Nonsymmorphic Symmetry

Pair-density-wave (PDW) order is a superconducting state with a spatially modulated order parameter and is generally subleading to uniform superconductivity within the conventional weak-coupling BCS paradigm. Here, using a checkerboard-lattice model, we show that momentum-space nonsymmorphic symmetry…

Theory

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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.

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

Superconducting vortex

A tiny whirlpool of current in a superconductor, threaded by a single quantum of magnetic flux. Many superconductors do not shut a magnetic field out completely: above a certain field it enters as thin threads, each with a core where superconductivity is destroyed, a few to tens of nanometres across, and a ring of current circling around it. The threads repel each other and settle into a regular lattice. When they move, they waste energy – so a superconductor stays lossless only if they are pinned in place – and their cores can hold electronic states of their own, among them the zero-energy states searched for as Majorana modes.

A line of magnetic flux h/2e (2.07 × 10⁻¹⁵ Wb) through a type-II superconductor, around which the superconducting phase winds by 2π; its core, about a coherence length wide, has the gap suppressed and hosts bound states, and its circulating supercurrent screens the field over the penetration depth. Between the lower and upper critical fields, vortices form the Abrikosov lattice, which scanning tunnelling microscopy imaged in NbSe₂ together with the core states. Moving vortices dissipate energy; in two dimensions, thermally created vortex–antivortex pairs unbind at the Berezinskii–Kosterlitz–Thouless transition. In a topological superconductor a vortex core can bind a Majorana zero mode, the interpretation offered for zero-energy peaks in Fe(Te,Se).

Full explanation

Quantum tunnelling

An electron can pass through a barrier it does not have the energy to climb over. Because it behaves partly as a wave, a little of it reaches into the barrier and, if the barrier is thin enough, out the other side. The chance falls off steeply with thickness, so it matters only across a nanometre or two – the scale of 2D materials. It is how a scanning tunnelling microscope sees single atoms, and it is the leak that limits how thin the insulator in a transistor can be.

Transmission through a classically forbidden region, with a probability that falls exponentially with the barrier’s width times the square root of its height above the particle’s energy. Across vacuum it gives the scanning tunnelling microscope its atomic resolution; through hBN the current falls exponentially with the number of layers down to a monolayer, which makes thin hBN a uniform tunnel barrier and sets the leakage floor when it serves as a gate dielectric. In twisted bilayers, tunnelling between the π orbitals of the two layers is the coupling that produces moiré bands and the magic angle.

Full explanation

Topological superconductivity

Superconductivity whose paired electrons carry a twist that cannot be undone smoothly – the superconducting cousin of a topological insulator. Inside, the material behaves like an ordinary superconductor, but its edges, surfaces and the cores of its vortices must hold special states, among them Majorana modes, which could store quantum information in a way that local disturbances cannot easily spoil. Few materials are clearly topological superconductors on their own, so researchers also build them by bringing an ordinary superconductor into contact with a topological or magnetic material.

Superconductivity whose Bogoliubov quasiparticle bands carry a nontrivial topological invariant, so that a full or nodal bulk gap coexists with protected Andreev boundary states, including Majorana zero modes bound to vortices and wire ends. Intrinsic candidates include odd-parity pairing and strongly spin–orbit-coupled systems such as the surface of FeTe₀.₅₅Se₀.₄₅, PtBi₂ and UTe₂; engineered versions combine s-wave pairing with spin–orbit coupling and broken time-reversal symmetry, following the Fu–Kane proposal for topological-insulator surfaces, semiconductor nanowires and magnetic atom chains. A zero-bias conductance peak alone is not proof: disorder and ordinary Andreev bound states mimic it.

Full explanation

Bernal and rhombohedral stacking

The two ways graphene sheets usually sit on one another in graphite. In Bernal, or AB, stacking every second layer lines up with the one two below it; in rhombohedral, or ABC, stacking each layer is shifted the same way as the one before, so the pattern repeats only every third layer. Natural graphite is mostly Bernal with some rhombohedral regions, and the difference matters: a few rhombohedral layers have very flat electron bands, and such flakes have turned out to superconduct and to hold unusual kinds of magnetism.

The two common stacking sequences of graphene layers: Bernal (AB, hexagonal graphite) and rhombohedral (ABC), which differ in the lateral position of every third layer; 3R TMDCs follow the same rhombohedral sequence. In the simplest model the low-energy bands of N-layer ABC graphene disperse as the Nth power of momentum and sit on the two outer layers, so they flatten with thickness and a perpendicular displacement field opens a tunable gap; Bernal multilayers instead decompose into bilayer-like bands plus, for odd N, a monolayer-like one. Rhombohedral stacking is metastable and relaxes to Bernal under heat, strain or processing.

Full explanation