Condensed Matter Physics
Matter made of very many interacting electrons, atoms or spins: metals, magnets, superconductors and new materials.
arXiv: cond-mat.str-el, cond-mat.supr-con, cond-mat.mes-hall, cond-mat.dis-nn, cond-mat.mtrl-sci
67 topics
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Altermagnets
3 problemsAltermagnets are magnets in which neighboring spins point opposite ways so there is no net magnetization, yet electron energy bands split by spin as in a ferromagnet because the two spin sublattices are related by a crystal rotation. They were identified as a separate magnetic class around 2022.
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Below about 1 K, glasses of every chemical kind store heat, conduct heat and absorb sound in almost the same way, very differently from crystals. A model of small groups of atoms tunneling between two nearby positions fits the data, but nobody knows what these tunneling objects are or why their strength is the same in every glass.
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In a disordered solid, interference can trap electron waves and turn a metal into an insulator, a process called Anderson localization. The exponents of this transition are known numerically only for electrons that do not repel each other, and even then the theory of key cases such as the quantum Hall transition is unknown.
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Many-body quantum chaos and operator growth
4 problemsIn a chaotic quantum system a small local disturbance spreads until it involves the whole system, scrambling information. This spreading is measured by out-of-time-order correlators (OTOCs), and a conjectured universal limit bounds how fast it can grow.
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Contact electrification of insulators
5 problemsRubbing or touching two insulators, like a balloon and hair, leaves them oppositely charged, a fact known since antiquity. Which charged particles move, and why one material ends up positive and the other negative, is still not understood.
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Dislocation dynamics and crystal plasticity
6 problemsMetals bend permanently because line-shaped crystal defects called dislocations move and multiply. Huge numbers of them interact, tangle and organize into patterns, and no theory yet predicts from first principles how strong a deformed metal becomes.
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Underdoped cuprates, which carry fewer added holes than the optimum, lose many low-energy electron states above the superconducting temperature (the pseudogap) and develop weak periodic ripples in electron density. Whether these effects mark a new phase of matter, and what reorganizes the Fermi surface (the boundary between occupied and empty electron momenta), is not settled.
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Copper-oxide ceramics called cuprates carry current with zero resistance up to about 135 K at normal pressure in stable samples, and up to 151 K in a pressure-quenched metastable sample (2026), far above what the standard theory of superconductivity anticipated. How their electrons pair, and what the superconducting state looks like in space, is still disputed.
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Deconfined quantum criticality
4 problemsNormally a material can switch between two unrelated ordered patterns only through a sudden jump or an intermediate phase. Deconfined criticality predicts a smooth switch between magnetic order and a pattern of paired spins, driven by fractional particles that exist only at the transition.
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Most superconductors are metals crowded with electrons, but some, like doped strontium titanate, superconduct with a thousand times fewer carriers. In these materials the usual theory, which assumes electrons move much faster than the vibrating ions that pair them, breaks down.
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Real crystals contain defects and randomly mixed atoms, so the magnetic couplings vary from place to place. In frustrated magnets this randomness can lock spins into pairs or into a glass that, in many experiments, looks like a quantum spin liquid.
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Dynamical quantum phase transitions
6 problemsAfter a sudden change of a parameter, the probability that a quantum system is found back in its starting state can show sharp kinks at specific times, by analogy with phase transitions at specific temperatures. How these kinks relate to ordinary order and whether they have universal features is unsettled.
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Driven-dissipative quantum matter
4 problemsSome quantum systems are continuously pumped with energy while losing particles or energy to their surroundings, like lasers or light-matter condensates. They settle into steady states that are not in thermal equilibrium and can have their own kinds of phase transitions.
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In small metal wires and semiconductor devices, electrons keep a definite quantum phase for a time that theory says should grow without limit as temperature falls. In many samples this phase-coherence time stops growing below roughly 0.1 to 1 K, and the cause is disputed.
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In very clean materials electrons collide with each other more often than with defects, so they flow together like a viscous liquid instead of as independent particles. This produces measurable effects such as enhanced conduction through narrow channels and whirlpools of current.
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An isolated system of many interacting quantum particles usually reaches thermal equilibrium on its own, because each of its energy eigenstates already looks thermal to small probes (the eigenstate thermalization hypothesis, ETH). Systems with many extra conserved quantities (integrable systems) violate this, and what happens in between is poorly understood.
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Excitonic insulators and exciton condensates
5 problemsIn some materials, electrons and the holes they leave behind attract so strongly that they bind into excitons (electron-hole pairs) and open an energy gap on their own. If these pairs condense into one quantum state, they could flow without friction, much like a superfluid.
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Ferroelectrics are crystals whose ions shift to create a built-in electric dipole that an electric field can flip. Some of them, like relaxors and thin hafnium oxide films, behave in ways existing theory cannot explain, and thin layered films can host swirling dipole patterns.
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A single atomic layer of iron selenide grown on a strontium titanate crystal opens a superconducting gap that survives to about 65 K, roughly seven times higher than bulk FeSe (about 9 K). Why the substrate raises superconductivity so much, and even how high the true transition temperature is, remain disputed.
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In a perfectly flat band electrons have no kinetic energy, so ordinary theory says they cannot carry a supercurrent, yet flat-band materials superconduct. The shape of the electron wavefunctions in momentum space (their quantum geometry) is thought to give the pairs the mobility they need.
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Shaking a quantum system periodically can create phases impossible in equilibrium, such as a time crystal, which responds at a multiple of the driving period. The drive also adds energy, and the system eventually heats to a featureless state unless something prevents it.
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Fractional Chern insulators are states in a crystal where electrons act together as particles carrying a fraction of the electron charge, as in the fractional quantum Hall effect, but produced by band topology instead of a strong magnetic field.
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When competing couplings prevent spins from satisfying every bond, many arrangements have nearly the same energy. Quantum or thermal fluctuations can then pick one of them (order by disorder), or melt order completely.
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Lead-halide perovskites are crystals made cheaply from solution that convert light to electricity almost as well as silicon, despite being full of defects. Tiny semiconductor crystals of these and other materials also glow but randomly switch on and off, which is called blinking.
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In some uranium and cerium compounds the heavy electrons pair up in patterns unlike those of ordinary superconductors, including pairs with parallel spins and states that switch to a different pattern in a magnetic field. Identifying these patterns tests theories in which magnetic fluctuations glue electrons into pairs.
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In some cerium, ytterbium, samarium and uranium compounds, localized f-electron magnetic moments bind to conduction electrons and make electrons behave as if they were hundreds of times heavier. Tuning these materials with field or pressure drives zero-temperature phase transitions, and some of them become insulators or enter ordered phases whose nature is unidentified.
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Superfluid helium-3 and quantum solids
6 problemsBelow about 0.0025 K, helium-3 atoms pair up and form superfluids with several distinct phases, some of which are topological. Solid helium is so quantum that its atoms and crystal defects can move in ways no ordinary solid allows.
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The Hubbard model is the simplest picture of electrons hopping between atoms and repelling each other when two occupy the same atom. At one electron per atom strong repulsion freezes the electrons in place (a Mott insulator), and what happens when electrons are added or removed is unsolved.
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Hydrogen-rich compounds squeezed to more than a million atmospheres in diamond anvil cells superconduct near 200 to 250 K, with one unreplicated 2025 report near 298 K. Pure hydrogen is predicted to become a metal, and possibly a room-temperature superconductor, at still higher pressure.
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Quantum oscillations in insulators
5 problemsIn a metal, resistance and magnetization oscillate as a magnetic field is raised because mobile electrons move on closed orbits; an insulator has no mobile electrons, so this should not happen. Yet the Kondo insulators SmB6 and YbB12 and the two-dimensional insulator monolayer WTe2 show such oscillations.
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Topological phases are states of matter whose differences show up only in global properties of the wavefunction, such as protected edge modes, with no local order parameter. Once particles interact strongly, the full list of possible phases is not known.
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Iron arsenides and selenides superconduct up to about 55 K in bulk, and many first pass through a nematic transition, where electrons pick out one direction in the crystal before the lattice distorts. Several electron orbitals are active, which allows pairing patterns not available in cuprates.
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In AV3Sb5 compounds ($A = \mathrm{K}, \mathrm{Rb}, \mathrm{Cs}$) vanadium atoms form a kagome net of corner-sharing triangles; electrons there form a charge-density wave (a periodic ripple in electron density) near 80 to 100 K and superconduct below about 3 K, and a chromium relative superconducts under pressure. Whether the vanadium charge order carries circulating currents is disputed.
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Kitaev honeycomb magnets and alpha-RuCl3
7 problemsIn the Kitaev model each spin on a honeycomb lattice couples to its three neighbors through three different spin directions, and the exact solution splits each spin into emergent particles called Majorana fermions. Materials such as $\alpha$-RuCl3 come close to this model but order magnetically unless a strong magnetic field is applied.
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At high temperature, conserved quantities such as spin or energy in a lattice of interacting quantum particles spread out like heat in a solid, but sometimes faster (superdiffusion) or slower (subdiffusion). Predicting which spreading law applies, and computing its rate, is a central unsolved task.
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Experiments report that intense infrared light pulses make certain materials behave briefly like superconductors at temperatures where they normally are not. Whether this is genuine superconductivity is disputed.
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Two or three graphene sheets stacked with a small twist (about 1.1 degrees for two sheets) form a long-wavelength interference pattern (a moire pattern) in which electrons move very slowly. Electron repulsion then dominates and produces insulators, magnetism and unusual metals whose nature depends on how many electrons a gate voltage adds.
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Adding magnetism to a topological insulator opens an energy gap in its conducting surface states, giving a quantized Hall current without a magnetic field, or, when top and bottom surfaces are magnetized oppositely, an axion insulator (a material whose electric and magnetic responses are locked together by a universal constant).
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A Majorana zero mode is half of an ordinary electron state, bound to the end of a special superconducting wire or to a vortex core; two separated halves store one quantum bit that local noise cannot easily disturb.
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Many-body localization in large systems
6 problemsDisorder can stop waves from spreading, and many-body localization (MBL) is the claim that this survives when particles interact, so the system never thermalizes. Whether it survives in truly large systems, and in two dimensions, is disputed.
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Theory of non-interacting electrons predicts that any disorder turns a thin sheet of electrons into an insulator at absolute zero. Yet clean, dilute electron sheets in silicon and gallium arsenide devices act like metals whose resistance falls on cooling, and they become insulators only below a critical electron density.
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Magic-angle twisted bilayer and trilayer graphene become superconductors (zero electrical resistance) at one to a few kelvin when a gate adds or removes electrons. The interaction that pairs the electrons and the symmetry of the pairs are unknown.
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Stacking two different semiconductor sheets, such as WSe2 on WS2 or MoTe2 on WSe2, creates a triangular grid of traps for electrons, a tunable version of the Hubbard model (electrons hopping between sites and repelling each other when they share one). Gates change the electron number and the hopping, so Mott insulators (insulators caused by repulsion), electron crystals and heavy-electron metals appear in one device.
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Multiferroics and magnetoelectric coupling
3 problemsMultiferroics are materials that are both magnetic and ferroelectric, meaning they hold a spontaneous electric polarization. In the best cases an electric field can flip the magnetism, which would allow memory written with voltage instead of current.
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Nickel oxides built like cuprates also superconduct: infinite-layer films such as Nd0.8Sr0.2NiO2 below about $15\,\mathrm{K}$ (near $40\,\mathrm{K}$ in samarium-based films), and bilayer La3Ni2O7 near $80\,\mathrm{K}$ under about $140\,\mathrm{kbar}$ (up to about $96\,\mathrm{K}$ in 2025 reports), with onset above $60\,\mathrm{K}$ in compressed thin films at normal pressure. Why they superconduct, and how high the transition temperature $T_c$ can go, are open questions.
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In some quantum Hall states, quasiparticles called non-Abelian anyons store information in how they are wound around each other, so that swapping them performs an operation that depends on the order of swaps. The $5/2$ state in gallium arsenide and half-integer states in bilayer graphene are the main candidates, but their identity and braiding are still being established.
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After a sudden strong disturbance, a quantum gas can pass through a long stage in which its correlations keep the same shape while stretching in time by a power law, before it reaches equilibrium. These stages, called nonthermal fixed points, appear universal in the way critical points are universal in equilibrium.
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Origin of 1/f noise in solids and devices
6 problemsAlmost every electronic device shows slow random fluctuations whose strength grows as frequency falls, roughly as one over frequency, down to the lowest frequencies ever measured. A single explanation for why this law is so common, and what produces it in each material, is missing.
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Phonon thermal Hall effect in insulators
4 problemsIn a magnetic field, heat flowing through many electrical insulators is pushed sideways, even though the heat is carried by lattice vibrations (phonons) that have no charge. Why phonons respond to the field so strongly in materials as different as cuprates, SrTiO3 and quartz is not understood.
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Quantum spin glasses and quantum annealing
7 problemsIn a spin glass the tiny magnets inside a material freeze in random directions because their interactions conflict. In a quantum spin glass a sideways magnetic field adds quantum fluctuations, and how the system freezes as that field is lowered decides how well quantum annealing machines can find low-energy states.
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Quantum bits built from superconducting circuits or single electron spins lose their information to tiny defects in nearby materials and to stray broken electron pairs. Which atoms and processes are responsible, and how to remove them, is not known in detail.
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Four to seven graphene layers stacked in a staircase (rhombohedral) order have very flat electron bands at low density. With or without a moire pattern from a boron nitride substrate they show zero-field fractional Hall states and superconductivity that appears to break time-reversal symmetry.
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Some interacting quantum systems contain a few special states that do not thermalize while almost all others do (scars), or have their set of states broken into many disconnected pieces by constraints (fragmentation). Both produce long-lived oscillations seen in cold-atom experiments.
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Computer simulations of many interacting electrons often require adding huge numbers of positive and negative terms that nearly cancel, so errors grow exponentially with system size; this is the sign problem. It is why different methods disagree on basic questions about two-dimensional electron models.
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Thin superconducting films can be turned into insulators by disorder, a magnetic field or a gate voltage. In between, many films show an anomalous metal whose resistance stops falling on cooling and stays at a small finite value, which standard theory says should not happen at zero temperature.
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Skyrmions are tiny whirlpools of spins that cannot be smoothly unwound, so they behave like stable particles. They form in many magnets, but why they appear in some crystals and how quantum mechanics affects them are open.
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Quantum spin chains
1 problemsA spin chain is a line of interacting quantum spins, often exactly solvable on paper, yet how spin and heat move along it at finite temperature has turned out unexpected. Some chains also have phases whose existence is still disputed.
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Spin ice, monopoles and quantum spin ice
5 problemsIn spin ice, magnetic moments on corner-sharing tetrahedra obey an ice rule of two pointing in and two out, and flipping one spin creates a pair of particles that behave like magnetic monopoles. Adding quantum tunneling between ice configurations is predicted to give a quantum spin liquid with emergent light, a photon-like wave of an internal gauge field.
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Strontium ruthenate is an exceptionally clean layered oxide that superconducts below 1.5 K; for two decades it was thought to pair electrons with parallel spins, until a 2019 measurement overturned the main evidence. No proposed pairing state now fits all the data.
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Strange metals and Planckian dissipation
7 problemsIn many correlated metals the electrical resistance grows in exact proportion to temperature down to the lowest temperatures, which standard metal theory does not allow. The electrons seem to scatter at a rate set only by temperature and Planck's constant, called the Planckian rate.
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The Sachdev-Ye-Kitaev (SYK) model is a solvable model of many particles that all interact with each other through random couplings; it has no particle-like excitations and shares features with black holes. It serves as a template for strange metals and for quantum gravity experiments in the lab.
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No known law of physics forbids a superconductor at room temperature and normal pressure, yet every known material falls short. Theorists try to derive limits on the transition temperature from the energies of electrons and lattice vibrations.
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On triangular and kagome (corner-sharing triangle) lattices, antiparallel spin alignment cannot satisfy every bond, and quantum fluctuations may prevent any order down to zero temperature. The resulting quantum spin liquids are predicted to host spinons, particles that carry spin but no charge.
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Twisting two sheets of a semiconductor such as MoTe2 or WSe2 creates narrow electron bands whose electrons can show quantized Hall currents without an applied magnetic field, and can superconduct. These bands are topological: their wavefunctions have a winding that forces current-carrying states at the sample edges.
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Ultrafast magnetism and spin-orbit transport
6 problemsA laser pulse lasting less than a trillionth of a second can erase or even reverse a magnet's magnetization, and currents in heavy metals can twist nearby magnets through spin-orbit coupling (the link between an electron's motion and its spin). Where the angular momentum goes, and how these twisting forces arise, are still argued.
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In Weyl and Dirac semimetals the electrons behave like massless relativistic particles with a definite handedness, so parallel electric and magnetic fields should transfer electrons from one handedness to the other (the chiral anomaly). Measuring the resulting currents cleanly has proved hard.
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Wigner crystals of two-dimensional electrons
5 problemsWhen electrons in a flat sheet are spread thin enough, their mutual repulsion beats their kinetic energy and they freeze into a regular lattice called a Wigner crystal. How this crystal melts into a liquid as density rises, and what lies between the two, is not known.