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Quantum materials

Quantum materials are a broad class of condensed matter systems in which quantum mechanical effects, including strong electron correlations, topological order, and quantum geometry, dominate to produce emergent, non-trivial electronic properties observable at macroscopic scales and often at elevated temperatures.^[1] These properties extend beyond conventional materials, encompassing phenomena such as dissipationless transport in superconductors and robust, spin-polarized surface states in topological insulators.^[2] Key examples include high-temperature superconductors, graphene exhibiting the fractional quantum Hall effect, Weyl semimetals hosting exotic quasiparticles like Weyl fermions, and skyrmion lattices in chiral magnets, all of which arise from interactions that defy classical descriptions.^[1] The field bridges physics, materials science, and engineering, with quantum geometry—encoded in the Berry curvature and quantum metric—playing a central role in influencing transport, superconductivity, and nonlinear responses in these systems.^[2] Historically, the study of quantum materials evolved from the 1960s focus on symmetry breaking and order parameters, through the 1980s discoveries of high-temperature superconductivity and the fractional quantum Hall effect, to recent advances in synthesizing two-dimensional van der Waals materials and imaging their quantum states.^[1] These developments have enabled precise control over emergent excitations, such as magnetic monopoles and fractional charges, which underpin topological order and potential dissipationless quantum states.^[1] In terms of significance, quantum materials hold promise for transformative applications in quantum computing, spintronics, and optoelectronics, where their exotic properties like quantized Hall conductivity and enhanced superfluid weight can lead to energy-efficient devices and novel quantum technologies.^[3] The year 2025 has been designated by the United Nations as the International Year of Quantum Science and Technology, highlighting ongoing global efforts in the field.^[4] Ongoing research emphasizes data-driven discovery and advanced synthesis techniques to explore entanglement, topology, and high-temperature quantum effects in diverse platforms, from kagome lattices to iron-based superconductors.^[3]

Fundamentals

Definition and Scope

Quantum materials are defined as condensed matter systems in which quantum mechanical effects, such as coherence, entanglement, and superposition, manifest at macroscopic scales and dominate over classical behaviors, requiring a full quantum description to explain their properties.^[5] Unlike classical materials, where quantum effects are typically confined to atomic or molecular levels and averaged out by statistical mechanics, quantum materials exhibit emergent phenomena driven by strong electron correlations, topological order, or disorder that persist across larger scales.^[6] This distinction arises because, in quantum materials, interactions like Coulomb repulsion or spin-orbit coupling lead to collective states that cannot be predicted from semiclassical models.^[5] The scope of quantum materials lies primarily within condensed matter physics, encompassing a broad class of solids from atomic lattices to mesoscopic structures where quantum confinement or many-body interactions amplify non-trivial electronic or magnetic behaviors.^[1] Examples include systems exhibiting superconductivity, where paired electrons flow without resistance due to quantum coherence, or topological insulators that host protected edge states insensitive to defects from disorder.^[6] These materials bridge scales from nanoscale quantum dots to bulk crystals, enabling applications in quantum information science and energy technologies by leveraging phenomena like the quantum Hall effect or anomalous Hall conductivity.^[5] The term "quantum materials" emerged in the 2010s as a unifying framework for diverse fields in condensed matter physics, including high-temperature superconductivity and topological phases, to highlight shared quantum origins amid rapid experimental advances.^[1] This nomenclature reflects a paradigm shift from traditional studies of symmetry breaking to exploring exotic states like Weyl semimetals, fostering interdisciplinary research without implying a single theoretical model.^[1]

Key Quantum Phenomena

Quantum materials exhibit emergent phenomena arising from collective quantum effects that cannot be captured by simple single-particle models, distinguishing them from conventional solids. These include strong electron correlations, where interactions like Coulomb repulsion lead to states such as Mott insulators or unconventional superconductivity, defying predictions from band theory alone.^[5] Topological order manifests in protected surface or edge states, as in topological insulators, where spin-momentum locking ensures robust transport insensitive to backscattering.^[6] Foundational to these is Bloch's theorem, which describes electron wavefunctions in periodic potentials as ψ_k(r) = e^{i k · r} u_k(r), where u_k(r) matches the lattice periodicity and k is the wavevector, enabling band structure analysis in the Brillouin zone.^[1] Quantum coherence preserves phase relations, crucial for collective excitations like Cooper pairs in superconductors, while many-body entanglement correlates electrons non-locally, underpinning fractionalized excitations in quantum spin liquids. Quantum geometry, encoded in the Berry curvature, influences anomalous transport and Hall responses in materials like Weyl semimetals.^[2] Band theory provides a starting point, with energy levels forming bands under Fermi-Dirac statistics: f(ε) = 1 / (e^{(ε - μ)/kT} + 1), where μ is the chemical potential, k Boltzmann's constant, and T temperature. The time evolution follows the Schrödinger equation i ħ ∂ψ/∂t = Ĥ ψ, incorporating interactions. Simplified models like tight-binding capture hopping: Ĥ = -t ∑_{⟨i,j⟩} (c_i† c_j + h.c.), illustrating correlation effects when extended to include on-site repulsion.^[5]

Historical Development

Early Foundations

The discovery of superconductivity by Heike Kamerlingh Onnes in 1911 marked an early experimental anomaly in condensed matter physics, observed when the electrical resistance of mercury abruptly vanished at temperatures near 4.2 K, though this phenomenon preceded the full framework of quantum mechanics and was initially interpreted through classical theories.^[7] Onnes's work at the Leiden laboratory, enabled by his liquefaction of helium in 1908, highlighted unexpected behaviors in metals at low temperatures but lacked a quantum explanation at the time.^[8] The foundational theory of quantum mechanics emerged in the mid-1920s, with Werner Heisenberg introducing matrix mechanics in 1925 as a non-commutative algebra for atomic observables, resolving inconsistencies in the old quantum theory.^[9] Independently, Erwin Schrödinger developed wave mechanics in 1926, formulating a differential equation for matter waves that described electron behavior in atoms, providing an intuitive continuous framework equivalent to Heisenberg's approach.^[10] In 1927, Paul Dirac developed transformation theory, which unified the matrix mechanics and wave mechanics approaches. In 1928, he formulated the relativistic Dirac equation, bridging quantum mechanics with special relativity and laying the groundwork for applying quantum principles to complex systems like solids.^[11] These quantum developments were swiftly applied to solid-state physics. In 1927, Max Born and J. Robert Oppenheimer introduced the adiabatic approximation, separating electronic and nuclear motions in molecules due to the mass disparity, enabling quantum treatment of multi-particle systems in periodic structures.^[12] That same year, Clinton Davisson and Lester Germer experimentally confirmed the wave nature of electrons through diffraction patterns from a nickel crystal, aligning de Broglie's hypothesis with quantum predictions and validating wave mechanics for particles in solids.^[13] Felix Bloch advanced the theory in 1928 by deriving wave functions for electrons in a periodic crystal potential, known as Bloch waves, which exhibit a plane-wave-like form modulated by the lattice periodicity and underpin the concept of energy bands E(k), where E denotes energy as a function of wave vector k.^[14] Léon Brillouin extended this in 1930 by developing the zone scheme for electron propagation in metals, delineating Brillouin zones in reciprocal space to account for Bragg reflections that create band gaps, thus formalizing initial band theory for understanding electrical conductivity in crystals.^[15]

Modern Breakthroughs

In 1957, John Bardeen, Leon Cooper, and John Schrieffer developed the BCS theory, providing a microscopic quantum mechanical explanation for superconductivity in conventional materials by describing how electrons form Cooper pairs through electron-phonon interactions, leading to zero electrical resistance below a critical temperature. This theory not only resolved long-standing puzzles in low-temperature superconductivity but also earned its authors the 1972 Nobel Prize in Physics. Building on this foundation, the discovery of high-temperature superconductors in 1986 by J. Georg Bednorz and K. Alex Müller marked a revolutionary shift, as they observed superconductivity above 30 K in a barium-lanthanum-copper-oxide compound, challenging the conventional limits predicted by BCS and opening pathways to practical applications at higher temperatures. Their work, recognized with the 1987 Nobel Prize in Physics, spurred global research into cuprate materials and exotic pairing mechanisms. The advent of topological concepts further expanded the scope of quantum materials in the late 20th century. In 1980, Klaus von Klitzing discovered the integer quantum Hall effect while studying two-dimensional electron gases in semiconductor heterostructures under strong magnetic fields, revealing quantized Hall conductance in discrete steps of e^2/h, where e is the electron charge and h is Planck's constant. This phenomenon, which demonstrated robustness against impurities and established a new quantum resistance standard, earned von Klitzing the 1985 Nobel Prize in Physics and laid the groundwork for topological insulators and other protected quantum states. In 1982, Daniel Tsui, Horst Störmer, and Arthur Gossard observed the fractional quantum Hall effect in GaAs heterostructures at high magnetic fields and low temperatures, revealing quantized Hall conductance at fractional fillings of e^2/h, indicating emergent quasiparticles with fractional charge and anyonic statistics. This discovery, awarded the 1998 Nobel Prize in Physics, further advanced understanding of topological phases in quantum materials.^[16] Two decades later, in 2004, Andre Geim and Konstantin Novoselov isolated graphene—a single layer of carbon atoms—using mechanical exfoliation, unveiling its unique properties as a Dirac material with massless Dirac fermions and linear dispersion relations near the Dirac points. Their breakthrough, awarded the 2010 Nobel Prize in Physics, highlighted graphene's exceptional electronic mobility and sparked interest in two-dimensional quantum materials beyond traditional semiconductors. The 2010s witnessed the unification of these diverse strands into the distinct field of quantum materials, driven by conferences such as the American Physical Society March Meetings, which increasingly featured dedicated sessions on emergent phenomena in topological and correlated systems.^[1] This consolidation emphasized materials exhibiting strong quantum effects like unconventional superconductivity and topological order, fostering interdisciplinary collaboration across condensed matter physics and materials science. Complementing this, the U.S. Materials Genome Initiative, launched in 2011, accelerated discoveries by integrating computational modeling, high-throughput screening, and data-driven approaches to design novel quantum materials more efficiently.^[17]

Classification and Types

Topological Materials

Topological materials are a class of quantum materials characterized by non-trivial topological order in their electronic band structure, leading to robust, protected states at their surfaces or edges that are insulated from the gapped bulk.^[18] These materials exhibit a bulk energy gap like conventional insulators but host conducting states on boundaries due to global symmetries, such as time-reversal symmetry, which prevent backscattering and ensure dissipationless transport.^[18] The quantum Hall effect in two dimensions provided an early precursor to this paradigm, demonstrating quantized edge conductance tied to topological invariants.^[19] Classification of topological materials includes topological insulators (TIs), which are gapped in the bulk but feature helical surface states with spin-momentum locking; topological semimetals, such as Weyl and Dirac semimetals, where band crossings form low-energy excitations analogous to relativistic particles; and Chern insulators, which break time-reversal symmetry to realize chiral edge states without an external magnetic field.^[18] A prototypical example of a three-dimensional TI is bismuth selenide (Bi₂Se₃), identified in 2009 through angle-resolved photoemission spectroscopy (ARPES) revealing a single Dirac cone surface state within a bulk gap of approximately 0.3 eV. For Weyl semimetals, tantalum arsenide (TaAs) was experimentally confirmed in 2015 as the first material hosting Weyl fermions, with ARPES observing topological Fermi arcs connecting bulk Weyl points.^[20] Dirac semimetals, like Cd₃As₂, feature four-fold degenerate Dirac points protected by crystal symmetries. Chern insulators were realized in magnetic topological insulators, such as Cr-doped (Bi,Sb)₂Te₃ thin films, exhibiting the quantum anomalous Hall effect with Chern number |C| = 1 at zero field in 2013. Central to these materials are concepts like the Berry phase, which arises from the geometric phase acquired by wavefunctions during adiabatic evolution in momentum space, and the associated Berry curvature \mathbf{F}(\mathbf{k}), acting as a magnetic field in k-space.^[18] Topological invariants, such as the Chern number for two-dimensional systems, quantify this non-triviality:

C = \frac{1}{2\pi} \int_{BZ} F_z(\mathbf{k}) \, d^2k,

where the integral over the Brillouin zone (BZ) yields an integer classifying the topology; non-zero C ensures protected edge modes in Chern insulators.^[18] The bulk-boundary correspondence principle dictates that the number of robust boundary states equals the difference in bulk topological invariants across an interface, guaranteeing gapless surface modes in TIs when the bulk is topologically non-trivial.^[18] Experimental realizations rely heavily on ARPES to directly visualize Dirac-like dispersion in surface states, as demonstrated for Bi₂Se₃ where the linear band crossing at the surface was confirmed without bulk interference. These states exhibit remarkable robustness to non-magnetic disorder, owing to time-reversal symmetry protection that forbids elastic backscattering between counter-propagating modes with opposite spins.^[21] This disorder tolerance persists as long as symmetry is preserved, enabling potential applications in spintronics despite imperfections in real samples.^[18]

Strongly Correlated Materials

Strongly correlated materials are a class of quantum materials in which electron-electron interactions play a dominant role, often overriding the effects of the underlying lattice structure and leading to emergent collective behaviors that cannot be explained by conventional band theory. In these systems, the Coulomb repulsion between electrons is comparable to or stronger than their kinetic energy, resulting in complex phases such as Mott insulators, where strong correlations suppress charge mobility despite partial band filling. This competition between kinetic energy, which favors delocalization, and on-site Coulomb repulsion, which promotes localization, is paradigmatically captured by the Hubbard model, a minimal theoretical framework for understanding such phenomena.^[22] The Hubbard model Hamiltonian is given by

H = -t \sum_{\langle i,j \rangle, \sigma} (c^\dagger_{i\sigma} c_{j\sigma} + h.c.) + U \sum_i n_{i\uparrow} n_{i\downarrow},

where t represents the hopping amplitude between nearest-neighbor sites \langle i,j \rangle, c^\dagger_{i\sigma} (c_{i\sigma}) creates (annihilates) an electron with spin \sigma at site i, U is the on-site repulsion strength, and n_{i\sigma} = c^\dagger_{i\sigma} c_{i\sigma} is the number operator. This model, introduced in 1963, highlights how increasing U/t drives the system from a metallic state toward insulating behavior through the enhancement of local correlations.^[22] In real materials, additional terms like longer-range interactions or lattice distortions refine this picture, but the core interplay remains central to describing strongly correlated electron dynamics.^[23] Prominent examples of strongly correlated materials include high-temperature cuprate superconductors, such as La_{2-x}Ba_xCuO_4, where doping introduces holes into a Mott insulating parent compound, enabling unconventional superconductivity at elevated temperatures up to around 35 K. Another class is heavy fermion compounds like CeCu_6, in which localized f-electrons from cerium hybridize with conduction electrons, yielding quasiparticles with effective masses hundreds of times larger than the bare electron mass due to Kondo screening effects.^[24] Quantum spin liquids, realized in frustrated lattices such as the kagome structure of herbertsmithite (ZnCu_3(OH)_6Cl_2), exhibit no magnetic order down to the lowest temperatures, with spin degrees of freedom remaining dynamically disordered; this material, synthesized in 2005, serves as a key realization of a spin-1/2 antiferromagnet on a kagome lattice. Key phenomena in these materials include the Mott metal-insulator transition, where tuning parameters like temperature, pressure, or doping shifts the system from a correlated metal to an insulator without structural change, as the effective bandwidth is renormalized by interactions. This transition manifests in cuprates as a doping-driven crossover from the antiferromagnetic Mott insulator at half-filling to a superconducting dome. Fractionalized excitations, such as spinons—neutral spin-1/2 quasiparticles that carry spin but no charge—emerge in spin liquid phases or gapped Mott states, deconfined from holons in theories like the slave-boson approach to the t-J model derived from the Hubbard model at strong coupling. In high-Tc cuprates, the pseudogap phase appears above the superconducting transition in underdoped regimes, characterized by a suppression of low-energy density of states and partial pairing of electrons, distinct from the full gap in the superconducting state and linked to stripe-like charge order or preformed pairs.^[25]

Properties and Behaviors

Electronic Properties

Quantum materials exhibit distinctive electronic properties arising from quantum mechanical effects that govern charge carrier behavior at the nanoscale. In these systems, the band structure often deviates from the parabolic dispersion typical of conventional semiconductors, leading to unique electronic states. For instance, Dirac and Weyl cones feature linear energy dispersion relations near the Fermi level, described by E = v_F | \mathbf{k} |, where v_F is the Fermi velocity and \mathbf{k} is the wave vector relative to the cone vertex. This linear dispersion, first observed in graphene, results in massless Dirac fermions with high mobility and relativistic-like transport characteristics. In Weyl semimetals, such as tantalum arsenide (TaAs), pairs of Weyl nodes of opposite chirality emerge, enabling topologically protected electronic states with similar linear dispersion. In one-dimensional (1D) quantum materials, electron interactions dominate, leading to Luttinger liquid behavior rather than Fermi liquid states. In Luttinger liquids, charge and spin degrees of freedom separate into collective bosonic modes, resulting in power-law correlations and suppressed single-particle excitations. This phenomenon has been experimentally confirmed in carbon nanotubes, where conductance measurements reveal characteristic suppression of tunneling density of states at low energies, consistent with interaction parameter g < 1.^[26] Such 1D systems, including semiconductor nanowires and organic conductors, showcase fractionalized excitations and enhanced susceptibility to perturbations like impurities or magnetic fields. Transport phenomena in quantum materials are profoundly influenced by these band structures, manifesting quantized conductance in ballistic regimes. In quantum point contacts, the conductance G = (2e^2/h) N quantizes in steps of the conductance quantum $2e^2/h, where N is the number of occupied one-dimensional modes, as observed in two-dimensional electron gases in GaAs heterostructures.^[27] The anomalous Hall effect (AHE) further highlights chiral properties in materials like Weyl semimetals, where transverse conductivity arises from Berry curvature without external magnetic fields, yielding large Hall angles due to intrinsic topological contributions.^[28] This effect is briefly linked to topological protection in Hall conductivities, distinguishing it from classical origins. Electronic properties are quantified through measurements of conductivity and Hall states under quantized conditions. The Drude conductivity \sigma = ne^2 \tau / m, with carrier density n, relaxation time \tau, and effective mass m, provides a baseline but is modified in quantum regimes by coherence effects. In the integer quantum Hall effect, observed in high-mobility two-dimensional systems, longitudinal resistivity vanishes while Hall resistivity quantizes as \rho_{xy} = h / (e^2 \nu), with integer filling factor \nu. Fractional quantum Hall states, arising from electron correlations in strong magnetic fields, feature filling factors \nu = n h / (e B) as fractions like $1/3, indicating quasiparticle excitations with fractional charge. These states underscore the role of many-body interactions in defining robust, dissipationless transport channels.

Magnetic and Spin Properties

Quantum materials exhibit a rich variety of magnetic orders driven by the interplay of quantum mechanics and electron correlations, where spin degrees of freedom play a central role. In antiferromagnetic systems, spins align in an antiparallel fashion on neighboring sites, leading to zero net magnetization, but quantum fluctuations can significantly alter the ground state. These fluctuations arise from zero-point motion of spins, reducing the sublattice magnetization below its classical value, as seen in the spin-1/2 Heisenberg antiferromagnet on a square lattice, where the ordered moment is renormalized to about 0.303 μ_B per site. In ferromagnetic quantum materials, parallel spin alignment dominates, yet quantum fluctuations introduce corrections to the magnon spectrum and can stabilize non-collinear states in low dimensions. For instance, in one-dimensional ferromagnets, quantum effects suppress long-range order entirely, resulting in algebraic correlations rather than true spontaneous symmetry breaking. A particularly striking example of quantum magnetism is the formation of skyrmions in chiral magnets, which are topologically protected spin textures resembling particle-like whirls in the magnetization field. In materials like MnSi, lacking inversion symmetry, the Dzyaloshinskii-Moriya interaction stabilizes a lattice of skyrmions under modest magnetic fields, observed via neutron scattering in 2009.^[29] These skyrmions exhibit a hexagonal arrangement with a period of approximately 18 nm at low temperatures, and their stability stems from the topological charge, preventing annihilation without energy barriers. Such configurations highlight how quantum effects enable emergent topological orders in bulk magnetic materials. Spin phenomena in quantum materials are profoundly influenced by spin-orbit coupling (SOC), which entangles spin and orbital degrees of freedom through the relativistic interaction described by the Hamiltonian H_{\text{SO}} = \lambda \mathbf{L} \cdot \mathbf{S}, where \lambda is the coupling strength, \mathbf{L} the orbital angular momentum, and \mathbf{S} the spin. This term, dominant in heavy-element compounds, lifts degeneracies and drives phenomena like the quantum spin Hall effect (QSHE), where edge states conduct spin-polarized currents without dissipation in the bulk insulator. The QSHE was theoretically predicted in graphene with intrinsic SOC, yielding a quantized spin Hall conductivity of \frac{e}{2\pi}, though experimental realization required stronger SOC materials like HgTe quantum wells.^[30] In spin chains, SOC can also facilitate the emergence of Majorana fermions, zero-energy quasiparticles that are their own antiparticles, appearing at the ends of topological superconductors or in Kitaev-like models. For example, in a one-dimensional spin-1/2 chain with bond-directional interactions, the ground state fractionalizes into itinerant Majorana modes, enabling non-Abelian statistics useful for quantum computing. Itinerant electron magnetism, where magnetism arises from delocalized electrons near the Fermi surface, is prominent in Fe-based superconductors, such as LaFeAsO. Here, stripe-like antiferromagnetic order with a wavevector (\pi,0) emerges from nesting of electron and hole pockets, competing with superconductivity; the magnetic moment is about 0.3–2 μ_B per Fe atom, tuned by doping.^[31] Quantum spin liquids represent another paradigm, where strong frustration prevents long-range magnetic order, resulting in a correlated state of fluctuating spins with no static magnetism down to absolute zero. In the triangular lattice Heisenberg antiferromagnet, geometric frustration from 120-degree spin alignments leads to a resonating valence bond ground state, as proposed in 1973, with short-range spin singlets and potential fractional excitations like spinons. Recent candidates like herbertsmithite confirm the absence of order via muon spin relaxation, showing power-law correlations.

Synthesis and Characterization

Fabrication Methods

Fabrication of quantum materials requires precise control over atomic-scale structures to preserve their exotic quantum properties, such as topological protection or strong correlations. Bulk synthesis methods enable the production of larger-scale samples suitable for initial studies, while nanoscale techniques allow for the creation of low-dimensional structures critical for device integration. These approaches must address inherent challenges like maintaining defect-free interfaces and tuning electronic states through external parameters. Chemical vapor deposition (CVD) is a widely used bulk method for synthesizing two-dimensional (2D) quantum materials, particularly graphene, by decomposing hydrocarbon precursors on metal substrates at elevated temperatures. In this process, carbon atoms nucleate and grow into continuous graphene sheets on copper foils under atmospheric or low-pressure conditions, enabling large-area films up to several square centimeters with high uniformity. This technique has been pivotal for scaling up graphene production beyond laboratory constraints, though it often results in polycrystalline films that introduce grain boundaries affecting electronic transport. Molecular beam epitaxy (MBE) represents another key bulk approach for fabricating thin films of quantum materials, offering atomic-layer precision through the sequential deposition of elemental beams in an ultrahigh-vacuum environment. For instance, MBE has been employed to grow high-quality Bi₂Se₃ topological insulator films on substrates like Si(111) or sapphire, achieving quintuple layer thicknesses with minimal defects and preserved surface states essential for topological transport. These epitaxial films are crucial for realizing topological thin films, as detailed in studies on their integration into heterostructures.^[32] At the nanoscale, mechanical exfoliation provides a simple yet effective top-down method to isolate atomically thin layers from bulk precursors, famously demonstrated for graphene using the "Scotch tape" technique. Developed in 2004, this involves repeatedly peeling layers from highly oriented pyrolytic graphite with adhesive tape until single-layer flakes are obtained, yielding pristine samples with exceptional electronic quality for early quantum Hall effect observations. Though low-yield and non-scalable, it remains a benchmark for defect-free 2D material isolation. Bottom-up self-assembly offers a complementary nanoscale strategy for quantum dots, where colloidal synthesis leverages solution-phase reactions to form size-tunable semiconductor nanocrystals through nucleation and growth. In this process, precursors like cadmium and selenium are injected into hot solvents, promoting the self-assembly of uniform dots (e.g., CdSe) with diameters of 2–10 nm, exhibiting quantum confinement effects tunable by size. This method has enabled high-density arrays for optoelectronic applications, with advancements in ligand control improving monodispersity.^[33] Challenges in quantum material fabrication include precise doping control to introduce carriers without disrupting quantum coherence, as impurities can scatter electrons and alter band structures in materials like topological insulators. Strain engineering further complicates synthesis, requiring substrates or encapsulation to induce lattice mismatches that tune properties like bandgap or spin-orbit coupling, yet uniform strain distribution remains difficult at the nanoscale. High-pressure synthesis addresses specific cases, such as hydride superconductors, where diamond anvil cells compress hydrogen-rich compounds to gigapascal levels; for example, sulfur hydride (H₃S) was synthesized at 155 GPa in 2015, achieving a critical temperature of 203 K through pressure-stabilized cubic phases.^[34] These pressures demand specialized equipment to prevent sample contamination, highlighting ongoing hurdles in reproducibility. Subsequent advances have explored ternary hydrides, with reports as of November 2025 indicating signs of superconductivity near room temperature in such systems under megabar pressures.^[35]

Experimental Techniques

Experimental techniques play a crucial role in probing the quantum properties of materials, allowing researchers to directly observe electronic band structures, local density of states, transport behaviors, and dynamic processes that underpin phenomena like topological protection and strong correlations. These methods often require ultra-high vacuum environments, low temperatures, and high magnetic fields to isolate quantum effects from thermal noise and decoherence. Spectroscopic and microscopic tools, in particular, provide momentum- and space-resolved insights into the exotic states of quantum materials. Angle-resolved photoemission spectroscopy (ARPES) is a cornerstone technique for mapping the electronic band structure in momentum space, revealing features such as Dirac cones and surface states in topological insulators. In ARPES, ultraviolet photons eject electrons from the material surface, and their kinetic energy and emission angle are measured to reconstruct the dispersion relation E(k), enabling identification of gapless boundary modes protected by topology. For instance, ARPES studies of Bi₂Se₃ have demonstrated a single Dirac cone at the surface with a linear dispersion and high spin polarization exceeding 50%, confirming its topological insulator nature. Scanning tunneling microscopy (STM) complements ARPES by providing real-space imaging of the local density of states (LDOS) at atomic resolution, which can visualize quantum interference patterns and band edges. In graphene, a prototypical quantum material, STM combined with spectroscopy (STS) has resolved the V-shaped LDOS near the Dirac point, showcasing the massless Dirac fermion behavior with energy resolution down to meV scales. Transport measurements, conducted in low-temperature cryostats often cooled to millikelvin temperatures using dilution refrigerators, quantify quantum Hall effects and conductivity anomalies indicative of protected edge states or fractionalized excitations. The Hall effect, where a transverse voltage develops under perpendicular magnetic fields, reveals quantized plateaus at σ_xy = ν e²/h, with filling factor ν signaling topological order; in graphene, anomalous half-integer quantization (ν = ±2, ±6, etc.) arises from the fourfold spin-valley degeneracy of Dirac fermions. Noise spectroscopy extends these transport probes by analyzing current fluctuations to detect non-classical correlations, such as those from entangled electron pairs in hybrid systems. In semiconductor quantum dots, excess partition noise or negative correlations in superconducting-normal metal junctions serve as signatures of spin singlet entanglement, with noise power spectra showing deviations from Poissonian statistics that quantify concurrence up to 0.7. Advanced scattering and time-resolved techniques further elucidate magnetic and ultrafast dynamics in quantum materials. Neutron scattering excels at determining bulk magnetic structures, including antiferromagnetic order and spin fluctuations, due to neutrons' magnetic moment interaction with electron spins. In cuprate superconductors like La_{1.48}Nd_{0.4}Sr_{0.12}CuO_4, polarized neutron diffraction has mapped stripe-like charge and spin order with periods of ~4-5 lattice spacings, linking magnetism to high-T_c superconductivity. Time-resolved pump-probe spectroscopy, using femtosecond laser pulses to excite and probe the sample, captures nonequilibrium dynamics such as ultrafast demagnetization, where magnetization quenches on picosecond timescales via spin-orbit or electron-magnon scattering. Pioneering experiments on nickel films showed demagnetization times as short as 150 fs, a process now studied in quantum materials to track Floquet states or light-induced phase transitions. These techniques, often integrated, provide a multifaceted verification of quantum behaviors in materials.

Applications

In Quantum Computing

Quantum materials play a pivotal role in quantum computing by enabling the realization of qubits with enhanced stability and fault tolerance. Topological qubits, for instance, leverage Majorana zero modes in hybrid semiconductor-superconductor nanowires, such as InAs/Al structures, where these modes emerge at the ends of the wire in the topological phase. Proposed theoretically in 2010, these platforms exploit the non-Abelian statistics of Majorana fermions for inherently protected quantum information storage and manipulation, reducing susceptibility to local noise. Recent advances include Microsoft's Majorana 1 processor in 2025, utilizing topological qubits for improved stability.^[36] Superconducting qubits, particularly transmon designs, utilize Josephson junctions formed by thin insulating barriers between superconducting electrodes, typically aluminum oxide between niobium or aluminum layers, to create an anharmonic oscillator with controllable energy levels. This architecture, introduced in 2007, suppresses charge noise through a large shunt capacitance, allowing for robust single- and two-qubit gates essential for scalable quantum processors. Spin qubits in quantum materials like diamond offer another platform, with nitrogen-vacancy (NV) centers providing electron spins that couple to nuclear spins for extended coherence. These defect centers in diamond exhibit long spin dephasing times, often exceeding 1 ms under optimized conditions, far surpassing many other solid-state qubits and enabling room-temperature operation in some setups. A key advantage of topological qubits lies in their intrinsic error correction via topological protection, where quantum information is encoded non-locally across Majorana modes, making it robust against single-particle errors without active correction overhead. In contrast, spin qubits benefit from long coherence times that support more quantum operations before decoherence, while superconducting transmons enable fast gate speeds on the order of nanoseconds. Prominent examples include Google's Sycamore processor, a 53-qubit device using tunable transmon qubits fabricated from superconducting aluminum on silicon, which in 2019 demonstrated quantum supremacy by sampling random quantum circuits in 200 seconds—a task intractable for classical supercomputers. However, challenges persist, such as decoherence times limited to around 50–100 μs for superconducting qubits, necessitating advanced error mitigation techniques to scale beyond noisy intermediate-scale quantum regimes.^[37]^[38]

In Energy and Sensing Technologies

Quantum materials have revolutionized energy technologies by enabling efficient conversion and storage solutions. High-temperature superconductors (HTS), such as those based on rare-earth barium copper oxide tapes, are integral to advanced fusion reactors, where they generate strong magnetic fields necessary for plasma confinement. For instance, HTS current leads have been qualified for use in the International Thermonuclear Experimental Reactor (ITER), reducing cryogenic cooling requirements and improving overall system efficiency compared to traditional low-temperature superconductors.^[39] These materials operate at temperatures up to 77 K using liquid nitrogen, making them more practical for large-scale applications like fusion energy production.^[40] In thermoelectric energy harvesting, topological materials like bismuth-based topological insulators exhibit enhanced performance due to their protected surface states, which contribute to high Seebeck coefficients. The Seebeck coefficient S = -\frac{\Delta V}{\Delta T} quantifies the voltage generated per unit temperature difference, and in these materials, surface conduction boosts S while minimizing thermal conductivity, leading to potential figure-of-merit values zT > 1 at room temperature, with recent magneto-thermoelectric enhancements achieving zT ≈1.9 at around 180 K.^[41]^[42] For example, Bi_{88}Sb_{12} alloys under magnetic fields achieve magneto-Seebeck enhancements, yielding zT ≈0.7 at 300 K without field and up to ~1.9 at around 180 K with 0.7 T field, surpassing conventional thermoelectrics for waste heat recovery.^[43] Quantum materials also advance sensing technologies with exceptional precision. Quantum Hall effect devices, leveraging the quantized Hall resistance R_H = \frac{h}{\nu e^2} (where h is Planck's constant, \nu is the filling factor, and e is the electron charge), serve as primary standards for electrical resistance in metrology, offering stability better than 1 part in $10^9.^[44] These graphene-based sensors enable accurate ohm measurements without external references, supporting global electrical standards.^[45] Spin-based sensors utilizing nitrogen-vacancy (NV) centers in diamond provide nanoscale magnetometry with sensitivities around 1–100 nT/√Hz, detecting weak magnetic fields via optically detected magnetic resonance.^[46] Ensemble NV centers achieve broadband sensitivities of approximately 30 nT/√Hz at room temperature, enabling applications in biomedical imaging and geophysical surveys.^[47] Gradiometer configurations further enhance this to 4.6 nT/√Hz by suppressing common-mode noise.^[48] Prominent examples include perovskite quantum dots in solar cells, where colloidal CsPbI_3 QDs have driven efficiencies up to 18.3% as of 2025 through improved charge extraction and stability.^[49]^[50] These advances stem from surface passivation techniques that reduce non-radiative recombination, achieving power conversion efficiencies up to 18.3% for small-area devices. Additionally, hydride superconductors, such as carbonaceous sulfur hydride, demonstrated superconductivity near room temperature (about 15°C) in 2020 under high pressure (267 GPa), sparking interest in hydrogen-rich compounds for potential energy storage, though ambient-pressure realization remains unrealized experimentally as of 2025, with theoretical predictions for high-Tc candidates sparking continued interest.^[51]^[52]

Current Research and Challenges

Emerging Directions

One prominent emerging direction in quantum materials research involves twistronics, where the relative twist angle between stacked two-dimensional layers creates moiré superlattices that host exotic quantum states. In magic-angle twisted bilayer graphene, discovered in 2018, a twist angle of approximately 1.1° flattens the electronic bands, enabling correlated phenomena such as unconventional superconductivity and insulating states at low temperatures.^[53] This framework has expanded to reveal quantum criticality in twisted bilayers, where tuning the twist angle drives continuous phase transitions between semimetallic and insulating phases, as evidenced by angle-tuned Gross-Neveu criticality observed in recent experiments.^[54] These moiré systems exemplify how precise structural engineering can access tunable quantum phases, influencing ongoing efforts to design materials with controllable electronic correlations. Interdisciplinary integrations are advancing quantum materials toward practical hardware, particularly in artificial intelligence applications through memristors based on correlated oxides. These devices leverage strong electron correlations in oxides like high-entropy variants to mimic synaptic plasticity, enabling energy-efficient neuromorphic computing with tunable conductance states driven by oxygen vacancies or phase transitions.^[55] For instance, pulse-tunable quantum conductance in oxygen-vacancy-engineered TiO_{2-\delta} memristors demonstrates multilevel states suitable for neural network acceleration.^[56] Complementing this, van der Waals heterostructures have become a 2020s focal point, allowing the stacking of diverse atomic layers to engineer emergent properties like topological states and spin-orbit effects without lattice mismatch constraints.^[57] Recent syntheses via chemical vapor deposition highlight their potential for scalable integration in quantum devices. Recent advances underscore the pursuit of room-temperature quantum effects in organic materials, broadening accessibility beyond cryogenic conditions. In 2023, studies on triangular-lattice organic Mott insulators revealed unconventional charge carriers persisting at room temperature, linked to proximity to quantum spin liquid phases where spins remain disordered due to geometric frustration.^[58] Further, 2025 reports on organic quantum spin liquids, such as those probed in frustrated molecular systems, confirm tunable frustration that stabilizes these states, offering pathways for ambient quantum information processing.^[59] Parallelly, AI-driven discovery via machine learning has accelerated post-2020 innovations, with frameworks like Materials Expert-AI quantifying expert intuition to predict novel quantum phases in vast chemical spaces.^[60] These generative models, integrating quantum-accurate simulations, have identified high-entropy oxides and organic candidates with targeted properties, reducing experimental timelines from years to months.^[61]

Open Questions

One of the central open questions in quantum materials research concerns the interplay between strong electronic correlations and topological order. In materials exhibiting strong correlations, such as heavy-fermion compounds or Mott insulators, the precise mechanisms by which electron interactions drive emergent topological states remain unresolved, as traditional perturbative methods fail to capture these phenomena accurately.^[3] Advanced computational approaches like dynamical mean-field theory (DMFT) and density matrix renormalization group (DMRG) provide insights but struggle with higher-dimensional systems and real-time dynamics.^[3] Similarly, the role of quantum geometry—encompassing the wave function's geometric properties beyond the Berry curvature—in macroscopic responses like orbital magnetizations and nonlinear transport is an active area of debate, with implications for designing novel phases of matter.^[62]^[63] Another unresolved issue is the microscopic origin of high-temperature superconductivity in cuprates and iron-based materials, where the pairing mechanism eludes a complete theoretical description despite decades of study. While cuprates achieve critical temperatures up to 138 K under ambient pressure, the debate persists between phonon-mediated and unconventional mechanisms involving spin fluctuations or d-wave symmetry.^[3] Recent experiments on twisted bilayer graphene have revealed correlated insulating states and superconductivity, yet the exact role of lattice strain, disorder, and moiré patterns in stabilizing these phases is unclear.^[64] In topological superconductors, identifying robust Majorana zero modes for fault-tolerant quantum computing faces challenges from quasiparticle poisoning and hybridization effects, as evidenced in iron-based candidates like FeTe_{0.55}Se_{0.45}.^[3] Scalability and material quality pose significant practical challenges, particularly for integrating quantum materials into devices. Achieving defect-free synthesis of 2D materials like transition metal dichalcogenides or Weyl semimetals is hindered by environmental sensitivity and inconsistencies in growth techniques such as chemical vapor deposition, limiting reproducible exotic properties.^[3] Noise sources, including two-level systems (TLS) and flux noise from surface spins (with densities around $5 \times 10^{17}/m² in superconducting qubits), degrade coherence times to microseconds, far below theoretical limits.^[65] Open problems also include engineering interfaces to minimize decoherence in hybrid systems, such as semiconductor-superconductor junctions for topological qubits, and developing high-throughput characterization methods at millikelvin temperatures to correlate material defects with performance.^[65] These hurdles underscore the need for interdisciplinary advances in theory, fabrication, and measurement to unlock quantum materials' full potential.^[64]

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