High-temperature superconductivity
High-temperature superconductivity is the ability of certain materials, primarily ceramic oxides based on copper (cuprates) and more recently iron-based compounds or hydrides, to conduct electricity with zero resistance and expel magnetic fields below a critical temperature (T_c) significantly higher than those of conventional superconductors—typically above 30 K (–243 °C), allowing cooling with liquid nitrogen rather than expensive liquid helium.[1] These materials exhibit superconductivity at temperatures up to 135 K under ambient pressure in cuprates like HgBa2Ca2Cu3O8+δ, marking a breakthrough from the previous limit of around 23 K for conventional superconductors explained by Bardeen-Cooper-Schrieffer (BCS) theory.[2] Unlike conventional low-temperature superconductors, which rely on phonon-mediated electron pairing, the mechanism in high-temperature superconductors involves unconventional pairing, possibly d-wave symmetry in cuprates, and remains a subject of intense research despite partial theoretical insights.[3] The discovery of high-temperature superconductivity began in 1986 when IBM researchers J. Georg Bednorz and K. Alex Müller observed superconductivity at 35 K in a lanthanum-barium-copper-oxide (La-Ba-Cu-O) ceramic, earning them the 1987 Nobel Prize in Physics for challenging the prevailing belief that higher T_c required unattainable conditions.[4] This sparked a global race, leading to the rapid identification of yttrium-barium-copper-oxide (YBa2Cu3O7, or YBCO) in 1987 with a T_c of 93 K—the first superconductor workable at liquid nitrogen temperatures (77 K)—and subsequent cuprate families like bismuth-strontium-calcium-copper-oxide (BSCCO) and thallium-based compounds pushing T_c to 135 K.[4] In 2008, iron-based superconductors (pnictides and chalcogenides) were discovered with T_c up to 56 K, offering new doping tunability and potentially simpler fabrication, while high-pressure hydride superconductors like H3S (T_c ≈ 203 K at 155 GPa) and LaH10 (T_c ≈ 250 K at 170 GPa) have approached room-temperature superconductivity, though practical applications remain limited by extreme conditions.[5][3] High-temperature superconductors hold transformative potential for energy-efficient technologies, including lossless power transmission cables, compact MRI magnets, efficient motors, and quantum computing components, due to their ability to carry currents and magnetic fields orders of magnitude higher than low-temperature superconductors at more accessible temperatures.[6] However, challenges persist, including the need for better understanding of the pairing mechanism—often linked to quantum critical points, stripe orders, or pseudogaps in cuprates—and fabrication of long, high-current wires free of weak links and impurities, with ongoing efforts focusing on scalable thin-film and tape technologies like REBCO (rare-earth barium copper oxide).[7] Recent advances, such as atomic-scale imaging confirming charge-density waves and pair-density waves in cuprates, the emergence of nickelate superconductors with T_c up to ~40 K at ambient pressure, and progress in stabilizing high-pressure hydrides, continue to refine theories toward a unified microscopic description as of 2025.[8][9][10]Overview and Fundamentals
Definition and Key Characteristics
High-temperature superconductivity (HTS) denotes the ability of certain materials to exhibit superconductivity—complete loss of electrical resistance and perfect diamagnetism—at temperatures substantially exceeding those of conventional superconductors, generally defined as critical temperatures (T_c) above 30 K. This threshold surpasses the theoretical upper limit predicted by Bardeen-Cooper-Schrieffer (BCS) theory for phonon-mediated pairing, around 30 K, enabling the use of more accessible cooling methods like liquid nitrogen (boiling point 77 K) instead of scarce liquid helium (4.2 K). The highest verified ambient-pressure T_c in HTS materials reaches approximately 133 K, highlighting their potential for practical applications despite ongoing challenges in scalability.[11][12] At its core, superconductivity in HTS materials relies on the formation of Cooper pairs, bound states of electrons mediated by interactions (often unconventional beyond phonons), which collectively occupy a single quantum state below T_c, resulting in macroscopic quantum coherence. This pairing opens an energy gap in the electronic density of states, suppressing single-particle excitations and enabling dissipationless current flow. Key observable characteristics include zero DC electrical resistance, allowing persistent currents without decay; the Meissner effect, where magnetic fields are expelled from the material's interior, manifesting perfect diamagnetism; and flux quantization, wherein magnetic flux through a superconducting loop is confined to discrete multiples of the flux quantum h/2e. These traits underscore the quantum nature of HTS, distinguishing it from normal metallic conduction.[13] The discovery of HTS in 1986 marked a pivotal shift, with initial observations of superconductivity above 30 K sparking global research into non-conventional mechanisms.[14]Distinction from Conventional Superconductivity
Conventional superconductivity, as described by the Bardeen-Cooper-Schrieffer (BCS) theory, arises from phonon-mediated pairing of electrons into Cooper pairs with isotropic s-wave symmetry. In these materials, the critical temperature (Tc) is typically limited to around 30 K under ambient pressure, with practical examples like Nb3Sn achieving a Tc of approximately 18 K.[15] This pairing mechanism relies on attractive interactions between electrons via lattice vibrations, leading to relatively long coherence lengths on the order of tens to hundreds of nanometers. High-temperature superconductors (HTS), in contrast, exhibit Tc values exceeding 30 K, often up to 130 K or higher in cuprates, enabling unconventional pairing symmetries such as d-wave in cuprate materials.[16] These systems, particularly cuprates, are characterized by stronger electron correlations, stemming from their parent compounds being Mott insulators, which necessitate doping to induce superconductivity.[17] The layered crystal structures of HTS materials introduce significant anisotropy in their superconducting properties, with superconductivity primarily confined to conducting planes, and their behavior is highly sensitive to chemical doping and applied pressure.[18] Unlike conventional superconductors, HTS display short coherence lengths, typically 1-2 nm, which enhances type-II behavior but complicates vortex management.[19] The higher Tc in HTS allows for cooling with liquid nitrogen at 77 K, substantially reducing cryogenic costs compared to the liquid helium required for conventional superconductors below 4.2 K.[20] This advantage opens pathways toward practical applications like power transmission and magnets at more accessible temperatures, with ongoing research aiming for room-temperature superconductivity under pressure.[20] However, HTS materials pose challenges, including their ceramic-like brittleness, which hinders fabrication into flexible wires, and difficulties in achieving effective flux pinning to maintain high critical currents in magnetic fields.[21][22] Empirically, HTS superconductivity is often non-phonon mediated, as evidenced by the negligible or inverse isotope effect on Tc, contrasting with the positive isotope effect in phonon-driven conventional systems.[23] Above Tc, many HTS exhibit a pseudogap phase, a partial suppression of low-energy electronic states without full superconducting order, observed through techniques like angle-resolved photoemission spectroscopy. Additionally, stripe phases—ordered modulations of spin and charge densities—emerge in underdoped cuprates, linking to the pseudogap and influencing the superconducting dome in phase diagrams.[24] Both HTS and conventional superconductors share the Meissner effect, expelling magnetic fields below Tc.Historical Development
Early Superconductivity and Low-Temperature Limits
The discovery of superconductivity occurred in 1911 when Dutch physicist Heike Kamerlingh Onnes observed that the electrical resistance of pure mercury abruptly dropped to zero at approximately 4.2 K, the boiling point of liquid helium, during low-temperature experiments at his Leiden laboratory.[25] This phenomenon, initially termed "superconductivity," was unexpected and marked the first evidence of a new quantum state of matter where electrons could flow without dissipation. Onnes subsequently confirmed zero resistance in other elemental metals, such as lead (Tc ≈ 7.2 K) and tin (Tc ≈ 3.7 K), establishing that superconductivity was a general property of certain materials at cryogenic temperatures below their critical temperature (Tc).[13] In 1933, German physicists Walther Meissner and Robert Ochsenfeld identified another defining characteristic: the expulsion of magnetic fields from the interior of superconductors below Tc, known as the Meissner effect, which distinguishes superconductivity from perfect conductivity and implies perfect diamagnetism.[26] This discovery, observed in lead and tin samples, provided crucial evidence that superconductivity involves a reorganization of the material's electronic structure. Experimental investigations in the following decades revealed an isotope effect, where the critical temperature inversely scaled with the atomic mass of the constituent atoms, as independently demonstrated in mercury isotopes by Emanuel Maxwell and by C. A. Reynolds and colleagues in 1950; for mercury, Tc followed the relation Tc ∝ M^{-1/2}, suggesting lattice vibrations (phonons) mediated the superconducting pairing.[27] The microscopic theory of superconductivity was formulated in 1957 by John Bardeen, Leon Cooper, and John Robert Schrieffer (BCS theory), which explained the isotope effect and Meissner effect through the formation of Cooper pairs—bound electron pairs arising from an attractive interaction mediated by phonons in the crystal lattice.[13] This theory predicted that conventional superconductors, primarily elemental metals and simple alloys with Tc below 10 K, operated via weak electron-phonon coupling. Efforts to raise Tc focused on intermetallic compounds, particularly A15-phase materials like Nb3Sn (Tc ≈ 18 K, discovered in 1954), which exhibited stronger coupling and higher Tc. By 1973, sputtered Nb3Ge films achieved the pre-1986 record of Tc ≈ 23 K, but further increases stalled due to theoretical limits from strong electron-phonon coupling, estimated around 30 K by the McMillan formula derived from BCS.[28] Pre-1986 research emphasized optimizing A15 compounds and other intermetallics through pressure, doping, and thin-film techniques, yet no material exceeded 23 K reliably, creating a perception of stagnation in achieving room-temperature superconductivity.[28] This low-temperature constraint necessitated liquid helium cooling (4.2 K), limiting practical applications and motivating the search for higher-Tc mechanisms. The stage was set for the revolutionary discovery of cuprate superconductors in 1986, which shattered these limits.[28]Discovery of Cuprates and the 1980s Revolution
In 1986, J. Georg Bednorz and K. Alex Müller at IBM's Zurich Research Laboratory reported the observation of superconductivity in a ceramic oxide material composed of lanthanum, barium, copper, and oxygen (La-Ba-Cu-O), with a critical temperature (Tc) onset of approximately 35 K. This marked the first time superconductivity had been achieved above the 30 K threshold in an oxide system, surpassing previous records limited by conventional metallic superconductors and challenging the prevailing understanding of superconducting mechanisms.[29] Their discovery, published in Zeitschrift für Physik B, demonstrated a sharp drop in electrical resistance and the Meissner effect in the material, confirming zero-resistance and perfect diamagnetism at these elevated temperatures. For this breakthrough, Bednorz and Müller were awarded the Nobel Prize in Physics in 1987, recognizing their role in opening the era of high-temperature superconductivity (HTS). Building on this foundation, in early 1987, Ching-Wu Chu and Maw-Kuen Wu at the University of Houston synthesized yttrium barium copper oxide (YBa₂Cu₃O₇, known as YBCO), achieving a Tc of 93 K under ambient pressure.[30] This was the first superconductor to operate above the boiling point of liquid nitrogen (77 K), eliminating the need for costly liquid helium cooling and enabling practical applications at more accessible temperatures.[30] The YBCO material exhibited stable and reproducible transitions, verified through resistive and magnetic measurements, and its orthorhombic perovskite structure with copper-oxygen planes became a hallmark of cuprate superconductors.[30] The discoveries ignited an international race to push Tc higher, resulting in a rapid escalation of records within the cuprate family. By 1988, bismuth- and thallium-based cuprates reached Tc values above 100 K, and in 1993, mercury-based cuprates (HgBa₂Ca₂Cu₃O₈+δ) achieved a record Tc of 135 K at ambient pressure, the highest for cuprates to date. This period saw an explosion of research activity, with over 12,000 scientific papers published on HTS materials by the early 1990s, reflecting collaborations across laboratories worldwide.[31] The 1980s revolution profoundly shifted the superconductivity paradigm from phonon-mediated electron pairing in conventional BCS theory to unconventional electronic mechanisms, such as those involving strong correlations and antiferromagnetic fluctuations in copper-oxide planes.[32] This prompted massive increases in global research funding, including a U.S. commitment of $100 million in 1987 for HTS studies, fostering advancements in materials synthesis and potential technologies like power transmission and magnets.[33]Post-1990 Advances and New Material Classes
Following the revolutionary discoveries of the 1980s, research in the 1990s and early 2000s focused on optimizing cuprate superconductors to achieve higher critical temperatures (Tc) and better material properties. In 1993, mercury-based cuprates such as HgBa2Ca2Cu3O8 were synthesized, reaching a record Tc of 135 K at ambient pressure, surpassing previous cuprate records and establishing mercury cuprates as the highest-Tc family to date. These advances involved precise control of oxygen stoichiometry and doping levels to enhance superconducting dome widths in phase diagrams. Concurrently, efforts improved flux pinning and critical current densities in cuprates like YBa2Cu3O7 for practical applications, though intrinsic Tc limits persisted. A significant milestone came in 2001 with the discovery of superconductivity in magnesium diboride (MgB2), an inexpensive intermetallic compound exhibiting bulk superconductivity at Tc = 39 K under ambient conditions.[34] Unlike cuprates, MgB2 operates via phonon-mediated pairing in a two-band BCS framework, bridging conventional and unconventional superconductivity, and its "high-Tc" status relative to earlier non-oxide materials spurred interest in phonon-based mechanisms for elevated temperatures. The 2000s also saw the emergence of iron-based superconductors in 2008, with LaFeAsO1-xFx achieving Tc up to 26 K initially, rapidly optimized to 55 K in SmFeAsO1-xFx through rare-earth substitutions. These iron pnictides introduced a new class with layered structures analogous to cuprates but featuring iron-arsenic planes, expanding the material landscape beyond oxides. The 2010s brought further diversification with the 2019 discovery of superconductivity in infinite-layer nickelates, such as Nd0.8Sr0.2NiO2 thin films, exhibiting Tc ≈ 15 K under ambient pressure. Subsequent refinements raised Tc to around 40 K in related systems like Pr0.8Sr0.2NiO2 and bilayers, highlighting d-electron correlations similar to cuprates but without copper, and prompting comparisons in electronic structure via angle-resolved photoemission spectroscopy. In 2024, high-entropy alloys emerged as a novel class, with disordered multicomponent structures like (NbTaHfZrTi) showing robust superconductivity (Tc ≈ 7.5 K) and enhanced mechanical stability due to entropy-stabilized phases, offering potential for wire applications.[35] Into the 2020s, pressurized hydrides marked dramatic progress, beginning with the 2015 discovery of superconductivity in hydrogen sulfide (H3S) with Tc ≈ 203 K at 155 GPa, followed by lanthanum decahydride (LaH10) achieving Tc > 200 K (up to 260 K) at megabar pressures around 170-200 GPa in 2019, confirmed via diamond anvil cell experiments and representing the closest approach to room-temperature superconductivity to date, though reproducibility and ambient viability remain debated.[36][37] By 2025, efforts to stabilize such phases at ambient pressure advanced, including University of Houston researchers' synthesis of pressure-quenched Bi0.5Sb1.5Te3 retaining superconductivity (Tc up to ≈ 10 K) without external pressure, demonstrating a pathway for high-pressure-induced states in topological materials.[38] Copper-free oxides also progressed, with engineered nickelate variants achieving Tc ≈ 40 K in 2025, bypassing copper's toxicity and scarcity while mimicking cuprate doping effects.[39] Additionally, the HTSC-2025 dataset compiled approximately 140 theoretically predicted ambient-pressure superconductors from 2023-2025, incorporating AI-driven screenings of hydrides and alloys to guide experimental pursuits toward room-Tc goals.[40] Ongoing research continues to target ambient room-temperature superconductivity through these diverse classes.Superconducting Materials
Cuprate Superconductors
Cuprate superconductors constitute the primary class of high-temperature superconductors, featuring layered structures derived from perovskite motifs where copper-oxygen (CuO₂) planes serve as the active layers for superconductivity. These planes are embedded within charge-reservoir blocks that provide doping carriers, typically through the incorporation of rare-earth or alkaline-earth elements, enabling hole doping into the CuO₂ layers. The general formula for many cuprates follows the pattern AO_{x} (A' O_y){m} (CuO₂){n+1}, where the number of CuO₂ planes (n) influences the critical temperature (T_c), with optimal performance often observed for n=2 or 3. The first cuprate superconductor discovered was La_{2-x}Sr_xCuO_4, reported in 1986 with a T_c of approximately 35 K, marking the onset of the high-temperature superconductivity era. Subsequent developments yielded yttrium barium copper oxide (YBCO), with the orthorhombic phase YBa_2Cu_3O_{7-δ} achieving a T_c of 93 K at ambient pressure, the first material to superconduct above liquid nitrogen temperature. Bismuth strontium calcium copper oxide (BSCCO), particularly the Bi_2Sr_2Ca_2Cu_3O_{10+δ} (Bi-2223) phase, has been pivotal for practical applications due to its formability into high-current wires exceeding 100 A at 77 K. Mercury-based cuprates, such as HgBa_2Ca_2Cu_3O_{8+δ} (Hg-1223), hold the ambient-pressure T_c record at 134 K, with enhancements to 138 K under modest pressure and up to 166 K at 23 GPa.[41][42] Superconductivity in cuprates emerges upon hole doping the parent antiferromagnetic Mott insulator, with T_c peaking at an optimal doping level of approximately 0.16 holes per Cu atom in the CuO₂ planes, beyond which an overdoped regime suppresses T_c. This doping dependence delineates a dome-shaped phase diagram, where underdoping leads to competing orders. Distinctive features include d-wave pairing symmetry, confirmed through phase-sensitive measurements, which contrasts with s-wave pairing in conventional superconductors and implies nodes in the superconducting gap. Additionally, cuprates exhibit stripe order—modulated charge and spin densities—in certain underdoped regimes, as observed in La-based compounds, and a pseudogap phase above T_c characterized by partial suppression of low-energy states. Strong anisotropy arises from the quasi-two-dimensional nature, with superconducting coherence lengths far shorter along the c-axis perpendicular to the ab-planes compared to in-plane directions.[43]Iron-Based Superconductors
Iron-based superconductors represent a major class of high-temperature superconductors discovered in 2008, more than two decades after the cuprates, featuring iron atoms as the key structural and electronic component rather than copper. The first member, LaFeAsO doped with fluorine, exhibited superconductivity at a critical temperature (Tc) of 26 K, marking the beginning of intensive research into this family.[44] Unlike cuprates, which rely on CuO2 planes, iron-based materials display structural diversity across several families, enabling a range of doping strategies and pressure effects to tune superconductivity. These compounds have achieved Tc values up to around 55 K in optimally doped variants, positioning them as the second-highest Tc class after cuprates.[45] The primary structural families include the 1111 (e.g., LnFeAsO, where Ln is a rare earth), 122 (e.g., AeFe2As2, Ae = Ba, Sr), 111 (e.g., AFeAs, A = Li, Na), and 11 (e.g., FeSe, FeTe) types, each characterized by layered architectures with iron-pnictogen or iron-chalcogen units. Representative examples and their maximum Tc values are summarized below:| Family | Prototype Compound | Initial/Maximum Tc (K) | Key Doping/Condition |
|---|---|---|---|
| 1111 | LaFeAsO | 26 / 55 | F-doping; rare-earth substitution (e.g., SmFeAsO)[44][45] |
| 122 | BaFe2As2 | ~38 | K-doping (e.g., Ba0.6K0.4Fe2As2)[46] |
| 111 | LiFeAs | 18 | Stoichiometric, no doping needed[47] |
| 11 | FeSe | 8 / 37 | Ambient; under pressure |