The discovery of cuprate high-temperature superconductors impacted science and technology considerably and the excitement in this field has been continuing for the past 30 years. To date, more than two hundreds of cuprate superconductors have been found,^[41] among which HgBa₂Ca₂Cu₃O_8+x exhibits the highest T_C up to 134 K at ambient pressure.^[28] Many efforts have been made to push T_C higher and the results have been documented in a long list. Pressure was found to play a key role in enhancing T_C in this family. Most impressive is the application of pressure on HgBa₂Ca₂Cu₃O_8+x, enhancing its T_C to 164 K at ∼ 30 GPa,^[29,30] as shown in Fig. 3, which remains the record for bulk superconducting materials. Another example that shows pressure-induced enhancement of T_C is found in optimally doped trilayer Bi₂Sr₂Ca₂Cu₃O_10+x (Bi-2223), in which its T_C is increased from 108 K at ambient pressure up to 136 K at 36 GPa.^[14] It is considered that the natural appearance of an inhomogeneous charge distribution among the inner and outer CuO₂ planes makes the trilayered Bi-2223 to obtain higher T_C under pressure.

Fig. 3.

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	Fig. 3. (color online) Pressure–temperature phase diagram of mercury-bearing cuprate superconductors, showing a TC up to 164 K. The data are taken from Ref. [29].

The discovery of LaFeAsO_1−xF_x superconductors with a T_C of 26 K in 2008^[31] brought new excitement to the field of superconductivity and sparked intense research activity in the past 10 years. Many research groups have made great advances in understanding this new kind of high-T_C superconductor with the apparent hope of gaining insight into the underlying superconducting mechanism.^[42–48] There are more than 15,000 papers that have been published so far.^[48]

Pressure as a ‘clean way’ plays a prominent role in the search for Fe-based superconductors with higher superconducting transition temperature. High-pressure resistivity measurements of LaFeAsO_1−xF_x in a DAC revealed that its T_C can be increased to 43 K at ∼ 4 GPa,^[18] as shown in Fig. 4. The obtained high pressure result aids the discoveries of REOFFeAs (where RE = Ce, Nd, Pr, Sm, Gd, or Tb) superconductors with T_C > 50 K at ambient pressure through replacing La with smaller RE ions.^[49–55]

Fig. 4.

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Fig. 4. (color online) Superconducting properties in compressed LaO0.89F0.11FeAs. (a) Results obtained from measurements in a piston–cylinder pressure device (b) Magnetic dependence of TC under pressure. (c) Results obtained from measurements in a DAC, showing pressure-induced enhancement of TC in the superconductor. (d) Pressure–temperature phase diagram. Reproduced with permission from Ref. [18].

Because parent compounds were found in one of the subsystems of FeAs-based superconductors, whose chemical formula is A′Fe₂As₂ (where A′ = Ca, Sr, or Ba) and EuFe₂As₂,^[56–59] this provides an opportunity to identify the effect of pressure in developing superconductivity and the correlation between the magnetic ordered state and the superconducting state in this new type of superconductor. High-pressure studies indicated that the superconductivity of these compounds is very sensitive to the pressure environments.^{[23–26,60–64]} The physics behind this is considered to be associated with pressure-induced lattice distortion.^[65–67]

More recently, high-pressure studies on the antiferromagnetic compound Ca_0.73La_0.27FeAs₂ revealed unexpected phenomena: a first-order transition between antiferromagnetic (AFM) and superconducting phases and a bi-critical point at ∼ 3 GPa and 26 K,^[37] as shown in Fig. 5. These results are expected to provide a valuable experimental foundation for understanding the interplay between the AFM and superconducting phases, a most challenging issue in the field of superconductivity.

Fig. 5.

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Fig. 5. (color online) Temperature–pressure phase diagrams obtained at different magnetic fields for Ca0.73La0.27FeAs2 single crystals. The acronyms PM, AFM, and SC stand for paramagnetic, antiferromagnetic, and superconducting phases, respectively. The magenta-colored circles and custom diamonds represent the temperature of the AMF phase transition detected from two-run electrical resistance measurements (TM(R-1) and TM(R-2)) and heat capacity TM(C) measurements under hydrostatic pressure conditions. The green diamonds and blue circles stand for the superconducting transition temperature determined from the resistance TC(R-1) and ac susceptibility TC(ac) measurements, respectively. The position of the red star denotes the location of the bi-critical point, which is determined by an intersection of extrapolated lines of the pressure-dependent TM and TC. The gray circles are the data extracted from the heat capacity results. The radial red line shows the suppressed tendency of TC by the magnetic field. Reproduced with permission from Ref. [37].

An FeSe superconductor with a T_C of 8 K was discovered by Wu’s group in 2008.^[32] Surprisingly, the T_C can be increased to ∼ 37 K at 8.9 GPa by application of pressure.^[17] The pressure-induced dramatic enhancement of T_C in FeSe was considered to be attributed to the pressure-driven increment of spin fluctuation.^[68]

In 2011, alkaline iron selenide superconductors, A_1−xFe_2−ySe₂ (where A = K, Rb, Tl/K, or Tl/Rb), with a transition temperature of ∼ 32 K were discovered,^[69–72] adding a new subsystem to the family of Fe-based superconductors. The remarkable feature of these superconductors is that the superconducting (SC) phase coexists with an antiferromagnetic insulating phase (245 phase) in the microstructure, which is different from that of the other known FeAs-based superconductors.^{[31,46,51,73–75]} Unexpectedly, high-pressure measurements on A_1−xFe_2−ySe₂ (where A = K, Rb, Tl/K, or Tl/Rb) revealed that the pressure induces a second superconducting phase with a T_C as high as 48.7 K after the first superconducting phase is suppressed by pressure,^[36] as shown in Fig. 6. This is the first example of a pressure-induced reemergence of superconductivity among all high-temperature superconductors. It was proposed that these two superconducting phases may originate from different microphysical mechanisms. Further studies demonstrated that such a pressure-induced reemergence of superconductivity is associated with a quantum criticality.^[76]

Fig. 6.

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Fig. 6. (color online) Pressure–superconducting transition temperature (TC) phase diagram for Tl0.6Rb0.4Fe1.67Se2, K0.8Fe1.7Se2 and K0.8Fe1.78Se2. The symbols represent the pressure–temperature conditions at which TC values were observed from the resistive and alternating current susceptibility measurements; symbols with downward arrows represent the absence of superconductivity to the lowest temperature (4 K). All Tl0.6Rb0.4Fe1.67Se2, K0.8Fe1.7Se2, and K0.8Fe1.78Se2 samples show two superconducting regions (SC-I and SC-II) separated by a critical pressure at ∼ 10 GPa. NSC is the nonsuperconducting region at pressure > 13.2 GPa. The maximum TC is found to be 48.7 K in K0.8Fe1.7Se2 at a pressure of 12.5 GPa. At higher pressures > 13.2 GPa, the samples are nonsuperconducting. Error bars are one standard deviation. Reproduced with permission from Ref. [36].

Owing to the coexistence of the antiferromagnetic insulating and superconducting phases in these superconductors, pressure plays a unique role in revealing its intrinsic physics. To uncover the puzzling issues on the role played by the antiferromagnetic insulating phase in developing the ambient-pressure superconducting phase, comprehensive experimental measurements on the compound with a pure antiferromagnetic insulating phase and mixed phases (antiferromagnetic insulating phase plus superconducting phase) were performed. The results revealed two important issues: 1. the antiferromagnetic insulating phase is not the parent phase of the SC-II phase, and 2. it is a crucial phase for stabilizing the SC-I phase.^[4,77,78]

The discovery of the first heavy-fermion superconductor, CeCu₂Si₂, by Steglich in 1979 not only imitated a new field for studies of unconventional superconductivity but posed a fundamental challenge for understanding the superconducting mechanism in a unified way.^[79] Up to now, more than 40 heavy-fermion superconductors have been found.^[80,81] Because most non-superconducting heavy-fermion compounds are antiferromagnetic, heavy-fermion superconductors belong to the family of unconventional superconductors.^[8,81–85]

A general consensus held for unconventional superconductors is that the superconductivity develops in the vicinity of a suppressed AFM order state, thus, pressure can be used as an effective control parameter to suppress the AFM phase and develop superconductivity.^[8,23,37] Based on a number of experimental results, it is believed that antiferromagnetic spin fluctuation is the driving force for the development of the superconducting transition. In addition, valence instability is considered to be another key factor for the development of superconductivity in heavy-fermion compounds.^[86] A famous example is the observation of pressure-induced reemergence of superconductivity in CeCu₂Si₂, whose pressure–T_C phase diagram exhibits two superconducting domes,^[8] as shown in Fig. 7. The accepted explanations are that the antiferromagnetic spin fluctuation is responsible for the first superconducting phase while the valence fluctuation is related to the emergence of the second superconducting phase.^[8,87]

Fig. 7.

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Fig. 7. (color online) Schematic phase diagram of Ce-based narrow-band metals. At low density, the Ce 4f orbitals are singly occupied and carry a static moment (arrows), subject to long-range antiferromagnetic order (red line). Increasing the lattice density (e.g., by hydrostatic pressure) raises the hybridization between more extended orbitals (single-hatched region) and the 4f states, leading to dynamical frustration (Kondo spin-flips; double arrows), which in turn suppresses long-range order and induces an anomalous normal state. In the simplest case, at some distance from the quantum critical point at Pc1, where magnetic order is fully suppressed, this state can be modeled as a high-effective-carrier-mass Fermi liquid. Sufficiently close to Pc1, magnetically mediated pairing may induce unconventional superconductivity (red dome). Further increasing the hybridization between localized and extended orbitals leads eventually to a less correlated, metallic state (intermediate valence region), in which the 4f electrons delocalize through stronger hybridization with ligand states and occupy wider energy bands at the Fermi energy (cross-hatched region). The transition from the heavy fermion to the intermediate valence configuration may proceed through a first-order phase transition that involves a collapse of the unit cell volume with no change in lattice symmetry (green dashed line), driven by the gain in cohesive energy associated with the wide-band 4f electron configuration. If the critical endpoint of the first-order line is low enough, the system may become sufficiently soft at low temperatures to allow a superconducting state to form around the quantum phase transition associated with the volume collapse, at Pc2 (green dome). Reproduced with permission from Ref. [8].

Recently, progress has been made in the pressurized non-centrosymmetric CeTX₃ (where T = Co, Rh, or Ir and X = Si or Ge) family. Though ambient-pressure unit-cell volumes and critical pressures for superconductivity vary substantially across the series, all family members reach a maximum superconducting transition temperature at a common critical cell volume (V_crit), and the at V_crit is found to increase with increasing spin–orbit coupling strength of the d electrons.^[88] These correlations show that substantial Kondo and spin–orbit couplings favor superconductivity in this family.

High-entropy alloys (HEAs) are a new class of materials that are made from multiple transition-metal elements in equimolar or near-equimolar ratios.^[89,90] The elements in HEAs arrange themselves randomly on the crystallographic positions of a simple lattice.^[91–94] In many respects, HEAs exhibit excellent properties, including excellent specific strength,^[95] ultrahigh fracture toughness at cryogenic temperatures,^[96,97] and superior mechanical performance at high temperatures,^[98] implying that HEAs have great potential for application. Significantly, superconductivity has been found in HEAs, making them more attractive in the field of materials science.^[99,100]

Intriguingly, one of the HEA superconductors, (TaNb)_0.67(HfZrTi)_0.33, displays extraordinarily robust zero-resistance superconductivity under pressure as high as 190 GPa, a pressure that falls within that of the outer core of the earth [101], as shown in Fig. 8. These results revealed by high-pressure studies indicate that this HEA superconductor is a promising candidate for applications under extreme conditions.

Fig. 8.

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Fig. 8. (color online) Phase diagram of superconducting transition temperature versus applied pressure up to 190.6 GPa for the HEAs, combined with plots of the corresponding resistance vs. temperature. Blue triangles and dark-yellow balls in the diagram represent the zero-resistance superconducting transition temperature TC obtained from measurements at pressure <60 GPa, while the red and green balls stand for zero-resistance TC from the measurements at pressures up to 179.2 and 190.6 GPa, respectively. Reproduced with permission from Ref. [101].

Superconductivity was first discovered in element Hg by Onnes,^[102] initiating the research field of superconductivity. Later on, numerous element superconductors were discovered. Up to now, thirty three elements are found to be superconducting at ambient pressure.^[103,104] By application of pressure, twenty four non-superconducting elements become superconductors,^[105,106] as described in the periodic table (Table 1).

Table 1.

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	Table 1. Periodic table displaying element superconductors at ambient pressure (highlighted in red) and superconductors (highlighted in blue) at high pressure.

Remarkably, pressure can also enhance the superconducting transition temperature for the ambient-pressure element superconductors. Examples can be found in compressed zirconium (with its T_C increasing from 0.55 K at ambient pressure to ∼ 11 K at 30 GPa^[107]) and vanadium (with its T_C increasing linearly with pressure and reaching ∼ 17 K at 120 GPa^[108]). The highest T_C value (29 K) in elements is found in pressurized calcium, as shown in Fig. 9.^[109,110]

Fig. 9.

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	Fig. 9. (color online) Pressure dependence of TC for element Ca. The data are taken from Refs. [109] and [110]

Because elements have a pure phase, they are ideal candidates to investigate fundamental physics. Recently, progress has been made in single-crystal black phosphorus.^[111,112] Complementary measurements of high-pressure resistance, the Hall effect, and the crystal structure on black phosphorus reveal that hole carriers play an important role in developing superconductivity and enhancing T_C in a single cubic superconductivity in a rhombohedral superconducting phase,^[113] as shown in Fig. 10.

Fig. 10.

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Fig. 10. (color online) Structural, superconducting, and Hall coefficient (RH) phase diagram of black phosphorus at different pressures. (a) Pressure–temperature phase diagram combined with structural phase information. Here SM and SCRho-h represent semimetal and superconducting phases with rhombohedral structures and dominant hole carriers, respectively. SCcubic-e and SCcubic-h stand for the superconducting phase with cubic structure and dominance of electron carriers and hole carriers, respectively. (R-1) and (R-2) represent the onset temperature of superconducting transitions determined from resistance measurements for run 1 and run 2. TC(ac) represents the superconducting transition temperature determined by ac susceptibility measurements. (b) Pressure dependent RH measured at 15 K. The inset displays the detailed changes in RH at the structural phase-transition boundaries. The pink and blue solid points represent Hall coefficients obtained from two independent runs. Pc1 and Pc2 stand for the critical pressures of the Lifshitz transitions. Reproduced with permission from Ref. [113].