The 2021 room-temperature superconductivity roadmap

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

Retraction: Pressure-Induced Superconducting State of Europium Metal at Low Temperatures [Phys. Rev. Lett. 102, 197002 (2009)]

Retraction of DOI: 10.1103/PhysRevLett.102.197002.

A15 Nb3Si: a 'high'Tcsuperconductor synthesized at a pressure of one megabar and metastable at ambient conditions

A15 Nb₃Si is, until now, the only 'high' temperature superconductor produced at high pressure (∼110 GPa) that has been successfully brought back to room pressure conditions in a metastable condition. Based on the current great interest in trying to create metastable-at-room-pressure high temperature superconductors produced at high pressure, we have restudied explosively compressed A15 Nb₃Si and its production from tetragonal Nb₃Si. First, diamond anvil cell pressure measurements up to 88 GPa were performed on explosively compressed A15 Nb₃Si material to traceT_cas a function of pressure.T_cis suppressed to ∼5.2 K at 88 GPa. Then, using theseT_c(P) data for A15 Nb₃Si, pressures up to 92 GPa were applied at room temperature (which increased to 120 GPa at 5 K) on tetragonal Nb₃Si. Measurements of the resistivity gave no indication of any A15 structure production, i.e. no indications of the superconductivity characteristic of A15 Nb₃Si. This is in contrast to the explosive compression (up toP∼ 110 GPa) of tetragonal Nb₃Si, which produced 50%-70% A15 material,T_c= 18 K at ambient pressure, in a 1981 Los Alamos National Laboratory experiment. This implies that the accompanying high temperature (1000 °C) caused by explosive compression is necessary to successfully drive the reaction kinetics of the tetragonal → A15 Nb₃Si structural transformation. Our theoretical calculations show that A15 Nb₃Si has an enthalpy vs the tetragonal structure that is 70 meV atom^-1smallerat 100 GPa, while at ambient pressure the tetragonal phase enthalpy is lower than that of the A15 phase by 90 meV atom^-1. The fact that 'annealing' the A15 explosively compressed material at room temperature for 39 years has no effect shows that slow kinetics can stabilize high pressure metastable phases at ambient conditions over long times even for large driving forces of 90 meV atom^-1.

Unusual effects of Be doping in the iron-based superconductor FeSe

Recent superconducting transition temperatures (T _c) over 100 K for monolayer FeSe on SrTiO₃ have renewed interest in the bulk parent compound. In KCl:AlCl₃ flux-transport-grown crystals of FeSe_0.94Be_0.06, FeSe_0.97Be_0.03 and, for comparison, FeSe, this work reports doping of FeSe using Be-among the smallest of possible dopants, corresponding to an effective 'chemical pressure'. According to lattice parameter measurements, 6% Be doping shrank the tetragonal FeSe lattice equivalent to a physical pressure of 0.75 GPa. Using this flux-transport method of sample preparation, 6% of Be was the maximum amount of dopant achievable. At this maximal composition of FeSe_0.94Be_0.06, the lattice unit cell shrinks by 2.4%, T _c-measured in the bulk via specific heat-increases by almost 10%, the T _c versus pressure behavior shifts its peak [Formula: see text] downwards by ~1 GPa, the high temperature structural transition around T _S  =  89 K increases by 1.9 K (in contrast to other dopants in FeSe which uniformly depress T _S), and the low temperature specific heat γ increases by 10% compared to pure FeSe. Also, upon doping by 6% Be the residual resistivity ratio, ρ(300 K)/ρ(T  →  0), increases by almost a factor of four, while ρ(300 K)/ρ([Formula: see text]) increases by 50%.

Evolution of the Fermi surface of BiTeCl with pressure

We report measurements of Shubnikov-de Haas oscillations in the giant Rashba semiconductor BiTeCl under applied pressures up to  ∼2.5 GPa. We observe two distinct oscillation frequencies, corresponding to the Rashba-split inner and outer Fermi surfaces. BiTeCl has a conduction band bottom that is split into two sub-bands due to the strong Rashba coupling, resulting in two spin-polarized conduction bands as well as a Dirac point. Our results suggest that the chemical potential lies above this Dirac point, giving rise to two Fermi surfaces. We use a simple two-band model to understand the pressure dependence of our sample parameters. Comparing our results on BiTeCl to previous results on BiTeI, we observe similar trends in both the chemical potential and the Rashba splitting with pressure.

Pressure-induced superconductivity in the giant Rashba system BiTeI

At ambient pressure, BiTeI exhibits a giant Rashba splitting of the bulk electronic bands. At low pressures, BiTeI undergoes a transition from trivial insulator to topological insulator. At still higher pressures, two structural transitions are known to occur. We have carried out a series of electrical resistivity and AC magnetic susceptibility measurements on BiTeI at pressure up to  ∼40 GPa in an effort to characterize the properties of the high-pressure phases. A previous calculation found that the high-pressure orthorhombic P4/nmm structure BiTeI is a metal. We find that this structure is superconducting with T _c values as high as 6 K. AC magnetic susceptibility measurements support the bulk nature of the superconductivity. Using electronic structure and phonon calculations, we compute T _c and find that our data is consistent with phonon-mediated superconductivity.

Frustrated magnetism in the spin-chain metal Yb2Fe12P7

Magnetization measurements for magnetic fields [Formula: see text] up to 60 T are reported for the noncentrosymmetric spin-chain metal Yb2Fe12P7. These measurements reveal behavior that is consistent with Ising-like spin chain magnetism that produces pronounced spin degeneracy. In particular, we find that although a Brillouin field dependence is observed in M(H) for [Formula: see text] with a saturation moment that is close to the expected value for free ions of Yb(3+) , non-Brillouin-like behavior is seen for [Formula: see text] with an initial saturation moment that is nearly half the free ion value. In addition, hysteretic behavior that extends above the ordering temperature [Formula: see text] is seen for [Formula: see text] but not for [Formula: see text], suggesting out-of-equilibrium physics. This point of view is strengthened by the observation of a spin reconfiguration in the ordered state for [Formula: see text] which is only seen for [Formula: see text] and after polarizing the spins. Together with the heat capacity data, these results suggest that the anomalous low temperature phenomena that were previously reported (Baumbach 2010 et al Phys. Rev. Lett. 105 106403) are driven by spin degeneracy that is related to the Ising-like one dimensional chain-like configuration of the Yb ions.

Crossover between Fermi liquid and non-Fermi liquid behavior in the non-centrosymmetric compound Yb2Ni12P7

A crossover from a non-Fermi liquid to a Fermi liquid phase in Yb2Ni12P7 is observed by analyzing electrical resistivity ρ(T), magnetic susceptibility χ(T), specific heat C(T), and thermoelectric power S(T) measurements. The electronic contribution to specific heat, Ce(T), behaves as Ce(T)/T∼-ln(T) for 5 K<T<15 K, which is consistent with non-Fermi liquid behavior. Below T∼4 K, the upturn in Ce(T)/T begins to saturate, suggesting that the system crosses over into a Fermi-liquid ground state. This is consistent with robust ρ(T)-ρ0=AT2 behavior below T∼4 K, with the power-law exponent becoming sub-quadratic for T>4 K. A crossover between Fermi-liquid and non-Fermi liquid behavior suggests that Yb2Ni12P7 is in close proximity to a quantum critical point, in agreement with results from recent measurements of this compound under applied pressure.

Pressure tuning the Fermi level through the Dirac point of giant Rashba semiconductor BiTeI

We report measurements of Shubnikov-de Haas oscillations in the giant Rashba semiconductor BiTeI under applied pressures up to ∼2 GPa. We observe one high frequency oscillation at all pressures and one low frequency oscillation that emerges between ∼0.3-0.7 GPa indicating the appearance of a second small Fermi surface. BiTeI has a conduction band bottom that is split into two sub-bands due to the strong Rashba coupling, resulting in a 'Dirac point'. Our results suggest that the chemical potential starts below the Dirac point in the conduction band at ambient pressure and moves upward, crossing it as pressure is increased. The presence of the chemical potential above this Dirac point results in two Fermi surfaces. We present a simple model that captures this effect and can be used to understand the pressure dependence of our sample parameters. These extracted parameters are in quantitative agreement with first-principles calculations and other experiments. The parameters extracted via our model support the notion that pressure brings the system closer to the predicted topological quantum phase transition.

Persistent non-metallic behavior in Sr2IrO4 and Sr3Ir2O7 at high pressures

Iridium-based 5d transition-metal oxides are attractive candidates for the study of correlated electronic states due to the interplay of enhanced crystal-field, Coulomb and spin-orbit interaction energies. At ambient pressure, these conditions promote a novel Jeff = 1/2 Mott-insulating state, characterized by a gap of the order of ~0.1 eV. We present high-pressure electrical resistivity measurements of single crystals of Sr2IrO4 and Sr3Ir2O7. While no indications of a pressure-induced metallic state up to 55 GPa were found in Sr2IrO4, a strong decrease of the gap energy and of the resistance of Sr3Ir2O7 between ambient pressure and 104 GPa confirm that this compound is in the proximity of a metal-insulator transition.

Pressure-induced unconventional superconducting phase in the topological insulator Bi2Se3

Simultaneous low-temperature electrical resistivity and Hall effect measurements were performed on single-crystalline Bi2Se3 under applied pressures up to 50 GPa. As a function of pressure, superconductivity is observed to onset above 11 GPa with a transition temperature Tc and upper critical field Hc2 that both increase with pressure up to 30 GPa, where they reach maximum values of 7 K and 4 T, respectively. Upon further pressure increase, Tc remains anomalously constant up to the highest achieved pressure. Conversely, the carrier concentration increases continuously with pressure, including a tenfold increase over the pressure range where Tc remains constant. Together with a quasilinear temperature dependence of Hc2 that exceeds the orbital and Pauli limits, the anomalously stagnant pressure dependence of Tc points to an unconventional pressure-induced pairing state in Bi2Se3 that is unique among the superconducting topological insulators.

High pressure transport properties of the topological insulator Bi2Se3

We report x-ray diffraction, electrical resistivity, and magnetoresistance measurements on Bi2Se3 under high pressure and low temperature conditions. Pressure induces profound changes in both the room temperature value of the electrical resistivity as well as the temperature dependence of the resistivity. Initially, pressure drives Bi2Se3 toward increasingly insulating behavior and then, at higher pressures, the sample appears to enter a fully metallic state coincident with a change in the crystal structure. Within the low pressure phase, Bi2Se3 exhibits an unusual field dependence of the transverse magnetoresistance Δρ(xx) that is positive at low fields and becomes negative at higher fields. Our results demonstrate that pressures below 8 GPa provide a non-chemical means to controllably reduce the bulk conductivity of Bi2Se3.

Correlated electron state in Ce(1-x)Yb(x)CoIn5 stabilized by cooperative valence fluctuations

X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements on Ce(1-x)Yb(x)CoIn5 (0≤x≤1) reveal that many of the characteristic features of the x=0 correlated electron state are stable for x≤0.775 and that phase separation occurs for x>0.775. The stability of the correlated electron state is apparently due to cooperative behavior of the Ce and Yb ions, involving their unstable valences. Low-temperature non-Fermi liquid behavior is observed and varies with x, even though there is no readily identifiable quantum critical point. The superconducting critical temperature T(c) decreases linearly with x towards 0 K as x→1, in contrast with other HF superconductors where T(c) scales with T(coh).

Magnetic, thermal, and transport properties of the actinide based noncentrosymmetric compounds Th₂Fe₁₂P₇ and U₂Fe₁₂P₇

Magnetization, specific heat, and electrical resistivity measurements on single crystals of the noncentrosymmetric actinide based compounds U2Fe12P7 and Th2Fe12P7 are reported. The measurements reveal that U2Fe12P7 displays antiferromagnetic order at a Néel temperature T(N) ≈ 14 K, while Th2Fe12P7 is a metal which exhibits Pauli paramagnetism with no evidence for superconductivity for T ≥ 1.1 K. Magnetization measurements on U2Fe12P7 show complicated magnetic behavior involving the U and, possibly, Fe ions, as well; e.g., hysteretic temperature and field dependences and metamagnetism. Electrical resistivity measurements on U2Fe12P7 also indicate large spin disorder scattering of conduction electrons for T ≥ T(N).

The non-centrosymmetric heavy fermion ferromagnet Sm₂Fe₁₂P₇

We report measurements of the electrical resistivity, magnetization and specific heat on single crystals of the non-centrosymmetric compound Sm2Fe12P7. The magnetization measurements demonstrate that Sm2Fe12P7 exhibits ferromagnetic order below TM, 1 = 6.3 K. The ratio of the effective magnetic moment obtained from a Curie-Weiss fit to the magnetic susceptibility in the paramagnetic state, to the saturation magnetic moment in the ordered state indicates that the ordered state is associated with itinerant electrons. The specific heat measurements reveal an enhanced value for the coefficient of the electronic specific heat γ ∼ 450 mJ mol (-1) K (-2) that is accompanied by a large coefficient A of the T(2) term in the electrical resistivity at low temperatures, suggesting a heavy fermion ground state. Several consecutive magnetic phase transitions indicative of competing magnetic energy scales and the observation of a metamagnetic transition in the magnetization data additionally suggest proximity to a quantum critical point.

Unconventional T-H phase diagram in the noncentrosymmetric compound Yb2Fe12P7

The temperature-(T-)magnetic-field (H) phase diagram for the noncentrosymmetric compound Yb(2)Fe(12)P(7), [corrected] determined from electrical resistivity (ρ), specific heat (C), and magnetization (M) measurements on single crystal specimens, is reported. This system exhibits a crossover from a magnetically ordered non-Fermi-liquid (NFL) phase at low H to another NFL phase at higher H. The crossover occurs near the value of H where the magnetic ordering temperature (T(M)) is no longer observable in C(T,H)/T and ρ(T,H), but not where T(M) extrapolates smoothly to T=0 K at a possible quantum critical point (QCP). This indicates the occurrence of a quantum phase transition between the two NFL phases. The lack of a clear relationship between the extrapolated QCP and NFL behavior suggests an unconventional route to the NFL ground states.

Pressure-induced superconducting state of europium metal at low temperatures

Divalent Eu (4f;{7}, J=7/2) possesses a strong local magnetic moment which suppresses superconductivity. Under sufficient pressure it is anticipated that Eu will become trivalent (4f;{6}, J=0) and a weak Van Vleck paramagnet, thus opening the door for a possible superconducting state, in analogy with Am metal (5f;{6}, J=0) which superconducts at 0.79 K. We present ac susceptibility and electrical resistivity measurements on Eu metal for temperatures 1.5-297 K to pressures as high as 142 GPa. At approximately 80 GPa Eu becomes superconducting at T_{c} approximately 1.8 K; T_{c} increases linearly with pressure to 2.75 K at 142 GPa. Eu metal thus becomes the 53rd known elemental superconductor in the periodic table.

Pressure-induced superconducting phase in the charge-density-wave compound terbium tritelluride

A series of high-pressure electrical resistivity measurements on single crystals of TbTe3 reveal a complex phase diagram involving the interplay of superconducting, antiferromagnetic and charge-density-wave order. The onset of superconductivity reaches a maximum of almost 4 K (onset) near approximately 12.4 GPa.

Pressure-induced superconductivity in CaLi(2)

A search for superconductivity has been carried out on the hexagonal polymorph of Laves-phase CaLi(2), a compound for which Feng, Ashcroft, and Hoffmann predict highly anomalous behavior under pressure. No superconductivity is observed above 1.10 K at ambient pressure. However, high-pressure ac susceptibility and electrical resistivity studies to 81 GPa reveal bulk superconductivity in CaLi(2) at temperatures as high as 13 K. The normal-state resistivity displays a dramatic increase with pressure.