Ordered and tunable Majorana-zero-mode lattice in naturally strained LiFeAs.

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits1,2. Iron-based superconductors with topological bandstructures have emerged as promising hosting materials, because isolated candidate MZMs in the quantum limit have been observed inside the topological vortex cores3-9. However, these materials suffer from issues related to alloying induced disorder, uncontrolled vortex lattices10-13 and a low yield of topological vortices5-8. Here we report the formation of an ordered and tunable MZM lattice in naturally strained stoichiometric LiFeAs by scanning tunnelling microscopy/spectroscopy. We observe biaxial charge density wave (CDW) stripes along the Fe-Fe and As-As directions in the strained regions. The vortices are pinned on the CDW stripes in the As-As direction and form an ordered lattice. We detect that more than 90 per cent of the vortices are topological and possess the characteristics of isolated MZMs at the vortex centre, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Notably, with decreasing the spacing of neighbouring vortices, the MZMs start to couple with each other. Our findings provide a pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (µSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field µSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Structure Responsible for the Superconducting State in La3Ni2O7 at High-Pressure and Low-Temperature Conditions.

Very recently, a new superconductor with Tc = 80 K has been reported in nickelate (La3Ni2O7) at around 15-40 GPa conditions (Nature, 621, 493, 2023), which is the second type of unconventional superconductor, besides cuprates, with Tc above liquid nitrogen temperature. However, the phase diagram plotted in this report was mostly based on the transport measurement under low-temperature and high-pressure conditions, and the assumed corresponding X-ray diffraction (XRD) results were carried out at room temperature. This encouraged us to carry out in situ high-pressure and low-temperature synchrotron XRD experiments to determine which phase is responsible for the high Tc state. In addition to the phase transition from the orthorhombic Amam structure to the orthorhombic Fmmm structure, a tetragonal phase with the space group of I4/mmm was discovered when the sample was compressed to around 19 GPa at 40 K where the superconductivity takes place in La3Ni2O7. The calculations based on this tetragonal structure reveal that the electronic states that approached the Fermi energy were mainly dominated by the eg orbitals (3dz2 and 3dx2-y2) of Ni atoms, which are located in the oxygen octahedral crystal field. The correlation between Tc and this structural evolution, especially Ni-O octahedra regularity and the in-plane Ni-O-Ni bonding angles, is analyzed. This work sheds new light to identify what is the most likely phase responsible for superconductivity in double-layered nickelate.

Antiferroelectricity-Induced Negative Thermal Expansion in Double Perovskite Pb2 CoMoO6.

Materials with negative thermal expansion (NTE) attract significant research attention owing to their unique physical properties and promising applications. Although ferroelectric phase transitions leading to NTE are widely investigated, information on antiferroelectricity-induced NTE remains limited. In this study, single-crystal and polycrystalline Pb2 CoMoO6 samples are prepared at high pressure and temperature conditions. The compound crystallizes into an antiferroelectric Pnma orthorhombic double perovskite structure at room temperature owing to the opposite displacements dominated by Pb2+ ions. With increasing temperature to 400 K, a structural phase transition to cubic Fm-3m paraelectric phase occurs, accompanied by a sharp volume contraction of 0.41%. This is the first report of an antiferroelectric-to-paraelectric transition-induced NTE in Pb2 CoMoO6 . Moreover, the compound also exhibits remarkable NTE with an average volumetric coefficient of thermal expansion αV = -1.33 × 10-5 K-1 in a wide temperature range of 30-420 K. The as-prepared Pb2 CoMoO6 thus serves as a prototype material system for studying antiferroelectricity-induced NTE.

High-Pressure Synthesis, Crystal Structure, and Physical Properties of a Spinel Compound Co0.7Al2S4.

In this paper, we report on the discovery of a spinel compound, Co0.7Al2S4, which was synthesized at high-pressure. The systematic characterizations were carried out by structural, magnetic, and heat capacity measurements. The compound crystallizes into a cubic structure with the space group Fd3̅m (no. 227) and the lattice constant a = 9.9580(1) Å. Magnetic susceptibility measurements suggest that Co0.7Al2S4 exhibits a spin glass ground state, freezing at Tf ∼ 7.2 K with a Weiss temperature Tθ ∼ -115.9 K, which is verified by ac magnetic susceptibility and heat capacity measurements. The frustration parameter f for Co0.7Al2S4 is calculated to be about 16.6, based on the formula f = | Tθ/Tf |, indicating that Co0.7Al2S4 is a high-frustration magnet. Specific heat data displays a T2 dependence below the freezing temperature, which is different from the linear dependence observed in a common spin glass system. Compared with the similar compound CoAl2O4, it is suggested that the vacancies in the Co sites should be responsible for the occurrence of the spin glass behavior of Co0.7Al2S4.

Nanoscale Manipulation of Wrinkle-Pinned Vortices in Iron-Based Superconductors.

The controlled manipulation of Abrikosov vortices is essential for both fundamental science and logical applications. However, achieving nanoscale manipulation of vortices while simultaneously measuring the local density of states within them remains challenging. Here, we demonstrate the manipulation of Abrikosov vortices by moving the pinning center, namely one-dimensional wrinkles, on the terminal layers of Fe(Te,Se) and LiFeAs, by utilizing low-temperature scanning tunneling microscopy/spectroscopy (STM/S). The wrinkles trap the Abrikosov vortices induced by the external magnetic field. In some of the wrinkle-pinned vortices, robust zero-bias conductance peaks are observed. We tailor the wrinkle into short pieces and manipulate the wrinkles by using an STM tip. Strikingly, we demonstrate that the pinned vortices move together with these wrinkles even at high magnetic field up to 6 T. Our results provide a universal and effective routine for manipulating wrinkle-pinned vortices and simultaneously measuring the local density of states on the iron-based superconductor surfaces.

Local structure of Sr2CuO3.3, a 95 K cuprate superconductor without CuO2 planes.

The local structure of the highly "overdoped" 95 K superconductor Sr2CuO3.3 determined by Cu K X-ray absorption fine structure (XAFS) at 62 K in magnetically oriented samples shows that 1) the magnetization is perpendicular to the c axis; 2) at these levels of precision the Cu sublattice is tetragonal in agreement with the crystal structure; the O sublattice has 3) continuous -Cu-O- chains that orient perpendicular to an applied magnetic field; 4) approximately half-filled -Cu-O- chains that orient parallel to this field; 5) a substantial number of apical O vacancies; 6) O ions at some apical positions with expanded Cu-O distances; and 7) interstitial positions that imply highly displaced Sr ions. These results contradict the universally accepted features of cuprates that require intact CuO2 planes, magnetization along the c axis, and a termination of the superconductivity when the excess charge on the CuO2 Cu ions exceeds 0.27. These radical differences in charge and structure demonstrate that this compound constitutes a separate class of Cu-O-based superconductors in which the superconductivity originates in a different, more complicated structural unit than CuO2 planes while retaining exceptionally high transition temperatures.

Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr2Cu2.75Mo0.25O7.54 and Sr2CuO3.3.

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr2Cu2.75Mo0.25O7.54 with superconducting critical temperature, Tc = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr2CuO3.3 with Tc = 95 K and p = 0.6. In YSr2Cu2.75Mo0.25O7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at Tc, with the energy difference between the two minima increasing by ∼6 meV between Tc and 52 K. Sr2CuO3.3 undergoes a radically larger transformation at Tc, >1-Šdisplacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu-O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

Local lattice distortions and dynamics in extremely overdoped superconducting YSr2Cu2.75Mo0.25O7.54.

A common characteristic of many "overdoped" cuprates prepared with high-pressure oxygen is Tc values ≥ 50 K that often exceed that of optimally doped parent compounds, despite O stoichiometries that place the materials at the edge or outside of the conventional boundary between superconducting and normal Fermi liquid states. X-ray absorption fine-structure (XAFS) measurements at 52 K on samples of high-pressure oxygen (HPO) YSr2Cu2.75Mo0.25O7.54, Tc = 84 K show that the Mo is in the (VI) valence in an unusually undistorted octahedral geometry with predominantly Mo neighbors that is consistent with its assigned substitution for Cu in the chain sites of the structure. Perturbations of the Cu environments are minimal, although the Cu X-ray absorption near-edge structure (XANES) differs from that in other cuprates. The primary deviation from the crystal structure is therefore nanophase separation into Mo- and Cu-enriched domains. There are, however, indications that the dynamical attributes of the structure are altered relative to YBa2Cu3O7, including a shift of the Cu-apical O two-site distribution from the chain to the plane Cu sites. Another effect that would influence Tc is the possibility of multiple bands at the Fermi surface caused by the presence of the second phase and the lowering of the Fermi level.

Novel Valence Transition in Elemental Metal Europium around 80 GPa.

Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase (Pnma). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.

High-Pressure Synthesis and Physical Properties of a Spinel Compound FeAl2S4.

A spinel compound FeAl2S4 was successfully synthesized under high-pressure and high-temperature conditions and was systematically characterized via the structural, magnetic, and specific heat measurements. It crystallizes into a cubic structure with the space group Fd3̅m (no. 227) and the lattice constant a = 10.0207(2) Å. A Fe/Al site inversion is found; that is, the molecular formula can be rewritten as (Fe1-xAlx)(Al2-xFex)S4, and the inversion parameter x is about 0.22. Magnetic susceptibility measurements indicate that FeAl2S4 undergoes a spin glass behavior, which is confirmed by ac susceptibility and specific heat measurements. The freezing temperature Tf ∼ 10.5 K and Weiss temperature Tθ ∼ -107.4 K lead to a high frustration parameter f = |Tθ/Tf| of about 10, which suggests that FeAl2S4 is a high-frustration magnet. Our results indicate that high pressure can help stabilize the spinel structure with small R̅σ and the cation inversion plays an important role in the formation of the spin glass state.

Pressure-induced phase transitions and superconductivity in a quasi-1-dimensional topological crystalline insulator α-Bi4Br4.

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi-1-dimensional bismuth bromide, Bi4Br4, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi4Br4 crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator-metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

High-Pressure Synthesis of Double Perovskite Ba2NiIrO6: In Search of a Ferromagnetic Insulator.

Double perovskite oxides with d8-d3 electronic configurations are expected to be ferromagnetic from the Goodenough-Kanamori rules, such as ferromagnetic La2NiMnO6. In search of new ferromagnetic insulators, double perovskite Ba2NiIrO6 was successfully synthesized by high-pressure and high-temperature methods (8 GPa and 1573 K). Ba2NiIrO6 crystallizes in a cubic double perovskite structure (space group: Fm3̅m), with an ordered arrangement of NiO6 and IrO6 octahedra. X-ray absorption near-edge spectroscopy confirms the nominal Ni(II) and Ir(VI) valence states. Ba2NiIrO6 displays an antiferromagnetic order at 51 K. The positive Weiss temperature, however, indicates that ferromagnetic interactions are dominant. Isothermal magnetization curves at low temperatures support a field-induced spin-flop transition.

Tl2Ir2O7: A Pauli Paramagnetic Metal, Proximal to a Metal Insulator Transition.

A polycrystalline sample of Tl2Ir2O7 was synthesized by high-pressure and high-temperature methods. Tl2Ir2O7 crystallizes in the cubic pyrochlore structure with space group Fd3̅m (No. 227). The Ir4+ oxidation state is confirmed by Ir-L3 X-ray absorption near-edge spectroscopy. Combined temperature-dependent magnetic susceptibility, resistivity, specific heat, and DFT+DMFT calculation data show that Tl2Ir2O7 is a Pauli paramagnetic metal, but it is close to a metal-insulator transition. The effective ionic size of Tl3+ is much smaller than that of Pr3+ in metallic Pr2Ir2O7; hence, Tl2Ir2O7 would be expected to be insulating according to the established phase diagram of the pyrochlore iridate compounds, A3+2Ir4+2O7. Our experimental and theoretical studies indicate that Tl2Ir2O7 is uniquely different from the current A3+2Ir4+2O7 phase diagram. This uniqueness is attributed primarily to the electronic configuration difference between Tl3+ and rare-earth ions, which plays a substantial role in determining the Ir-O-Ir bond angle, and the corresponding electrical and magnetic properties.

Sequential Spin State Transition and Intermetallic Charge Transfer in PbCoO3.

Spin state transitions and intermetallic charge transfers can essentially change material structural and physical properties while excluding external chemical doping. However, these two effects have rarely been found to occur sequentially in a specific material. In this article, we show the realization of these two phenomena in a perovskite oxide PbCoO3 with a simple ABO3 composition under high pressure. PbCoO3 possesses a peculiar A- and B-site ordered charge distribution Pb2+Pb4+3Co2+2Co3+2O12 with insulating behavior at ambient conditions. The high spin Co2+ gradually changes to low spin with increasing pressure up to about 15 GPa, leading to an anomalous increase of resistance magnitude. Between 15 and 30 GPa, the intermetallic charge transfer occurs between Pb4+ and Co2+ cations. The accumulated charge-transfer effect triggers a metal-insulator transition as well as a first-order structural phase transition toward a Tetra.-I phase at the onset of ∼20 GPa near room temperature. On further compression over 30 GPa, the charge transfer completes, giving rise to another first-order structural transformation toward a Tetra.-II phase and the reentrant electrical insulating behavior.

High-Pressure, High-Temperature Synthesis and Characterization of Polar and Magnetic LuCrWO6.

A new polar and magnetic oxide, LuCrWO6, was synthesized under high pressure (6 GPa) and high temperature (1673 K). LuCrWO6 is isostructural with the previously reported polar YCrWO6 (SG: Pna21, no. 33). The ordering of CrO6 and WO6 octahedra in the edge-shared dimers induce the polar structure. The effective size of rare earth, Ln cation does not seem to affect the symmetry of LnCrWO6. Second harmonic generation measurements of LuCrWO6 confirmed the noncentrosymmetric character and strong piezoelectric domains are observed from piezoresponse force microscopy at room temperature. LuCrWO6 exhibits antiferromagnetic behavior, TN, of ∼18 K with a Weiss temperature of -30.7 K.

The Synthesis of a Quasi-One-Dimensional Iron-Based Telluride with Antiferromagnetic Chains and a Spin Glass State.

The report on the superconductivity of the two-legged spin ladders BaFe2S3 and BaFe2Se3 has established 123-type iron chalcogenides as a novel subgroup in the iron-based superconductor family and has stimulated the continuous exploration of other iron-based materials with new structures and potentially novel properties. In this paper, we report the systematic study of a new quasi-one-dimensional (1D) iron-based compound, Ba9Fe3Te15, including its synthesis and magnetic properties. The high-pressure synthesized Ba9Fe3Te15 crystallized in a hexagonal structure that mainly consisted of face-sharing FeTe6 octahedral chains running along the c axis, with a lattice constant of a = 10.23668 Å; this led to weak interchain coupling and an enhanced one-dimensionality. The systematic static and dynamic magnetic properties were comprehensively studied experimentally. The dc magnetic susceptibility showed typical 1D antiferromagnetic characteristics, with a Tmax at 190 K followed by a spin glass (SG) state with freezing at Tf ≈ 6.0 K, which were also unambiguously proved by ac susceptibility measurements. Additionally, X-ray magnetic circular dichroism (XMCD) experiments revealed an unexpected orbital moment for Fe2+, i.e., 0.84 µB per Fe in Ba9Fe3Te15. The transport property is electrically insulating, with a thermal activation gap of 0.32 eV. These features mark Ba9Fe3Te15 as an alternative type of iron-based compound, providing a diverse candidate for high-pressure studies in order to pursue some emerging physics.

A Pressure-Induced Inverse Order-Disorder Transition in Double Perovskites.

Given the consensus that pressure improves cation ordering in most of known materials, a discovery of pressure-induced disordering could require recognition of an order-disorder transition in solid-state physics/chemistry and geophysics. Double perovskites Y2 CoIrO6 and Y2 CoRuO6 polymorphs synthesized at 0, 6, and 15 GPa show B-site ordering, partial ordering, and disordering, respectively, accompanied by lattice compression and crystal structure alteration from monoclinic to orthorhombic symmetry. Correspondingly, the long-range ferrimagnetic ordering in the B-site ordered samples are gradually overwhelmed by B-site disorder. Theoretical calculations suggest that unusual unit-cell compressions under external pressures unexpectedly stabilize the disordered phases of Y2 CoIrO6 and Y2 CoRuO6 .

Quantum Phase Transition of Correlated Iron-Based Superconductivity in LiFe_{1-x}Co_{x}As.

The interplay between unconventional Cooper pairing and quantum states associated with atomic scale defects is a frontier of research with many open questions. So far, only a few of the high-temperature superconductors allow this intricate physics to be studied in a widely tunable way. We use scanning tunneling microscopy to image the electronic impact of Co atoms on the ground state of the LiFe_{1-x}Co_{x}As system. We observe that impurities progressively suppress the global superconducting gap and introduce low energy states near the gap edge, with the superconductivity remaining in the strong-coupling limit. Unexpectedly, the fully opened gap evolves into a nodal state before the Cooper pair coherence is fully destroyed. Our systematic theoretical analysis shows that these new observations can be quantitatively understood by the nonmagnetic Born-limit scattering effect in an s±-wave superconductor, unveiling the driving force of the superconductor to metal quantum phase transition.