Iron-based magnetic superconductors AEuFe4As4 (A= Rb, Cs): Natural superconductor-ferromagnet hybrids

Superconductivity (SC) and ferromagnetism (FM) are normally antagonistic, and their coexistence in a single crystalline material appears to be very rare. Over a decade ago, the iron-based pnictides of doped EuFe2As2 were found to render such a coexistence primarily because of the Fe-3d multiorbitals which simultaneously satisfy the superconducting pairing of Fe-3d electrons and the ferromagnetic exchange interaction among Eu local spins. In 2016, the discovery of the iron-based superconductors AEuFe4As4 (A= Rb, Cs) provided an additional and complementary material basis for the study of the coexistence and interplay between SC and FM. The two sibling compounds, which can be viewed as the intergrowth or hybrid between AFe2As2 and EuFe2As2, show SC in the FeAs bilayers at T c = 35 – 37 K, followed by a magnetic ordering at T m ∼ 15 K in the sandwiched Eu2+-ion sheets. Below T m, the Eu2+ spins align ferromagnetically within each Eu plane, making the system as a natural atomic-thick superconductor-ferromagnet superlattice. This paper reviews the main research progress in the emerging topic during the past five years, and an outlook for the future research opportunities is also presented.

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

A Majorana perspective on understanding and identifying axion insulators

An axion insulator is theoretically introduced to harbor unique surface states with half-integer Chern number $${{{{{{{\mathcal{C}}}}}}}}$$ C . Recently, experimental progress has been made in different candidate systems, while a unique Hall response to directly reflect the half-integer Chern number is still lacking to distinguish an axion state from other possible insulators. Here we show that the $${{{{{{{\mathcal{C}}}}}}}}=\frac{1}{2}$$ C = 1 2 axion state corresponds to a topological state with Chern number $${{{{{{{\mathcal{N}}}}}}}}=1$$ N = 1 in the Majorana basis. In proximity to an s − wave superconductor, a topological phase transition to an $${{{{{{{\mathcal{N}}}}}}}}=0$$ N = 0 phase takes place at critical superconducting pairing strength. Our theoretical analysis shows that a chiral Majorana hinge mode emerges at the boundary of $${{{{{{{\mathcal{N}}}}}}}}=1$$ N = 1 and $${{{{{{{\mathcal{N}}}}}}}}=0$$ N = 0 regions on the surface of an axion insulator. Furthermore, we propose a half-integer quantized thermal Hall conductance via a thermal transport measurement, which is a signature of the gapless chiral Majorana mode and thus confirms the $${{{{{{{\mathcal{C}}}}}}}}=\frac{1}{2}$$ C = 1 2 ($${{{{{{{\mathcal{N}}}}}}}}=1$$ N = 1 ) topological nature of an axion state. Our proposals help to theoretically comprehend and experimentally identify the axion insulator and may benefit the research of topological quantum computation.

Quasi-one-dimensional superconductivity in the pressurized charge-density-wave conductor HfTe3

HfTe3 single crystal undergoes a charge-density-wave (CDW) transition at TCDW = 93 K without the appearance of superconductivity (SC) down to 50 mK at ambient pressure. Here, we determined its CDW vector q = 0.91(1) a* + 0.27(1) c* via low-temperature transmission electron microscope and then performed comprehensive high-pressure transport measurements along three major crystallographic axes. Our results indicate that the superconducting pairing starts to occur within the quasi-one-dimensional (Q1D) -Te2-Te3- chain at 4–5 K but the phase coherence between the superconducting chains cannot be realized along either the b- or c-axis down to at least 1.4 K, giving rise to an extremely anisotropic SC rarely seen in real materials. We have discussed the prominent Q1D SC in pressurized HfTe3 in terms of the anisotropic Fermi surfaces arising from the unidirectional Te-5px electronic states and the local pairs formed along the -Te2-Te3- chains based on the first-principles electronic structure calculations.

High temperature superconductivity at FeSe/LaFeO3 interface

Enormous enhancement of superconducting pairing temperature (Tg) to 65 K in FeSe/SrTiO3 has made it a spotlight. Despite the effort of interfacial engineering, FeSe interfaced with TiOx remains the unique case in hosting high Tg, hindering a decisive understanding on the general mechanism and ways to further improving Tg. Here we constructed a new high-Tg interface, single-layer FeSe interfaced with FeOx-terminated LaFeO3. Large superconducting gap and diamagnetic response evidence that the superconducting pairing can emerge near 80 K, highest amongst all-known interfacial superconductors. Combining various techniques, we reveal interfacial charge transfer and strong interfacial electron-phonon coupling (EPC) in FeSe/LaFeO3, showing that the cooperative pairing mechanism works beyond FeSe-TiOx. Intriguingly, the stronger interfacial EPC than that in FeSe/SrTiO3 is likely induced by the stronger interfacial bonding in FeSe/LaFeO3, and can explain the higher Tg according to recent theoretical calculations, pointing out a workable route in designing new interfaces to achieve higher Tg.

Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?

Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.

Emergence of topological superconductivity in doped topological Dirac semimetals under symmetry-lowering lattice distortions

Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

Absence of Superconductivity in the Hubbard Dimer Model for κ-(BEDT-TTF)2X

In the most studied family of organic superconductors κ-(BEDT-TTF)2X, the BEDT-TTF molecules that make up the conducting planes are coupled as dimers. For some anions X, an antiferromagnetic insulator is found at low temperatures adjacent to superconductivity. With an average of one hole carrier per dimer, the BEDT-TTF band is effectively 12-filled. Numerous theories have suggested that fluctuations of the magnetic order can drive superconducting pairing in these models, even as direct calculations of superconducting pairing in monomer 12-filled band models find no superconductivity. Here, we present accurate zero-temperature Density Matrix Renormalization Group (DMRG) calculations of a dimerized lattice with one hole per dimer. While we do find an antiferromagnetic state in our results, we find no evidence for superconducting pairing. This further demonstrates that magnetic fluctuations in the effective 12-filled band approach do not drive superconductivity in these and related materials.

Minimal Zeeman field requirement for a topological transition in superconductors

Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to s-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.

Synthesis of Superconducting InxSn1−xTe (0.04 < x < 0.1) Large Single Crystal by Liquid Transport Method

In this work, a new crystal growth technique called the liquid transport method was introduced to synthesize single crystals of a topological superconductor candidate, InxSn1−xTe (IST). Crystals with the size of several millimeters were successfully synthesized, and were characterized by X-ray diffraction, scanning electron microscopy with energy-dispersive spectroscopy as well as electronic transport measurements. Lattice parameters decreased monotonously with the increase of indium content while hole density varied in reverse. Superconductivity with the critical temperature (Tc) around 1.6 K were observed, and the hole densities were estimated to be in the order of 1020 cm−3. The upper critical fields (Bc2) were estimated to be 0.68 T and 0.71 T for In0.04Sn0.96Te and In0.06Sn0.94Te, respectively. The results indicated that the quality of our crystals is comparable to that grown by the chemical vapor transport method, but with a relatively larger size. Our work provides a new method to grow large single crystals of IST and could help to solve the remaining open questions in a system that needs large crystals, such as a superconducting pairing mechanism, unconventional superconductivity, and so on.