Magnetic parity violation and parity-time-reversal-symmetric magnets.

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Fully gapped pairing state in spin-triplet superconductor UTe2.

The recently discovered superconductor UTe2 is a promising candidate for spin-triplet superconductors, but the symmetry of the superconducting order parameter remains highly controversial. Here, we determine the superconducting gap structure by the thermal conductivity of ultraclean UTe2 single crystals. We find that the a-axis thermal conductivity divided by temperature κ/T in zero-temperature limit is vanishingly small for both magnetic field H‖a and H‖c axes up to H/Hc2 ∼ 0.2, demonstrating the absence of nodes around the a axis contrary to the previous belief. The present results, combined with the reduction of nuclear magnetic resonance Knight shift, indicate that the superconducting order parameter belongs to the isotropic Au representation with a fully gapped pairing state, analogous to the B phase of superfluid 3He. These findings reveal that UTe2 is likely to be a long-sought three-dimensional strong topological superconductor, hosting helical Majorana surface states on any crystal plane.

Spin-Triplet Superconductivity from Quantum-Geometry-Induced Ferromagnetic Fluctuation.

We show that quantum geometry induces ferromagnetic fluctuation resulting in spin-triplet superconductivity. The criterion for ferromagnetic fluctuation is clarified by analyzing contributions from the effective mass and quantum geometry. When the non-Kramers band degeneracy is present near the Fermi surface, the Fubini-Study quantum metric strongly favors ferromagnetic fluctuation. Solving the linearized gap equation with the effective interaction obtained by the random phase approximation, we show that the spin-triplet superconductivity is mediated by quantum-geometry-induced ferromagnetic fluctuation.

Magnetization Control of Zero-Field Intrinsic Superconducting Diode Effect.

The superconducting diode effect (SDE), which causes a superconducting state in one direction and a normal-conducting state in another, has significant potential for developing ultralow power consumption circuits and non-volatile memory. However, the practical control of the SDE necessities the precise tuning of current, temperature, magnetic field, or magnetism. Therefore, the mechanisms of the SDE must be understood to develop novel materials and devices capable of realizing the SDE under more controlled and robust conditions. This study demonstrates an intrinsic zero-field SDE with an efficiency of up to 40% in Fe/Pt-inserted non-centrosymmetric Nb/V/Ta superconducting artificial superlattices. The polarity and magnitude of the zero-field SDE are controllable by the direction of magnetization, indicating that the effective exchange field acts on Cooper pairs. Furthermore, the first-principles calculation indicates that the SDE can be enhanced by an asymmetric configuration of proximity induced magnetic moments in superconducting layers, which induces a magnetic toroidal moment. This study has important implications regarding the development of novel materials and devices that can effectively control the SDE. Moreover, the magnetization control of the SDE is expected to aid in the designing of superconducting quantum devices and establishing a material platform for topological superconductors.

Direct measurement of the evolution of magnetism and superconductivity toward the quantum critical point.

Nontrivial quantum states can be realized in the vicinity of the quantum critical point (QCP) in many strongly correlated electron systems. In particular, an emergence of unconventional superconductivity around the QCP strongly suggests that the quantum critical fluctuations play a central role in the superconducting pairing mechanism. However, a clear signature of the direct coupling between the superconducting pairing states and the quantum criticality has not yet been elucidated by the microscopic probes. Herein, we present muon spin rotation/relaxation and neutron diffraction measurements in the superconducting dome of CeCo(In1 - xZnx)5. It was found that a magnetically ordered state develops at x≥ 0.03, coexisting with the superconductivity. The magnitude of the ordered magnetic moment is continuously reduced with decreasing x, and it disappears below x∼ 0.03, indicating a second-order phase transition and the presence of the QCP at this critical Zn concentration. Furthermore, the magnetic penetration depth diverges toward the QCP. These facts provide evidence for the intimate coupling between quantum criticality and Cooper pairing.

Polarization-controlled tunable directional spin-driven photocurrents in a magnetic metamaterial with threefold rotational symmetry.

Future spintronics and quantum technologies will require a portfolio of techniques for manipulating electron spins in functional nanodevices. Especially, the establishment of the methods to control spin current is the key ingredient essential for the transfer and processing of information, enabling faster and low-energy operation. However, a universal method for manipulating spin currents with full-directional controllability and tunable magnitude has not been established. Here we show that an artificial material called a magnetic metamaterial (MM), which possesses a novel spintronic functionality not exhibited by the original substance, generates photo-driven ultrafast spin currents at room temperature via the magneto-photogalvanic effect. By tuning the polarization state of the excitation light, these spin currents can be directed with tunable magnitude along an arbitrary direction in the two-dimensional plane of the MM. This new concept may guide the design and creation of artificially engineered opto-spintronic functionalities beyond the limitations of conventional material science.

Field-free superconducting diode effect in noncentrosymmetric superconductor/ferromagnet multilayers.

The diode effect is fundamental to electronic devices and is widely used in rectifiers and a.c.-d.c. converters. At low temperatures, however, conventional semiconductor diodes possess a high resistivity, which yields energy loss and heating during operation. The superconducting diode effect (SDE)1-8, which relies on broken inversion symmetry in a superconductor, may mitigate this obstacle: in one direction, a zero-resistance supercurrent can flow through the diode, but for the opposite direction of current flow, the device enters the normal state with ohmic resistance. The application of a magnetic field can induce SDE in Nb/V/Ta superlattices with a polar structure1,2, in superconducting devices with asymmetric patterning of pinning centres9 or in superconductor/ferromagnet hybrid devices with induced vortices10,11. The need for an external magnetic field limits their practical application. Recently, a field-free SDE was observed in a NbSe2/Nb3Br8/NbSe2 junction; it originates from asymmetric Josephson tunnelling that is induced by the Nb3Br8 barrier and the associated NbSe2/Nb3Br8 interfaces12. Here, we present another implementation of zero-field SDE using noncentrosymmetric [Nb/V/Co/V/Ta]20 multilayers. The magnetic layers provide the necessary symmetry breaking, and we can tune the SDE by adjusting the structural parameters, such as the constituent elements, film thickness, stacking order and number of repetitions. We control the polarity of the SDE through the magnetization direction of the ferromagnetic layers. Artificially stacked structures13-18, such as the one used in this work, are of particular interest as they are compatible with microfabrication techniques and can be integrated with devices such as Josephson junctions19-22. Energy-loss-free SDEs as presented in this work may therefore enable novel non-volatile memories and logic circuits with ultralow power consumption.

Intrinsic Superconducting Diode Effect.

Stimulated by the recent experiment [F. Ando et al., Nature (London) 584, 373 (2020).NATUAS0028-083610.1038/s41586-020-2590-4], we propose an intrinsic mechanism to cause the superconducting diode effect (SDE). SDE refers to the nonreciprocity of the critical current for the metal-superconductor transition. Among various mechanisms for the critical current, the depairing current is known to be intrinsic to each material and has recently been observed in several superconducting systems. We clarify the temperature scaling of the nonreciprocal depairing current near the critical temperature and point out its significant enhancement at low temperatures. It is also found that the nonreciprocal critical current shows sign reversals upon increasing the magnetic field. These behaviors are understood by the nonreciprocity of the Landau critical momentum and the change in the nature of the helical superconductivity. The intrinsic SDE unveils the rich phase diagram and functionalities of noncentrosymmetric superconductors.

Observation of superconducting diode effect.

Nonlinear optical and electrical effects associated with a lack of spatial inversion symmetry allow direction-selective propagation and transport of quantum particles, such as photons1 and electrons2-9. The most common example of such nonreciprocal phenomena is a semiconductor diode with a p-n junction, with a low resistance in one direction and a high resistance in the other. Although the diode effect forms the basis of numerous electronic components, such as rectifiers, alternating-direct-current converters and photodetectors, it introduces an inevitable energy loss due to the finite resistance. Therefore, a worthwhile goal is to realize a superconducting diode that has zero resistance in only one direction. Here we demonstrate a magnetically controllable superconducting diode in an artificial superlattice [Nb/V/Ta]n without a centre of inversion. The nonreciprocal resistance versus current curve at the superconducting-to-normal transition was clearly observed by a direct-current measurement, and the difference of the critical current is considered to be related to the magnetochiral anisotropy caused by breaking of the spatial-inversion and time-reversal symmetries10-13. Owing to the nonreciprocal critical current, the [Nb/V/Ta]n superlattice exhibits zero resistance in only one direction. This superconducting diode effect enables phase-coherent and direction-selective charge transport, paving the way for the construction of non-dissipative electronic circuits.

Insulator-Metal Transition and Topological Superconductivity in UTe_{2} from a First-Principles Calculation.

We theoretically study superconductivity in UTe_{2}, which is a recently discovered strong candidate for an odd-parity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA+U method and show the insulator-metal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of U, we clarify topological properties of possible superconducting states. Fermi surface formulas for the three-dimensional winding number and three two-dimensional Z_{2} numbers indicate topological superconductivity at an intermediate U for all the odd-parity pairing symmetry in the Immm space group. Symmetry and topology of superconducting gap nodes are analyzed and the gap structure of UTe_{2} is predicted. Topologically protected low-energy excitations are highlighted, and experiments by bulk and surface probes are proposed to link Fermi surfaces and pairing symmetry. Based on the results, we also discuss multiple superconducting phases under magnetic fields, which were implied by recent experiments.

Z_{4} Topological Superconductivity in UCoGe.

Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCSs are classified into Z_{4} topological phases, which have unique surface states referred to as a Möbius strip or an hourglass, and they have not been achieved in symmorphic superconductors. However, material realization of Z_{4} TNCS has never been known, to the best of our knowledge. Here, we propose that the paramagnetic superconducting phase of UCoGe under pressure is a promising candidate of Z_{4}-nontrivial TNCS enriched by glide symmetry. We evaluate Z_{4} invariants of UCoGe by deriving the formulas relating Z_{4} invariants to the topology of Fermi surfaces. Applying the formulas and previous ab initio calculations, we clarify that three odd-parity representations out of four are Z_{4}-nontrivial TNCS, whereas the other is also Z_{2}-nontrivial TNCS. We also discuss possible Z_{4} TNCS in CrAs and related materials.

Anomalous Change in the de Haas-van Alphen Oscillations of CeCoIn_{5} at Ultralow Temperatures.

We perform de Haas-van Alphen (dHvA) measurements of the heavy-fermion superconductor CeCoIn_{5} down to 2 mK above the upper critical field. We find that the dHvA amplitudes show an anomalous suppression, concomitantly with a shift of the dHvA frequency, below the transition temperature T_{n}=20 mK. We suggest that the change is owing to magnetic breakdown caused by a field-induced antiferromagnetic (AFM) state emerging below T_{n}, revealing the origin of the field-induced quantum critical point (QCP) in CeCoIn_{5}. The field dependence of T_{n} is found to be very weak for 7-10 T, implying that an enhancement of AFM order by suppressing the critical spin fluctuations near the AFM QCP competes with the field suppression effect on the AFM phase. We suggest that the appearance of a field-induced AFM phase is a generic feature of unconventional superconductors, which emerge near an AFM QCP, including CeCoIn_{5}, CeRhIn_{5}, and high-T_{c} cuprates.

Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}.

Discoveries of marked similarities to high-T_{c} cuprate superconductors point to the realization of superconductivity in the doped J_{eff}=1/2 Mott insulator Sr_{2}IrO_{4}. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+. In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective J_{eff}=1/2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Fate of Majorana Modes in CeCoIn_{5}/YbCoIn_{5} Superlattices: A Test Bed for the Reduction of Topological Classification.

In this paper, we propose CeCoIn_{5}/YbCoIn_{5} superlattice systems as a test bed for the reduction of topological classification in free fermions. We find that the system with a quadlayer of CeCoIn_{5} shows a topological crystalline superconducting phase with the mirror Chern number eight at the noninteracting level. Furthermore, we demonstrate that in the presence of two-body interactions, gapless edge modes are no longer protected by the symmetry in the system with a quadlayer, but are protected in the system with a bilayer or trilayer. This clearly exemplifies the reduction of topological classification from Z⊕Z to Z⊕Z_{8}.

Topological Crystalline Superconductivity in Locally Noncentrosymmetric Multilayer Superconductors.

Topological crystalline superconductivity in locally noncentrosymmetric multilayer superconductors (SCs) is proposed. We study the odd-parity pair-density wave (PDW) state induced by the spin-singlet pairing interaction through the spin-orbit coupling. It is shown that the PDW state is a topological crystalline SC protected by a mirror symmetry, although it is topologically trivial according to the classification based on the standard topological periodic table. The topological property of the mirror subsectors is intuitively explained by adiabatically changing the Bogoliubov-de Gennes Hamiltonian. A subsector of the bilayer PDW state reduces to the two-dimensional noncentrosymmetric SC, while a subsector of the trilayer PDW state is topologically equivalent to the spinless p-wave SC. Chiral Majorana edge modes in trilayers can be realized without Cooper pairs in the spin-triplet channel and chemical potential tuning.

Magnetic structure of the antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state.

The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are studied by solving the Bogoliubov-de Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, and its magnitude is enhanced around the FFLO nodal planes. (III) In the extended case, the AFM staggered moment is nearly homogeneous and slightly suppressed in the vicinity of the FFLO nodal planes. The structure of Bragg peaks in the momentum resolved structure factor is studied in each case. We discuss the possibility of an AFM-FFLO state in the heavy fermion superconductor CeCoIn5 by comparing these results with the neutron scattering data of CeCoIn5. Experimentally the magnetic structure and its dependence on the magnetic field orientation in the high-field superconducting phase of CeCoIn5 are consistent with case (II).

Superconductivity in compensated and uncompensated semiconductors.

We investigate the localization and superconductivity in heavily doped semiconductors. The crossover from the superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. The microscopic inhomogeneity and the thermal superconducting fluctuation are taken into account using the self-consistent 1-loop order theory. The superconductor-insulator transition accompanies the crossover from the host band to the impurity band. We point out an enhancement of the critical temperature Tc around the crossover. Further localization of electron wave functions leads to the localization of Cooper pairs and induces the pseudogap. We find that both the doping compensation by additional donors and the carrier increase by additional acceptors suppress the superconductivity. A theoretical interpretation is proposed for the superconductivity in the boron-doped diamond, SiC, and Si.

Ferromagnetic fluctuation and possible triplet superconductivity in NaxCoO2.yH2O: fluctuation-exchange study of the multiorbital Hubbard model.

Spin and charge fluctuations and superconductivity in NaxCoO2.yH(2)O are studied based on a multiorbital Hubbard model. Tight-binding parameters are determined to reproduce the results of band calculations. By applying the fluctuation-exchange approximation, we show that the Hund's-rule coupling between the Co t(2g) orbitals causes ferromagnetic (FM) spin fluctuation. Triplet fy((y(2)-3x(2)))-wave and p-wave pairings are favored by this FM fluctuation on the hole-pocket band. We propose that, in NaxCoO2.yH(2)O, the Co t(2g) orbitals and interorbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor in which the orbital degrees of freedom play substantial roles.