Magnetic-field-induced pattern of coexisting condensates in the superconducting state of CeCoIn5

Spontaneous Formation of Altermagnetism from Orbital Ordering

Altermagnetism has emerged as a third type of collinear magnetism. In contrast to standard ferromagnets and antiferromagnets, altermagnets exhibit extra even-parity wave spin order parameters resulting in a spin splitting of electronic bands in momentum space. In real space, sublattices of opposite spin polarization are anisotropic and related by rotational symmetry. In the hitherto identified altermagnetic candidate materials, the anisotropies arise from the local crystallographic symmetry. Here, we show that altermagnetism can also form as an interaction-induced electronic instability in a lattice without the crystallographic sublattice anisotropy. We provide a microscopic example of a two-orbital model showing that the coexistence of staggered antiferromagnetic and orbital order can realize robust altermagnetism. We quantify the spin-splitter conductivity as a key experimental observable and discuss material candidates for the interaction-induced realization of altermagnetism.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Alternative paths to realize Majorana Fermions in Superconductor-Ferromagnet Heterostructures

A fundamental obstacle for achieving quantum computation is local decoherence. One way to circumvent this problem rests on the concepts of topological quantum computation using non-local information storage, for example on pairs of Majorana fermions (MFs). The arguably most promising way to generate MFs relies at present on spin-triplet p-wave states of superconductors (SC), which are not abundant in nature, unfortunately. Thus, proposals for their engineering in devices, usually via proximity effect from a conventional SC into materials with strong spin-orbit coupling (SOC), are intensively investigated nowadays. Here we take an alternative path, exploiting the different connections between fields based on a quartet coupling rule for fields introduced by one of us, we demonstrate that, for instance, coexisting Zeeman field with a charge current would provide the conditions to induce p-wave pairing in the presence of singlet superconductivity. This opens new avenues for the engineering of robust MFs in various, not necessarily (quasi-)one-dimensional, superconductor-ferromagnet heterostructures, including such motivated by recent pioneering experiments that report MFs, in particular, without the need of any exotic materials or special structures of intrinsic SOC.

Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5

Layered material structures play a key role in enhancing electron–electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn₅. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

The electronic properties along the out-of-plane direction of layered materials are often inferred indirectly. Here, Gyenis et al. directly probe in cross-section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn₅.

Field-induced magnetic instability within a superconducting condensate

The application of magnetic fields, chemical substitution, or hydrostatic pressure to strongly correlated electron materials can stabilize electronic phases with different organizational principles. We present evidence for a field-induced quantum phase transition, in superconducting Nd_0.05Ce_0.95CoIn₅, that separates two antiferromagnetic phases with identical magnetic symmetry. At zero field, we find a spin-density wave that is suppressed at the critical field μ₀H* = 8 T. For H > H*, a spin-density phase emerges and shares many properties with the Q phase in CeCoIn₅. These results suggest that the magnetic instability is not magnetically driven, and we propose that it is driven by a modification of superconducting condensate at H*.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

Antiferromagnetic order in Pauli-limited unconventional superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.

Evolution of paramagnetic quasiparticle excitations emerged in the high-field superconducting phase of CeCoIn5

We present (115)In NMR measurements in a novel thermodynamic phase of CeCoIn(5) in a high magnetic field, where exotic superconductivity exists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.

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).