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Finite-momentum Cooper pairing is an unconventional form of superconductivity that is widely believed to require finite magnetization. Altermagnetism is an emerging magnetic phase with highly anisotropic spin-splitting of specific symmetries, but zero net magnetization. Here, we study Cooper pairing in metallic altermagnets connected to conventional s -wave superconductors. Remarkably, we find that the Cooper pairs induced in the altermagnets acquire a finite center-of-mass momentum, despite the zero net magnetization in the system. This anomalous Cooper-pair momentum strongly depends on the propagation direction and exhibits unusual symmetric patterns. Furthermore, it yields several unique features: (i) highly orientation-dependent oscillations in the order parameter, (ii) controllable 0- π transitions in the Josephson supercurrent, (iii) large-oblique-angle Cooper-pair transfer trajectories in junctions parallel with the direction where spin splitting vanishes, and (iv) distinct Fraunhofer patterns in junctions oriented along different directions. Finally, we discuss the implementation of our predictions in candidate materials such as RuO 2 and KRu 4 O 8 . An altermagnet has highly anisotropic spin splitting but zero net magnetization. Here, S.-B. Zhang et al. theoretically study the behavior of s -wave superconductor/altermagnet hybrid structures, finding that Cooper pairs in the proximitized altermagnet have an anisotropic non-zero momentum.

Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or superconducting ground-state wavefunctions, is crucial for enabling Majorana zero modes in solid-state systems. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivially superconducting topological materials. Here we show that Majorana-carrying superconducting vortex is not exclusive to bulk-state topology, but can arise from topologically trivial quantum materials as well. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topological physics that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and experimental signatures for vortex Majorana modes are also discussed. Our work provides new guidelines for vortex-based Majorana search in general superconductors. It is widely believed that bulk-state topology is crucial for enabling Majorana zero modes in solid-state systems. Here, the authors predict that superconducting vortices containing Majorana zero modes can arise from topologically-trivial electronic bands, expanding the pool of materials which may host such phenomena.

We show that lattice dislocations of topological iron-based superconductors such as FeTe 1− x Se x will intrinsically trap non-Abelian Majorana quasiparticles, in the absence of any external magnetic field. Our theory is motivated by the recent experimental observations of normal-state weak topology and surface magnetism that coexist with superconductivity in FeTe 1− x Se x , the combination of which naturally achieves an emergent second-order topological superconductivity in a two-dimensional subsystem spanned by screw or edge dislocations. This exemplifies a new embedded higher-order topological phase in class D, where Majorana zero modes appear around the “corners” of a low-dimensional embedded subsystem, instead of those of the full crystal. A nested domain wall theory is developed to understand the origin of these defect Majorana zero modes. When the surface magnetism is absent, we further find that s ± pairing symmetry itself is capable of inducing a different type of class-DIII embedded higher-order topology with defect-bound Majorana Kramers pairs. We also provide detailed discussions on the real-world material candidates for our proposals, including FeTe 1− x Se x , LiFeAs, β -PdBi 2 , and heterostructures of bismuth, etc. Our work establishes lattice defects as a new venue to achieve high-temperature topological quantum information processing. The authors propose that screw or edge dislocations can trap Majorana zero modes in the absence of an external magnetic field. They predict that the Majoranas will appear as second-order topological modes on the four corners of an embedded 2D subsystem defined by the cutting plane of the dislocation.

Altermagnetism, a kind of collinear magnetism that is characterized by a momentum-dependent band and spin splitting without net magnetization, has recently attracted considerable interest. Finding altermagnetic materials with large splitting near the Fermi level necessarily requires three-dimensional k -space mapping. While this is crucial for spintronic applications and emergent phenomena, it remains challenging. Here, using synchrotron-based angle-resolved photoemission spectroscopy (ARPES), spin-resolved ARPES and model calculations, we uncover a large altermagnetic splitting, up to  ~1.0 eV, near the Fermi level in CrSb. We verify its bulk-type g -wave altermagnetism through systematic three-dimensional k -space mapping, which unambiguously reveals the altermagnetic symmetry and associated nodal planes. Spin-resolved ARPES measurements further verify the spin polarizations of the split bands near Fermi level. Tight-binding model analysis indicates that the large altermagnetic splitting arises from strong third-nearest-neighbor hopping mediated by Sb ions. The large band/spin splitting near Fermi level in metallic CrSb, together with its high T N (up to 705 K) and simple spin configuration, paves the way for exploring emergent phenomena and spintronic applications based on altermagnets. Altermagnets combine the rapid dynamics and zero magnetization of collinear antiferromagnets with the spin-splitting of ferromagnets, making them an idea platform for both fundamental research and applications. Here, Yang, Li and coauthors map the large altermagnetic spin-splitting in CrSb located near the Fermi level.

Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors. When two superconducting gap functions with different symmetries compete, the relative phase channel ( θ − ≡ θ 1 − θ 2 ) exhibits an Ising-type Z 2 symmetry due to the second order Josephson coupling, where θ 1,2 are the phases of two gap functions. In contrast, the U (1) symmetry in the channel of is intact. The phase locking, i.e., ordering of θ − , can take place in the phase fluctuation regime before the onset of superconductivity, i.e., when θ + is disordered. If θ − is pinned at , then time-reversal symmetry is broken in the normal state, otherwise, if θ − = 0, or, π , rotational symmetry is broken, leading to a nematic normal state. In both cases, the order parameters possess a 4-fermion structure beyond the scope of mean-field theory, which can be viewed as a high order symmetry breaking. We employ an effective two-component XY -model assisted by a renormalization group analysis to address this problem. As a natural by-product, we also find the other interesting intermediate phase corresponds to ordering of θ + but with θ − disordered. This is the quartetting, or, charge-4 e , superconductivity, which occurs above the low temperature Z 2 -breaking charge-2 e superconducting phase. Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb) 2 Te 3 . By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer. The authors study (Bi,Sb) 2 Te 3 /FeTe bilayers, which feature emergent superconductivity at the interface with T c  ~ 12 K. Through angle-resolved photoemission spectroscopy and electrical transport measurements, they argue that the Dirac-fermion-mediated Ruderman-Kittel-Kasuya-Yosida-type interaction weakens antiferromagnetic order in FeTe layer, allowing for superconductivity.

Sau, Lutchyn, Tewari and Das Sarma (SLTD) proposed a heterostructure consisting of a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator and showed possible Majorana zero mode. Here we study spin polarization of the vortex core states and spin selective Andreev reflection at the vortex center of the SLTD model. In the topological phase, the differential conductance at the vortex center contributed from the Andreev reflection, is spin selective and has a quantized value ( d I / d V ) A t o p o = 2 e 2 / h at zero bias. In the topological trivial phase, ( d I / d V ) A t r i v i a l at the lowest quasiparticle energy of the vortex core is spin selective due to the spin-orbit coupling (SOC). Unlike in the topological phase, ( d I / d V ) A t r i v i a l is suppressed in the Giaever limit and vanishes exactly at zero bias due to the quantum destruction interference.

Searching for topological superconductors with non-Abelian states has been attracting broad interest. The most commonly used recipe for building topological superconductors utilizes the proximity effect, which significantly limits the working temperature. Here, we propose a mechanism to attain topological superconductivity via forward phonon scatterings. Our crucial observation is that electron-phonon interactions with small momentum transfers favor spin-triplet Cooper pairing under an applied magnetic field. This process facilitates the formation of chiral topological superconductivity even without Rashba spin-orbit coupling. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbit coupling, pairing symmetries, and the topological property of the superconducting state. This theory not only deepens our understanding of the superconductivity induced by the electron-phonon interaction but also sheds light on the critical role of the electron-phonon coupling in pursuing non-Abelian Majorana quasiparticles. Topological superconductors are deemed to carry great potential of realizing non-Abelian states for fault-tolerant quantum computing. Here, the authors propose a new theoretical mechanism to attain topological superconductivity via forward phonon scattering and hence provide a new possibility for engineering high-temperature topological superconductors.

Understanding the pairing symmetry is a crucial theoretical aspect in the study of unconventional superconductivity for interpreting experimental results. Here we study superconductivity of electron systems with both spin and pseudospin-1/2 degrees of freedom. By solving linearized gap equations, we derive a weak coupling criterion for the even-parity spin-singlet pseudospin-triplet pairing. It can generally mix with the on-site s-wave pairing since both of them belong to the same symmetry representation (A1g) and their mixture could naturally give rise to anisotropic intra-band pairing gap functions with or without nodes. This may directly explain why some of the iron-chalcogenide superconductors are fully gapped (e.g. FeSe thin film) and some have nodes (e.g. LaFePO and LiFeP). We also find that the anisotropy of gap functions can be enhanced when the principal rotation symmetry is spontaneously broken in the normal state such as nematicity, and the energetic stabilization of pseudospin-triplet pairings indicates the coexistence of nematicity and superconductivity. This could be potentially applied to bulk FeSe, where gap anisotropy has been experimentally observed.The underlying symmetry of a given system dictates the material properties from the electronic band structure to its spontaneous symmetry broken ordering. Here, the authors consider the effects of symmetry breaking and investigate spin-singlet orbital triplet pairings in unconventional superconductors with electronic nematicity, they apply their results to iron-based superconductors and twisted bilayer graphene.

Topological superconductors possess a bulk superconducting gap and boundary gapless excitations, known as “Majorana fermion”. Search for new systems with topological superconductivity is of fundamental and application importance due to the potential application of Majorana fermions in topological quantum computation. Here we show that the Larkin-Ovchinnikov superconducting phase with a finite momentum pairing can emerge in a model of bilayer superconducting topological insulator films, in which superconductivity appears for both the top and bottom surface states, and can be topologically non-trivial. This “topological Larkin-Ovchinnikov phase” is induced by an in-plane magnetic field and possesses a Majorana mode chain along the edge perpendicular to the in-plane magnetic field direction due to its non-trivial Z 2 topological nature. Our theoretical model can be naturally realized in superconductor/topological insulator sandwich structure or in Fe(Te, Se) film, a topological material with superconductivity, and thus provides a route to explore unconventional superconductivity in existing systems. Topological superconductors possess Majorana modes at the edge and are important in future quantum computational devices. The authors theoretically demonstrate the Larkin-Ovchinnikov superconducting phase can be topologically non-trivial in certain sandwich structure or iron-based superconductor films and possess a chain of Majorana modes.