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
and KRu
O
.
Abstract
When electric conductors differ from their mirror image, unusual chiral transport coefficients appear that are forbidden in achiral metals, such as a non-linear electric response known as ...electronic magnetochiral anisotropy (eMChA)
1–6
. Although chiral transport signatures are allowed by symmetry in many conductors without a centre of inversion, they reach appreciable levels only in rare cases in which an exceptionally strong chiral coupling to the itinerant electrons is present. So far, observations of chiral transport have been limited to materials in which the atomic positions strongly break mirror symmetries. Here, we report chiral transport in the centrosymmetric layered kagome metal CsV
3
Sb
5
observed via second-harmonic generation under an in-plane magnetic field. The eMChA signal becomes significant only at temperatures below
$${T}^{{\prime} }\approx $$
T
′
≈
35 K, deep within the charge-ordered state of CsV
3
Sb
5
(
T
CDW
≈ 94 K). This temperature dependence reveals a direct correspondence between electronic chirality, unidirectional charge order
7
and spontaneous time-reversal symmetry breaking due to putative orbital loop currents
8–10
. We show that the chirality is set by the out-of-plane field component and that a transition from left- to right-handed transport can be induced by changing the field sign. CsV
3
Sb
5
is the first material in which strong chiral transport can be controlled and switched by small magnetic field changes, in stark contrast to structurally chiral materials, which is a prerequisite for applications in chiral electronics.
The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the ...distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal.
The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to ...their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spinorbit-coupled kagome lattices with strong out-of-plane magnetization are lacking16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, and may enable the observation of topological quantum phenomena in the RMn6Sn6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization ofthe magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk but conducting surface states that are topologically protected by time-reversal (or spatial) symmetries. ...We extend the notion of three-dimensional topological insulators to systems that host no gapless surface states but exhibit topologically protected gapless hinge states. Their topological character is protected by spatiotemporal symmetries of which we present two cases: (i) Chiral higher-order topological insulators protected by the combination of time-reversal and a fourfold rotation symmetry. Their hinge states are chiral modes, and the bulk topology is
-classified. (ii) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs, and the bulk topology is
-classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi
TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline ...insulators (TCIs) and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures — including the theory of topological quantum chemistry (TQC) — researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85 per cent of the known stoichiometric materials host energetically isolated topological bands, and just under two-thirds of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.Solid-state materials have emerged as a platform for probing and manipulating topological phases of matter. This Review surveys topological materials discovery in nonmagnetic crystalline solids, focusing on the role of crystal symmetry and geometry in topological material predictions.
Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a non-trivial ...change of the quantum state of the system. The simplest non-Abelian quasiparticles--the Majorana bound states--can occur in one-dimensional electronic nano-structures proximity-coupled to a bulk superconductor. Here we propose a set-up, based on chains of magnetic adatoms on the surface of a thin-film superconductor, in which the control over an externally applied magnetic field suffices to create and manipulate Majorana bound states. We consider specifically rings of adatoms and show that they allow for the creation, annihilation, adiabatic motion and braiding of pairs of Majorana bound states by varying the magnitude and orientation of the external magnetic field.
A system is non-Hermitian when it exchanges energy with its environment and nonreciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial ...research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and nonreciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.
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Symmetry indicators have proven to be extremely helpful in identifying topological crystalline insulators using symmetry-group representations of their Bloch states. An extension of this approach to ...superconducting systems requires defining an appropriate atomic limit for Bogoliubov-de-Gennes Hamiltonians. Here, we introduce such a notion of atomic limit and derive a Z_{2^{d}}-valued symmetry indicator for inversion-symmetric superconductors in d dimensions. This indicator allows for a refined topological classification including higher-order phases for systems in the superconducting symmetry classes D and DIII. We further elucidate their bulk-boundary correspondence using Dirac surface theories. Requiring only the normal-state band structure and the superconducting order-parameter symmetry as input, this indicator is well suited for a search of topological superconductors using first-principles calculations.
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