Anomalous upper critical field in CeCoIn5/YbCoIn5 superlattices with a Rashba-type heavy Fermion interface

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.

Evidence for a finite-momentum Cooper pair in tricolor d-wave superconducting superlattices

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with finite-momentum pairs has long been a challenge, but establishing its existence has long suffered from the lack of an appropriate probe to reveal its momentum. Recently, it has been proposed that the nonreciprocal electron transport is the most powerful probe for the finite-momentum pairs, because it directly couples to the supercurrents. Here we reveal such a pairing state by the non-reciprocal transport on tricolor superlattices with strong spin-orbit coupling combined with broken inversion-symmetry consisting of atomically thin d-wave superconductor CeCoIn5. We find that while the second-harmonic resistance exhibits a distinct dip anomaly at the low-temperature (T)/high-magnetic field (H) corner in the HT-plane for H applied to the antinodal direction of the d-wave gap, such an anomaly is absent for H along the nodal direction. By carefully isolating extrinsic effects due to vortex dynamics, we reveal the presence of a non-reciprocal response originating from intrinsic superconducting properties characterized by finite-momentum pairs. We attribute the high-field state to the helical superconducting state, wherein the phase of the order parameter is spontaneously spatially modulated.

Valley-dimensionality locking of superconductivity in cubic phosphides

Two-dimensional superconductivity is primarily realized in atomically thin layers through extreme exfoliation, epitaxial growth, or interfacial gating. Apart from their technical challenges, these approaches lack sufficient control over the Fermiology of superconducting systems. Here, we offer a Fermiology-engineering approach, allowing us to desirably tune the coherence length of Cooper pairs and the dimensionality of superconducting states in arsenic phosphides AsxP1-x under hydrostatic pressure. We demonstrate how this turns these compounds into tunable two-dimensional superconductors with a dome-shaped phase diagram even in the bulk limit. This peculiar behavior is shown to result from an unconventional valley-dimensionality locking mechanism, driven by a delicate competition between three-dimensional hole-type and two-dimensional electron-type energy pockets spatially separated in momentum space. The resulting dimensionality crossover is further discussed to be systematically controllable by pressure and stoichiometry tuning. Our findings pave a unique way to realize and control superconducting phases with special pairing and dimensional orders.

Angular dependence of the upper critical induction of cleans- anddx2-y2-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies

We employ the Schrödinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm-Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic inductionBc2(θ,ϕ,T)at arbitrary directions and temperaturesTfor isotropics-wave and for anisotropicdx2-y2-wave superconducting order parameters. As for anisotropics-wave superconductors,Bc2is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factorα(θ,ϕ). However, fordx2-y2-wave pairing and vanishing planar effective mass anisotropy,Bc2(π/2,ϕ,T)exhibits a four-fold azimuthal pattern withC₄symmetry the maxima of which are along the crystal axes just below the transition temperatureT_c, but these maxima are rotated byπ/4about thezaxis asTis lowered to 0. However fordx2-y2-wave pairing with weak planar effective mass anisotropy,Bc2(π/2,ϕ,T)exhibits a two-fold pattern withC₂symmetry for allT ⩽ Tc, which also rotates byπ/4about thezaxis asTis lowered to 0. These low planar effective mass anisotropy cases provide a new method to distinguishs-wave anddx2-y2-wave pairing symmetries in clean unconventional superconductors.

Atomistic Engineering of Phonons in Functional Oxide Heterostructures

Engineering of phonons, that is, collective lattice vibrations in crystals, is essential for manipulating physical properties of materials such as thermal transport, electron-phonon interaction, confinement of lattice vibration, and optical polarization. Most approaches to phonon-engineering have been largely limited to the high-quality heterostructures of III-V compound semiconductors. Yet, artificial engineering of phonons in a variety of materials with functional properties, such as complex oxides, will yield unprecedented applications of coherent tunable phonons in future quantum acoustic devices. In this study, artificial engineering of phonons in the atomic-scale SrRuO₃ /SrTiO₃ superlattices is demonstrated, wherein tunable phonon modes are observed via confocal Raman spectroscopy. In particular, the coherent superlattices led to the backfolding of acoustic phonon dispersion, resulting in zone-folded acoustic phonons in the THz frequency domain. The frequencies can be largely tuned from 1 to 2 THz via atomic-scale precision thickness control. In addition, a polar optical phonon originating from the local inversion symmetry breaking in the artificial oxide superlattices is observed, exhibiting emergent functionality. The approach of atomic-scale heterostructuring of complex oxides will vastly expand material systems for quantum acoustic devices, especially with the viability of functionality integration.

Extremely high upper critical field in BiCh2-based (Ch: S and Se) layered superconductor LaO0.5F0.5BiS2-xSex (x = 0.22 and 0.69)

Centrosymmetric compounds with local inversion symmetry breaking have tremendously interesting and intriguing physical properties. In this study, we focus on a BiCh₂-based (Ch: S, Se) layered superconductor, as a system with local inversion asymmetry, because spin polarisation based on the Rashba–Dresselhaus-type spin–orbit coupling has been observed in centrosymmetric BiCh₂-based LaOBiS₂ systems, while the BiCh₂ layer lacks local inversion symmetry. Herein, we report the existence of extremely high in-plane upper critical fields in the BiCh₂-based system LaO_0.5F_0.5BiS_2−xSe_x (x = 0.22 and 0.69). The superconducting states are not completely suppressed by the applied magnetic fields with strengths up to 55 T. Thus, we consider that the in-plane upper critical field is enhanced by the local inversion symmetry breaking and its layered structure. Our study will open a new pathway for the discovery of superconductors that exhibit a high upper critical field by focusing on the local inversion symmetry breaking.

Pauli-limit violation and re-entrant superconductivity in moiré graphene

Moiré quantum matter has emerged as a materials platform in which correlated and topological phases can be explored with unprecedented control. Among them, magic-angle systems constructed from two or three layers of graphene have shown robust superconducting phases with unconventional characteristics^1-5. However, direct evidence of unconventional pairing remains to be experimentally demonstrated. Here we show that magic-angle twisted trilayer graphene exhibits superconductivity up to in-plane magnetic fields in excess of 10 T, which represents a large (2-3 times) violation of the Pauli limit for conventional spin-singlet superconductors^6,7. This is an unexpected observation for a system that is not predicted to have strong spin-orbit coupling. The Pauli-limit violation is observed over the entire superconducting phase, which indicates that it is not related to a possible pseudogap phase with large superconducting amplitude pairing. Notably, we observe re-entrant superconductivity at large magnetic fields, which is present over a narrower range of carrier densities and displacement fields. These findings suggest that the superconductivity in magic-angle twisted trilayer graphene is likely to be driven by a mechanism that results in non-spin-singlet Cooper pairs, and that the external magnetic field can cause transitions between phases with potentially different order parameters. Our results demonstrate the richness of moiré superconductivity and could lead to the design of next-generation exotic quantum matter.

Controlling unconventional superconductivity in artificially engineeredf-electron Kondo superlattices

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-T_ccuprates, iron pnictides, and heavy-fermion compounds. Interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures provide a new approach to this most fundamental and hotly debated subject. We have been able to use a recent state-of-the-art molecular-beam-epitaxy technique to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo superlattices provide a unique opportunity to study the mutual interaction between unconventional superconductivity and magnetic order through the atomic interface. Here, we design and fabricate hybrid Kondo superlattices consisting of alternating layers of superconducting CeCoIn₅withd-wave pairing symmetry and nonmagnetic metal YbCoIn₅or antiferromagnetic heavy fermion metals such as CeRhIn₅and CeIn₃. In these Kondo superlattices, superconducting heavy electrons are confined within the two-dimensional CeCoIn₅block layers and interact with neighboring nonmagnetic or magnetic layers through the interface. Superconductivity is strongly influenced by local inversion symmetry breaking at the interface in CeCoIn₅/YbCoIn₅superlattices. The superconducting and antiferromagnetic states coexist in spatially separated layers in CeCoIn₅/CeRhIn₅and CeCoIn₅/CeIn₃superlattices, but their mutual coupling via the interface significantly modifies the superconducting and magnetic properties. The fabrication of a wide variety of hybrid superlattices paves a new way to study the relationship between unconventional superconductivity and magnetism in strongly correlated materials.

Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO2 and RuO2

Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo (2CK) effect, including the emergence of an unconventional metallic state in the low-energy limit, also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have made the observation of the nonmagnetic, orbital 2CK effect in real quantum materials difficult, if not impossible. We report the observation of orbital one- and two-channel Kondo physics in the symmetry-enforced Dirac nodal line (DNL) metals IrO₂ and RuO₂ nanowires and show that the symmetries that enforce the existence of DNLs also promote the formation of nonmagnetic Kondo correlations. Rutile oxide nanostructures thus form a versatile quantum matter platform to engineer and explore intrinsic, interacting topological states of matter.

Strong electron correlations may give rise to an unconventional metallic state accompanying non-magnetic Kondo scattering. Here, the authors report signatures of orbital one- and two-channel Kondo physics in Dirac nodal line metals RuO₂ and IrO₂ nanowires.

Josephson coupled Ising pairing induced in suspended MoS2 bilayers by double-side ionic gating

Superconductivity in monolayer transition metal dichalcogenides is characterized by Ising-type pairing induced via a strong Zeeman-type spin-orbit coupling. When two transition metal dichalcogenides layers are coupled, more exotic superconducting phases emerge, which depend on the ratio of Ising-type protection and interlayer coupling strength. Here, we induce superconductivity in suspended MoS₂ bilayers and unveil a coupled superconducting state with strong Ising-type spin-orbit coupling. Gating the bilayer symmetrically from both sides by ionic liquid gating varies the interlayer interaction and accesses electronic states with broken local inversion symmetry while maintaining the global inversion symmetry. We observe a strong suppression of the Ising protection that evidences a coupled superconducting state. The symmetric gating scheme not only induces superconductivity in both atomic sheets but also controls the Josephson coupling between the layers, which gives rise to a dimensional crossover in the bilayer.

Tuning the Pairing Interaction in a d-Wave Superconductor by Paramagnons Injected through Interfaces

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials. A new approach to this most fundamental and hotly debated issue focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. Here we fabricate hybrid superlattices consisting of alternating atomic layers of the heavy-fermion superconductor CeCoIn_{5} and antiferromagnetic (AFM) metal CeRhIn_{5}, in which the AFM order can be suppressed by applying pressure. We find that the superconducting and AFM states coexist in spatially separated layers, but their mutual coupling via the interface significantly modifies the superconducting properties. An analysis of upper critical fields reveals that, upon suppressing the AFM order by applied pressure, the force binding superconducting electron pairs acquires an extreme strong-coupling nature. This demonstrates that superconducting pairing can be tuned nontrivially by magnetic fluctuations (paramagnons) injected through the interface.

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}.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions

Heavy fermions have served as prototype examples of strongly-correlated electron systems. The occurrence of unconventional superconductivity in close proximity to the electronic instabilities associated with various degrees of freedom points to an intricate relationship between superconductivity and other electronic states, which is unique but also shares some common features with high temperature superconductivity. The magnetic order in heavy fermion compounds can be continuously suppressed by tuning external parameters to a quantum critical point, and the role of quantum criticality in determining the properties of heavy fermion systems is an important unresolved issue. Here we review the recent progress of studies on Ce based heavy fermion superconductors, with an emphasis on the superconductivity emerging on the edge of magnetic and charge instabilities as well as the quantum phase transitions which occur by tuning different parameters, such as pressure, magnetic field and doping. We discuss systems where multiple quantum critical points occur and whether they can be classified in a unified manner, in particular in terms of the evolution of the Fermi surface topology.

From Kondo lattices to Kondo superlattices

The realization of new classes of ground states in strongly correlated electron systems continues to be a major issue in condensed matter physics. Heavy fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because of their intriguing properties associated with many-body effects. Recently, a state-of-the-art molecular beam epitaxy technique was developed to reduce the dimensionality of heavy electron systems by fabricating artificial superlattices that include heavy fermion compounds; this approach can produce a new type of electronic state in two-dimensional (2D) heavy fermion systems. In artificial superlattices of the antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3, the magnetic order is suppressed by a reduction in the thickness of the CeIn3 layers. In addition, the 2D confinement of heavy fermions leads to enhancement of the effective electron mass and deviation from the standard Fermi liquid electronic properties, which are both associated with the dimensional tuning of quantum criticality. In the superconducting superlattices of the heavy fermion superconductor CeCoIn5 and nonmagnetic metal YbCoIn5, signatures of superconductivity are observed even at the thickness of one unit-cell layer of CeCoIn5. The most remarkable feature of this 2D heavy fermion superconductor is that the thickness reduction of the CeCoIn5 layers changes the temperature and angular dependencies of the upper critical field significantly. This result is attributed to a substantial suppression of the Pauli pair-breaking effect through the local inversion symmetry breaking at the interfaces of CeCoIn5 block layers. The importance of the inversion symmetry breaking in this system has also been supported by site-selective nuclear magnetic resonance spectroscopy, which can resolve spectroscopic information from each layer separately, even within the same CeCoIn5 block layer. In addition, recent experiments involving CeCoIn5/YbCoIn5 superlattices have shown that the degree of the inversion symmetry breaking and, in turn, the Rashba splitting are controllable, offering the prospect of achieving even more fascinating superconducting states. Thus, these Kondo superlattices pave the way for the exploration of unconventional metallic and superconducting states.

Tuning the Magnetic Quantum Criticality of Artificial Kondo Superlattices CeRhIn_{5}/YbRhIn_{5}

The effects of reduced dimensions and the interfaces on antiferromagnetic quantum criticality are studied in epitaxial Kondo superlattices, with alternating n layers of heavy-fermion antiferromagnet CeRhIn_{5} and seven layers of normal metal YbRhIn_{5}. As n is reduced, the Kondo coherence temperature is suppressed due to the reduction of effective Kondo screening. The Néel temperature is gradually suppressed as n decreases and the quasiparticle mass is strongly enhanced, implying dimensional control toward a quantum critical point. Magnetotransport measurements reveal that a quantum critical point is reached for the n=3 superlattice by applying small magnetic fields. Remarkably, the anisotropy of the quantum critical field is opposite to the expectations from the magnetic susceptibility in bulk CeRhIn_{5}, suggesting that the Rashba spin-orbit interaction arising from the inversion symmetry breaking at the interface plays a key role for tuning the quantum criticality in the two-dimensional Kondo lattice.

Robust two-dimensional superconductivity and vortex system in Bi2Te3/FeTe heterostructures

The discovery of two-dimensional superconductivity in Bi2Te3/FeTe heterostructures provides a new platform for the search of Majorana fermions in condensed matter systems. Since Majorana fermions are expected to reside at the core of the vortices, a close examination of the vortex dynamics in superconducting interface is of paramount importance. Here, we report the robustness of the interfacial superconductivity and 2D vortex dynamics in four as-grown and aged Bi2Te3/FeTe heterostructure with different Bi2Te3 epilayer thickness (3, 5, 7, 14 nm). After two years' air exposure, superconductivity remains robust even when the thickness of Bi2Te3 epilayer is down to 3 nm. Meanwhile, a new feature at ~13 K is induced in the aged samples, and the high field studies reveal its relevance to superconductivity. The resistance of all as-grown and aged heterostructures, just below the superconducting transition temperature follows the Arrhenius relation, indicating the thermally activated flux flow behavior at the interface of Bi2Te3 and FeTe. Moreover, the activation energy exhibits a logarithmic dependence on the magnetic field, providing a compelling evidence for the 2D vortex dynamics in this novel system. The weak disorder associated with aging-induced Te vacancies is possibly responsible for these observed phenomena.

Controllable Rashba spin-orbit interaction in artificially engineered superlattices involving the heavy-fermion superconductor CeCoIn5

By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between the heavy-fermion superconductor CeCoIn5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn5. The introduction of the thickness modulation of YbCoIn5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considering the effect of the Rashba spin-orbit interaction arising from the inversion symmetry breaking and the associated weakening of the Pauli pair-breaking effect. Since the degree of thickness modulation is a design feature of this type of superlattices, the Rashba interaction and the nature of pair breaking are largely tunable in these modulated superlattices with strong spin-orbit coupling.