Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking

Engineering and enhancing the breaking of inversion symmetry in solids-that is, allowing electrons to differentiate between 'up' and 'down'-is a key goal in condensed-matter physics and materials science because it can be used to stabilize states that are of fundamental interest and also have potential practical applications. Examples include improved ferroelectrics for memory devices and materials that host Majorana zero modes for quantum computing. Although inversion symmetry is naturally broken in several crystalline environments, such as at surfaces and interfaces, maximizing the influence of this effect on the electronic states of interest remains a challenge. Here we present a mechanism for realizing a much larger coupling of inversion-symmetry breaking to itinerant surface electrons than is typically achieved. The key element is a pronounced asymmetry of surface hopping energies-that is, a kinetic-energy-coupled inversion-symmetry breaking, the energy scale of which is a substantial fraction of the bandwidth. Using spin- and angle-resolved photoemission spectroscopy, we demonstrate that such a strong inversion-symmetry breaking, when combined with spin-orbit interactions, can mediate Rashba-like spin splittings that are much larger than would typically be expected. The energy scale of the inversion-symmetry breaking that we achieve is so large that the spin splitting in the CoO₂- and RhO₂-derived surface states of delafossite oxides becomes controlled by the full atomic spin-orbit coupling of the 3d and 4d transition metals, resulting in some of the largest known Rashba-like spin splittings. The core structural building blocks that facilitate the bandwidth-scaled inversion-symmetry breaking are common to numerous materials. Our findings therefore provide opportunities for creating spin-textured states and suggest routes to interfacial control of inversion-symmetry breaking in designer heterostructures of oxides and other material classes.

Interplay of charge density wave and multiband superconductivity in 2H-PdxTaSe2

2H-TaSe2 has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-T is sequentially followed by an incommensurate charge density wave (ICDW) state at ≈122 K and a commensurate charge density wave (CCDW) state at ≈90 K, and superconductivity at TC ~ 0.14 K. Upon systematic intercalation of Pd ions into TaSe2, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at x ~ 0.09-0.10. Moreover, TC shows a dramatic enhancement up to 3.3 K at x = 0.08, ~24 times of TC in 2H-TaSe2, in proportional to the density of states N(EF). Investigations of upper critical fields Hc2 in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor γH = , quasi-linear increase of , and an upward, positive-curvature in near TC. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs x, we propose that the increase of N(EF) and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of TC in PdxTaSe2.

Field-induced transition within the superconducting state of CeRh2As2

Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh₂As₂ Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

In Situ Modification of a Delafossite-Type PdCoO2 Bulk Single Crystal for Reversible Hydrogen Sorption and Fast Hydrogen Evolution

The observation of extraordinarily high conductivity in delafossite-type PdCoO₂ is of great current interest, and there is some evidence that electrons behave like a fluid when flowing in bulk crystals of PdCoO₂. Thus, this material is an ideal platform for the study of the electron transfer processes in heterogeneous reactions. Here, we report the use of bulk single-crystal PdCoO₂ as a promising electrocatalyst for hydrogen evolution reactions (HERs). An overpotential of only 31 mV results in a current density of 10 mA cm^-2, accompanied by high long-term stability. We have precisely determined that the crystal surface structure is modified after electrochemical activation with the formation of strained Pd nanoclusters in the surface layer. These nanoclusters exhibit reversible hydrogen sorption and desorption, creating more active sites for hydrogen access. The bulk PdCoO₂ single crystal with ultrahigh conductivity, which acts as a natural substrate for the Pd nanoclusters, provides a high-speed channel for electron transfer.

Observation of Antiferromagnetic Order as Odd-Parity Multipoles inside the Superconducting Phase in CeRh_{2}As_{2}

Spatial inversion symmetry in crystal structures is closely related to the superconducting (SC) and magnetic properties of materials. Recently, several theoretical proposals that predict various interesting phenomena caused by the breaking of the local inversion symmetry have been presented. However, experimental validation has not yet progressed owing to the lack of model materials. Here we present evidence for antiferromagnetic (AFM) order in CeRh_{2}As_{2} (SC transition temperature T_{SC}∼0.37  K), wherein the Ce site breaks the local inversion symmetry. The evidence is based on the observation of different extents of broadening of the nuclear quadrupole resonance spectrum at two crystallographically inequivalent As sites. This AFM ordering breaks the inversion symmetry of this system, resulting in the activation of an odd-parity magnetic multipole. Moreover, the onset of antiferromagnetism T_{N} within an SC phase, with T_{N}<T_{SC}, is quite unusual in systems wherein superconductivity coexists or competes with magnetism. Our observations show that CeRh_{2}As_{2} is a promising system to study how the absence of local inversion symmetry induces or influences unconventional magnetic and SC states, as well as their interaction.

h/e oscillations in interlayer transport of delafossites

Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO₂ and PtCoO₂ The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck's constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T > 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.

Orbital selective Fermi surface shifts and mechanism of high T(c) superconductivity in correlated AFeAs (A=Li, Na)

Based on the dynamical mean field theory and angle resolved photoemission spectroscopy, we have investigated the mechanism of high T(c) superconductivity in stoichiometric LiFeAs. The calculated spectrum is in excellent agreement with the measured angle resolved photoemission spectroscopy. The Fermi surface (FS) nesting, which is predicted in the conventional density functional theory method, is suppressed due to the orbital-dependent correlation effect within the dynamical mean field theory method. We have shown that such marginal breakdown of the FS nesting is an essential condition to the spin-fluctuation mediated superconductivity, while the good FS nesting in NaFeAs induces a spin density wave ground state. Our results indicate that a fully charge self-consistent description of the correlation effect is crucial in the description of the FS nesting-driven instabilities.

Directional ballistic transport in the two-dimensional metal PdCoO2

In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO₂ yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.

Low-symmetry nonlocal transport in microstructured squares of delafossite metals

Intense work studying the ballistic regime of electron transport in two-dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, additional forms of ballistic transport have become accessible in the quasi-two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work and whose Fermi surfaces are nearly hexagonal in shape and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are nonintuitive at first sight, we show that they can be understood within a nonlocal Landauer-Büttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of nonlocal transport can be resolved for squares of linear dimension of nearly 100 µm, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.

Investigation of Planckian behavior in a high-conductivity oxide: PdCrO2

The layered delafossite metal PdCrO[Formula: see text] is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO[Formula: see text] layers. At high temperatures, T, it has a T-linear resistivity which is not seen in the isostructural but nonmagnetic PdCoO[Formula: see text]. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate "Planckian metal" physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio, and studying the sources of its high-temperature entropy. The T-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10[Formula: see text] of the Planckian value of k[Formula: see text]T/[Formula: see text].

Parity Transition of Spin-Singlet Superconductivity Using Sublattice Degrees of Freedom

Recently, a superconducting (SC) transition from low-field (LF) to high-field (HF) SC states was reported in CeRh_{2}As_{2}, indicating the existence of multiple SC states. It has been theoretically noted that the existence of two Ce sites in the unit cell, the so-called sublattice degrees of freedom owing to the local inversion symmetry breaking at the Ce sites, can lead to the appearance of multiple SC phases even under an interaction inducing spin-singlet superconductivity. CeRh_{2}As_{2} is considered as the first example of multiple SC phases owing to this sublattice degree of freedom. However, microscopic information about the SC states has not yet been reported. In this study, we measured the SC spin susceptibility at two crystallographically inequivalent As sites using nuclear magnetic resonance for various magnetic fields. Our experimental results strongly indicate a spin-singlet state in both SC phases. In addition, the antiferromagnetic phase, which appears within the SC phase, only coexists with the LF SC phase; there is no sign of magnetic ordering in the HF SC phase. The present Letter reveals unique SC properties originating from the locally noncentrosymmetric characteristics.

Quasiparticle interference and quantum confinement in a correlated Rashba spin-split 2D electron liquid

Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields-crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fermi surface exhibits the same spin texture as for weak ISB, but the orbital texture is completely different, raising questions about the effect on quasiparticle scattering. We demonstrate that the spin-orbital selection rules relevant for conventional Rashba system are obeyed as true spin selection rules in this correlated electron liquid and determine its spin coherence length from quasiparticle interference imaging.

Probing spin correlations using angle-resolved photoemission in a coupled metallic/Mott insulator system

A nearly free electron metal and a Mott insulating state can be thought of as opposite ends of the spectrum of possibilities for the motion of electrons in a solid. Understanding their interaction lies at the heart of the correlated electron problem. In the magnetic oxide metal PdCrO₂, nearly free and Mott-localized electrons exist in alternating layers, forming natural heterostructures. Using angle-resolved photoemission spectroscopy, quantitatively supported by a strong coupling analysis, we show that the coupling between these layers leads to an "intertwined" excitation that is a convolution of the charge spectrum of the metallic layer and the spin susceptibility of the Mott layer. Our findings establish PdCrO₂ as a model system in which to probe Kondo lattice physics and also open new routes to use the a priori nonmagnetic probe of photoemission to gain insights into the spin susceptibility of correlated electron materials.

Evidence for coexistence of superconductivity and magnetism in single crystals of Co-doped SrFe(2)As(2)

In order to investigate whether magnetism and superconductivity coexist in Co-doped SrFe(2)As(2), we have prepared single crystals of SrFe(2-x)Co(x)As(2), x = 0 and 0.4, and characterized them via x-ray diffraction, electrical resistivity in zero and applied field up to 9 T as well as at ambient and applied pressure up to 1.6 GPa, and magnetic susceptibility. At x = 0.4, there is both magnetic and resistive evidence for a spin density wave transition at 120 K, while T(c) = 19.5 K-indicating coexistent magnetism and superconductivity. A discussion of how these results compare with reported results, both in SrFe(2-x)Co(x)As(2) and in other doped 122 compounds, is given.

Avoided metallicity in a hole-doped Mott insulator on a triangular lattice

Doping of a Mott insulator gives rise to a wide variety of exotic emergent states, from high-temperature superconductivity to charge, spin, and orbital orders. The physics underpinning their evolution is, however, poorly understood. A major challenge is the chemical complexity associated with traditional routes to doping. Here, we study the Mott insulating CrO2 layer of the delafossite PdCrO2, where an intrinsic polar catastrophe provides a clean route to doping of the surface. From scanning tunnelling microscopy and angle-resolved photoemission, we find that the surface stays insulating accompanied by a short-range ordered state. From density functional theory, we demonstrate how the formation of charge disproportionation results in an insulating ground state of the surface that is disparate from the hidden Mott insulator in the bulk. We demonstrate that voltage pulses induce local modifications to this state which relax over tens of minutes, pointing to a glassy nature of the charge order.

Pressure-Tuned Quantum Criticality in the Locally Noncentrosymmetric Superconductor CeRh_{2}As_{2}

The unconventional superconductor CeRh_{2}As_{2} (critical temperature T_{c}≈0.4  K) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, which are enabled by a locally noncentrosymmetric structure. The superconductivity is preceded by a phase transition of unknown origin at T_{0}=0.5  K. Electronic low-temperature properties of CeRh_{2}As_{2} show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of the two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the T_{0} order vanishes completely at a modest pressure of P_{0}≈0.5  GPa, revealing a QCP. In line with the quantum criticality picture, the linear temperature dependence of the resistivity at P_{0} evolves into a Fermi-liquid quadratic dependence as quantum critical fluctuations are suppressed by increasing pressure. Furthermore, the domelike behavior of T_{c} around P_{0} implies that the fluctuations of the T_{0} order are involved in the SC pairing mechanism.