Zone Corner Research Articles

Superconducting pairing mechanism in CeCoIn5 revisited

Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) measurements have previously been applied to the study of the heavy-fermion system $\mathrm{CeCo}{\mathrm{In}}_{5}$ to examine the superconducting gap structure and band dispersions via quasiparticle intereference. Here we directly measure the dispersing electron bands with angle-resolved photoelectron spectroscopy (ARPES) and compare with first-principles electronic structure calculations. By autocorrelating the ARPES-resolved bands with themselves we can measure the potential $q$ vectors and discern exactly which bands the STM is measuring. We find that the STM results are dominated by scattering associated with a cloverleaf shaped band centered at the zone corners. This same band is also a viable candidate to host the superconducting gap. The electronic structure calculations indicate that this region of the Fermi surface involves significant contributions from the Co $d$ electrons, an indication that the superconductivity in these materials is more three dimensional than that found in the related unconventional superconductors, the cuprates and the pnictides.

Z2 -projective translational symmetry protected topological phases

Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel topological phases. We show that the $\mathbb{Z}_2$ projectively represented translational symmetry operators adopt a distinct commutation relation, and become momentum dependent analogous to twofold nonsymmorphic symmetries. Combined with other internal or external symmetries, they give rise to many exotic band topology, such as the degeneracy over the whole boundary of the Brillouin zone, the single fourfold Dirac point pinned at the Brillouin zone corner, and the Kramers degeneracy at every momentum point. Intriguingly, the Dirac point criticality can be lifted by breaking one primitive translation, resulting in a topological insulator phase, where the edge bands have a M\"{o}bius twist. Our work opens a new arena of research for exploring topological phases protected by projectively represented space groups.

Macrofracturing of Oceanic Lithosphere in Complex Large Earthquake Sequences

AbstractMajor earthquakes in oceanic lithosphere seaward of the subduction zone outer trench slope are relatively uncommon, but several recent occurrences have involved very complex sequences rupturing multiple nonaligned faults and/or having high aftershock productivity with diffuse distribution. This includes the 21 December 2010 MW 7.4 Ogasawara (Bonin), 11 April 2012 MW 8.6 Indo‐Australia, 23 January 2018 MW 7.9 Off‐Kodiak Island, and 20 December 2018 MW 7.3 Nikol'skoye (northwest Pacific) earthquakes. Major oceanic intraplate event sequences farther from plate boundaries do not tend to be as complex in faulting or aftershocks. Outer trench slope extensional faulting can involve complex distributed sequences, particularly when activated by great megathrust ruptures such as 11 March 2011 MW 9.1 Tohoku and 15 November 2006 MW 8.3 Kuril Islands. Intense faulting sequences also occur near subduction zone corners, with many fault geometries being activated, including some in nearby oceanic lithosphere, as for the 29 September 2009 MW 8.1 Samoa, 6 February 2013 MW 8.0 Santa Cruz Islands, and 16 November 2000 MW 8.0 New Ireland earthquakes. The laterally varying plate boundary stresses from heterogeneous locking, recent earthquakes, or boundary geometry influence the specific faulting geometries activated in nearby major intraplate ruptures in oceanic lithosphere. Preexisting lithospheric structures and fabrics exert secondary influences on the faulting. Intraplate stress release in oceanic lithosphere near subduction zones favors distributed macrofracturing of near‐critical fault systems rather than localized, single‐fault failures, both under transient loading induced by plate boundary ruptures and under slow loading by tectonic motions and slab pull.

Effective medium theory for a photonic pseudospin- 12 system

Photonic pseudospin-1/2 systems, which exhibit Dirac cone dispersion at Brillouin zone corners in analogy to graphene, have been extensively studied in recent years. However, it is known that a linear band crossing of two bands cannot emerge at the center of Brillouin zone in a two-dimensional photonic system respecting time reversal symmetry. Using a square lattice of elliptical magneto-optical cylinders, we constructed an unpaired Dirac point at the Brillouin zone center as the intersection of the second and third bands corresponding to the monopole and dipole excitations. Effective medium theory can be applied to the two linearly crossed bands with the effective constitutive parameters numerically calculated using the boundary effective medium approach. It is shown that only the effective permittivity approaches zero while the determinant of the nonzero effective permeability vanishes at the Dirac point frequency, showing a different behavior from the double-zero index metamaterials obtained from the pseudospin-1 triply degenerate points for time reversal symmetric systems. Exotic phenomena, such as the Klein tunneling and Zitterbewegung, in the pseudospin-1/2 system can be well understood from the effective medium description. When the Dirac point is lifted, the edge state dispersion near the $\Gamma$ point can be accurately predicted by the effective constitutive parameters. We also further realized magneto-optical complex conjugate metamaterials for a wide frequency range by introducing a particular type of non-Hermittian perturbations which make the two linear bands coalescence to form exceptional points at the real frequency.

Epitaxial growth and electronic structure of Ruddlesden–Popper nickelates (Lan+1NinO3n+1, n = 1–5)

We report the epitaxial growth of Ruddlesden–Popper nickelates, Lan+1NinO3n+1, with n up to 5 by reactive molecular beam epitaxy. X-ray diffractions indicate high crystalline quality of these films, and transport measurements show strong dependence on the n values. Angle-resolved photoemission spectroscopy reveals the electronic structure of La5Ni4O13, showing a large hole-like pocket centered around the Brillouin zone corner with a (π, π) back-folded copy.

Insight into the electronic structure of semiconducting ε−GaSe and ε−InSe

Metal monochalcogenides $(MX)$ have recently been rediscovered as two-dimensional materials with electronic properties highly dependent on the number of layers. Although some intriguing properties appear in the few-layer regime, the carrier mobility of $MX$ compounds increases with the number of layers, motivating the interest in multilayered heterostructures or bulk materials. By means of angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory calculations, we compare the electronic band structure of bulk $\ensuremath{\epsilon}\text{\ensuremath{-}}\mathrm{GaSe}$ and $\ensuremath{\epsilon}$-InSe semiconductors. We focus our attention on the top valence band of the two compounds along main symmetry directions, discussing the effect of spin-orbit coupling and contributions from post-transition-metal (Ga or In) and Se atoms. Our results show that the top valence band at $\mathrm{\ensuremath{\Gamma}}$ point is dominated by Se ${p}_{z}$ states, while the main effect of Ga or In appears more deeply in binding energy, at the Brillouin zone corners, and in the conduction band. These findings explain also the experimental observation of a hole effective mass rather insensitive to the post-transition metal. Finally, by means of spin-resolved ARPES and surface band structure calculations we describe Rashba-Bychkov spin splitting of surface states in $\ensuremath{\epsilon}\text{\ensuremath{-}}\mathrm{InSe}$.

Observation of flat bands due to band hybridization in the 3d -electron heavy-fermion compound CaCu3Ru4O12

We report angle-resolved photoemission spectroscopy and first-principles numerical calculations for the band structure evolution of the 3d heavy-fermion compound CaCu3Ru4O12. Below 200 K, we observed an emergent hybridization gap between the Cu 3d electron-like band and the Ru 4d hole-like band and the resulting flat band features near the Fermi energy centered around the Brillouin zone corner. Our results confirm the non-Kondo nature of CaCu3Ru4O12, in which the Cu 3dxy electrons are less correlated and not in the Kondo limit. Comparison between theory and experiment also suggests that other mechanism such as nonlocal interactions or spin fluctuations beyond the local dynamical mean-field theory may be needed in order to give a quantitative explanation of the peculiar properties in this material.

Revealing the single electron pocket of FeSe in a single orthorhombic domain

We measure the electronic structure of FeSe from within individual orthorhombic domains. Enabled by an angle-resolved photoemission spectroscopy beamline with a highly focused beamspot (nano-ARPES), we identify clear stripe-like orthorhombic domains in FeSe with a length scale of approximately 1-5~$\mu$m. Our photoemission measurements of the Fermi surface and band structure within individual domains reveal a single electron pocket at the Brillouin zone corner. This result provides clear evidence for a one-electron pocket electronic structure of FeSe, observed without the application of uniaxial strain, and calls for further theoretical insight into this unusual Fermi surface topology. Our results also showcase the potential of nano-ARPES for the study of correlated materials with local domain structures.

Anomalous spectral weight transfer in the nematic state of iron-selenide superconductor**Project supported by the National Natural Science Foundation of China (Grant Nos. 11888101, 91421107, and 11574004) and the National Key Research and Development Program of China (Grant Nos. 2016YFA0301003 and 2018YFA0305602).

Nematic phase intertwines closely with high-Tc superconductivity in iron-based superconductors. Its mechanism, which is closely related to the pairing mechanism of superconductivity, still remains controversial. Comprehensive characterization of the electronic state reconstruction in the nematic phase is thus crucial. However, most experiments focus only on the reconstruction of band dispersions. Another important characteristic of electronic state, the spectral weight, has not been studied in details so far. Here, we studied the spectral weight transfer in the nematic phase of FeSe0.9S0.1 using angle-resolved photoemission spectroscopy and in-situ detwinning technique. There are two elliptical electron pockets overlapping with each other orthogonally at the Brillouin zone corner. We found that, upon cooling, one electron pocket loses spectral weight and fades away, while the other electron pocket gains spectral weight and becomes pronounced. Our results show that the symmetry breaking of the electronic state is manifested by not only the anisotropic band dispersion but also the band-selective modulation of the spectral weight. Our observation completes our understanding of the nematic electronic state, and put strong constraints on the theoretical models. It further provides crucial clues to understand the gap anisotropy and orbital-selective pairing in iron-selenide superconductors.

Momentum-resolved measurement of electronic nematic susceptibility in the FeSe0.9S0.1 superconductor

Unveiling the driving force for a phase transition is normally difficult when multiple degrees of freedom are strongly coupled. One example is the nematic phase transition in iron-based superconductors. Its mechanism remains controversial due to a complex intertwining among different degrees of freedom. In this paper, we report a method for measuring the nematic susceptibly of FeSe$_{0.9}$S$_{0.1}$ using angle-resolved photoemission spectroscopy (ARPES) and an $in$-$situ$ strain-tuning device. The nematic susceptibility is characterized as an energy shift of band induced by a tunable uniaxial strain. We found that the temperature-dependence of the nematic susceptibility is strongly momentum dependent. As the temperature approaches the nematic transition temperature from the high temperature side, the nematic susceptibility remains weak at the Brillouin zone center while showing divergent behavior at the Brillouin zone corner. Our results highlight the complexity of the nematic order parameter in the momentum space, which provides crucial clues to the driving mechanism of the nematic phase transition. Our experimental method which can directly probe the electronic susceptibly in the momentum space provides a new way to study the complex phase transitions in various materials.

Absence of Y-pocket in 1-Fe Brillouin zone and reversed orbital occupation imbalance in FeSe

The FeSe nematic phase has been the focus of recent research on iron-based superconductors (IBSs) due to its unusual properties, which are distinct from those of the pnictides. A series of theoretical/experimental studies were performed to determine the origin of the nematic phase. However, they yielded conflicting results and caused additional controversies. Here, we report the results of angle-resolved photoemission and X-ray absorption spectroscopy studies on FeSe detwinned by a piezo stack. We fully resolved band dispersions with orbital characters near the Brillouin zone (BZ) corner, and revealed an absence of any Fermi pocket at the Y point in the 1-Fe BZ. In addition, the occupation imbalance between {d}_{{xz}} and {d}_{{yz}} orbitals was the opposite of that of iron pnictides, consistent with the identified band characters. These results resolve issues associated with the FeSe nematic phase and shed light on the origin of the nematic phase in IBSs.

Elastic phononic plates with first-order and second-order topological phases

Topologically protected 1D edge states and the 2D surface states have been observed in variant classical wave systems. By extending the quantized polarization, Berry phase, to higher multipole moments, the higher-order topological phases, expressed as 0D corner states, have been theoretically predicted and recently experimentally observed in electric, electromagnetic and acoustic systems. In this paper, we design an elastic phononic plate consisting of a bi-layered hexagonal lattice. The valley-polarized gapless 1D edge state is observed in the elastic phononic plate, by lifting the Dirac cones at the Brillouin zone (BZ) corners. When the bi-layered phononic plates are stacked one by one, the chirality of the oblique columns along the z axis guarantees this 2D elastic phononic plate to be a 3D chiral phononic system. Weyl cones and topologically protected gapless 2D surface states are yielded in this 3D chiral phononic system. The above topological phases are first-order ones with gapless (d-1)-dimensional edge/surface states. By defining a composite cell consisting of three-unit cells and modulating the intra- and inter-coupling within/among the composite cells, the folded double Dirac cone at the BZ center will be gapped and the topological phase of the elastic phononic plate will evolve to a second-order one, expressed as the robust 0D corner state, instead of the gapless 1D edge state. The realization of the first-order edge/surface states and second-order corner states in a unified elastic phononic platform opens up a new path for the design of on-chip topological devices for advanced elastic wave manipulation among the bulk, edge/surface and corner modes.

Role of the Lifshitz topological transitions in the thermodynamic properties of graphene.

The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. The peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, the zone corners K in the vicinity of the Dirac points, and at the saddle point M. A general formulation of the thermodynamics at the LTT in graphene is given. The thermodynamic characteristics of graphene are investigated at the Lifshitz topological transitions. Anomalies are found in the electron specific heat Ce, the electron thermal coefficient of pressure, and the coefficients of electron compressibility and thermal expansion in graphene at the LTT. All the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points. This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.

Nematic Energy Scale and the Missing Electron Pocket in FeSe

Superconductivity emerges in proximity to a nematic phase in most iron-based superconductors. It is therefore important to understand the impact of nematicity on the electronic structure. Orbital assignment and tracking across the nematic phase transition prove to be challenging due to the multiband nature of iron-based superconductors and twinning effects. Here, we report a detailed study of the electronic structure of fully detwinned FeSe across the nematic phase transition using angle-resolved photoemission spectroscopy. We clearly observe a nematicity-driven band reconstruction involving dxz, dyz, and dxy orbitals. The nematic energy scale between dxz and dyz bands reaches a maximum of 50 meV at the Brillouin zone corner. We are also able to track the dxz electron pocket across the nematic transition and explain its absence in the nematic state. Our comprehensive data of the electronic structure provide an accurate basis for theoretical models of the superconducting pairing in FeSe.

Band-dependent superconducting gap in SrFe2(As0.65P0.35)2 studied by angle-resolved photoemission spectroscopy

The isovalent-substituted iron pnictide compound SrFe2(As1−xPx)2 exhibits multiple evidence for nodal superconductivity via various experimental probes, such as the penetration depth, nuclear magnetic resonance and specific heat measurements. The direct identification of the nodal superconducting (SC) gap structure is challenging, partly because the presence of nodes is not protected by symmetry but instead caused by an accidental sign change of the order parameter, and also because of the three-dimensionality of the electronic structure. We have studied the SC gaps of SrFe2(As0.65P0.35)2 in three-dimensional momentum space by synchrotron and laser-based angle-resolved photoemission spectroscopy. The three hole Fermi surfaces (FSs) at the zone center have SC gaps with different magnitudes, whereas the SC gaps of the electron FSs at the zone corner are almost isotropic and kz-independent. As a possible nodal SC gap structure, we propose that the SC gap of the outer hole FS changes sign around the Z-X [(0, 0, 2π) − (π, π, 2π)] direction.

Crystal growth and quantum oscillations in the topological chiral semimetal CoSi

We survey the electrical transport properties of the single-crystalline, topological chiral semimetal CoSi which was grown via different methods. High-quality CoSi single crystals were found in the growth from tellurium solution. The sample's high carrier mobility enables us to observe, for the first time, quantum oscillations (QOs) in its thermoelectrical signals. Our analysis of QOs reveals two spherical Fermi surfaces around the R point in the Brillouin zone corner. The extracted Berry phases of these electron orbits are consistent with the -2 chiral charge as reported in DFT calculations. Detailed analysis on the QOs reveals that the spin-orbit coupling induced band-splitting is less than 2 meV near the Fermi level, one order of magnitude smaller than our DFT calculation result. We also report the phonon-drag induced large Nernst effect in CoSi at intermediate temperatures.

Observation of unconventional chiral fermions with long Fermi arcs in CoSi.

Chirality-the geometric property of objects that do not coincide with their mirror image-is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions-Weyl fermions-were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1-4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5-8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion-spin-1 and charge-2 fermions-at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.

A silicon-on-insulator slab for topological valley transport

Backscattering suppression in silicon-on-insulator (SOI) is one of the central issues to reduce energy loss and signal distortion, enabling for capability improvement of modern information processing systems. Valley physics provides an intriguing way for robust information transfer and unidirectional coupling in topological nanophotonics. Here we realize topological transport in a SOI valley photonic crystal slab. Localized Berry curvature near zone corners guarantees the existence of valley-dependent edge states below light cone, maintaining in-plane robustness and light confinement simultaneously. Topologically robust transport at telecommunication is observed along two sharp-bend interfaces in subwavelength scale, showing flat-top high transmission of ~10% bandwidth. Topological photonic routing is achieved in a bearded-stack interface, due to unidirectional excitation of valley-chirality-locked edge state from the phase vortex of a nanoscale microdisk. These findings show the prototype of robustly integrated devices, and open a new door towards the observation of non-trivial states even in non-Hermitian systems.

Correlation-driven Lifshitz transition in electron-doped iron selenides (Li,Fe)OHFeSe

Effects of electronic correlation and spin-orbit coupling (SOC) on electronic structure of iron selenides (${\mathrm{Li}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$)OHFeSe have been investigated with the combination of density functional theory (DFT) and dynamical mean-field theory. It is found that the electronic correlation substantially changes the Fermi surface topology for $x=0.2$, resulting in a tiny electron pocket around the zone center $\mathrm{\ensuremath{\Gamma}}$ and two large electron pockets around the zone corner $M$, respectively. Moreover, the SOC also considerably affects the low-energy electronic structure near the Fermi level, especially inducing a gap in the Dirac-like dispersion around $\mathrm{\ensuremath{\Gamma}}$ for $x=0.2$. Our calculations show a correlation-driven Lifshitz transition from FeSe to the heavily electron-doped compound, leading to a transition of the nesting wave vector from ($\ensuremath{\pi}$, 0) to ($\ensuremath{\pi}$, $0.5\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$) accompanied by an orbital-weight redistribution between the ${d}_{xy}$ and ${d}_{xz}/{d}_{yz}$ orbitals. These correlation-driven electronic structures enrich the understanding of different DFT and experimental results, suggesting a quite distinct superconducting state of (${\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}$)OHFeSe in comparison with FeSe.

Magnetic exchange parameters and anisotropy of the quasi-two-dimensional antiferromagnetNiPS3

Neutron inelastic scattering has been used to measure the magnetic excitations in powdered NiPS$_3$, a quasi-two dimensional antiferromagnet with spin $S = 1$ on a honeycomb lattice. The spectra show clear, dispersive magnons with a $\sim 7$ meV gap at the Brillouin zone center. The data were fitted using a Heisenberg Hamiltonian with a single-ion anisotropy assuming no magnetic exchange between the honeycomb planes. Magnetic exchange interactions up to the third intraplanar nearest-neighbour were required. The fits show robustly that NiPS$_3$ has an easy axis anisotropy with $\Delta = 0.3$ meV and that the third nearest-neighbour has a strong antiferromagnetic exchange of $J_3 = -6.90$ meV. The data can be fitted reasonably well with either $J_1 < 0$ or $J_1 > 0$, however the best quantitative agreement with high-resolution data indicate that the nearest-neighbour interaction is ferromagnetic with $J_1 = 1.9$ meV and that the second nearest-neighbour exchange is small and antiferromagnetic with $J_2 = -0.1$ meV. The dispersion has a minimum in the Brillouin zone corner that is slightly larger than that at the Brillouin zone center, indicating that the magnetic structure of NiPS$_3$ is close to being unstable.