Yung Jui Wang

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator

Half-Massless Certain materials, such as topological crystalline insulators (TCIs), host robust surface states that have a Dirac (graphene-like) dispersion associated with massless carriers; the breaking of protective symmetry within such materials should cause the carriers to acquire mass. Okada et al. (p. 1496, published online 29 August) used scanning tunneling microscopy to map out the energies of the electronic levels of the TCI Pb1-xSnxSe as a function of the strength of an external magnetic field. The massless Dirac fermions coexisted with massive ones, presumably as a consequence of a distortion of the crystalline structure affecting only one of the two mirror symmetries. Scanning tunneling spectroscopy of Pb1–xSnxSe in a magnetic field reveals two types of Dirac fermions. In topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with distinct characteristics. The breaking of crystal symmetry in TCIs is predicted to impart mass to the massless Dirac fermions. Here, we report high-resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe that reveal the coexistence of zero-mass Dirac fermions protected by crystal symmetry with massive Dirac fermions consistent with crystal symmetry breaking. In addition, we show two distinct regimes of the Fermi surface topology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs.

Phase Transformation and Lithiation Effect on Electronic Structure of LixFePO4: An In-Depth Study by Soft X-ray and Simulations

Through soft X-ray absorption spectroscopy, hard X-ray Raman scattering, and theoretical simulations, we provide the most in-depth and systematic study of the phase transformation and (de)lithiation effect on electronic structure in Li(x)FePO(4) nanoparticles and single crystals. Soft X-ray reveals directly the valence states of Fe 3d electrons in the vicinity of Fermi level, which is sensitive to the local lattice distortion, but more importantly offers detailed information on the evolution of electronic states at different electrochemical stages. The soft X-ray spectra of Li(x)FePO(4) nanoparticles evolve vividly with the (de)lithiation level. The spectra fingerprint the (de)lithiation process with rich information on Li distribution, valency, spin states, and crystal field. The high-resolution spectra reveal a subtle but critical deviation from two-phase transformation in our electrochemically prepared samples. In addition, we performed both first-principles calculations and multiplet simulations of the spectra and quantitatively determined the 3d valence states that are completely redistributed through (de)lithiation. This electronic reconfiguration was further verified by the polarization-dependent spectra collected on LiFePO(4) single crystals, especially along the lithium diffusion direction. The evolution of the 3d states is overall consistent with the local lattice distortion and provides a fundamental picture of the (de)lithiation effects on electronic structure in the Li(x)FePO(4) system.

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

Imaging Doped Holes in a Cuprate Superconductor with High-Resolution Compton Scattering

Inelastic x-ray scattering probed the doping dependence of the electronic environment within a cuprate superconductor. The high-temperature superconducting cuprate La2−xSrxCuO4 (LSCO) shows several phases ranging from antiferromagnetic insulator to metal with increasing hole doping. To understand how the nature of the hole state evolves with doping, we have carried out high-resolution Compton scattering measurements at room temperature together with first-principles electronic structure computations on a series of LSCO single crystals in which the hole doping level varies from the underdoped (UD) to the overdoped (OD) regime. Holes in the UD system are found to primarily populate the O 2px/py orbitals. In contrast, the character of holes in the OD system is very different in that these holes mostly enter Cu d orbitals. High-resolution Compton scattering provides a bulk-sensitive method for imaging the orbital character of dopants in complex materials.

Tailoring the nature and strength of electron-phonon interactions in the SrTiO3(001) 2D electron liquid

Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at the SrTiO3(001) surface to reveal a remarkably complex evolution of electron-phonon coupling with the tunable carrier density of this system. At low density, where superconductivity is found in the analogous 2DEL at the LaAlO3/SrTiO3 interface, our angle-resolved photoemission data show replica bands separated by 100 meV from the main bands. This is a hallmark of a coherent polaronic liquid and implies long-range coupling to a single longitudinal optical phonon branch. In the overdoped regime the preferential coupling to this branch decreases and the 2DEL undergoes a crossover to a more conventional metallic state with weaker short-range electron-phonon interaction. These results place constraints on the theoretical description of superconductivity and allow a unified understanding of the transport properties in SrTiO3-based 2DELs.

Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-Ray Scattering

Metallic liquid silicon at 1787 K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17% via a maximally localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state.

Nontrivial spin texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe

We present first-principles calculations of the nontrivial surface states and their spin textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin texture. The out-of-plane spin polarization is found to be zero due to the crystalline and time-reversal symmetries. The in-plane spin texture shows helicity with some distortion due to the interaction of the two coaxial Dirac cones, indicating a nontrivial mirror Chern number of

Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds

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Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

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Non-destructive measurement of in-operando lithium concentration in batteries via x-ray Compton scattering

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