Session U64: Topological Materials: Majoranas and Non-Conventional Topological States

Signature of Dispersing 1D Majorana Channels in an Iron-based superconductors

Selected by Focus Topic Organizer (Seongshik Oh and Peter Armitage)   

Physical Properties of XTSb[(X= Eu, Sr), (T= Ag, Au)] single crystals

Single crystals of XTSb [(X= Eu, Sr), (T= Ag, Au)] were grown by the solution growth by using self flux [1]. These single crystals were investigated by powder X-ray diffraction at room temperature and the structure was successfully refined to be the hexagonal (space group P63/mmc) crystal structure . Temperature dependent magnetic susceptibility measurements indicate antiferromagnetic ordering for magnetic compounds (e.g. T_N = 6 K for EuAgSb). Density functional theory calculations find that the band inversion giving a Dirac point is present in the non-magnetic Au compounds, but not the Ag compounds. Thermodynamic and transport data on the non-magnetic SrAgSb, SrAuSb and magnetic EuAgSb, EuAuSb will be presented and compared.
Reference:
[1] Paul C. Canfield, et al., arxiv: 1908.02369 (2019).
  

Ab initio study of surface states in Bi4Te3

The crystal structure of the layered material Bi₄Te₃, a member of the adaptive series of crystals (Bi₂)_m(Bi₂Te₃)_n, forms a superlattice of alternating Bi₂ and Bi₂Te₃ layers. Given the topological properties of its individual constituents, Bi₄Te₃ is expected to be a topological insulator or semimetal. Recent experimental results indicate the presence of unusual surface states in this material. In this work, we perform ab initio density functional theory calculations of bulk and slab geometries to investigate the surface states of Bi₄Te₃.   

Bond Disproportionation in the Silver Bismuthate Ag2BiO3

The stoichiometric silver bismuthate Ag₂BiO₃ is expected to contain bismuth in the nominal Bi⁺⁴ state, but the bismuth ions disproportionate into two distinct sites that render Ag₂BiO₃ insulating [1]. Recent theoretical predictions of metal-insulator transition and Weyl semimetal state in Ag₂BiO₃ have revived the interest in this material [2]. However, such novel properties are only expected in the absence of disproportionation of bismuth, where Ag₂BiO₃ is in the Pnna phase. Here, we examine nature of disproportionation in Ag₂BiO₃ via X-ray absorption and photoemission spectroscopies. We present an updated band structure for Ag₂BiO₃ in the Pnn2 (disproportionated) phase, where we have a band gap of 1 eV in agreement with our optical spectroscopy measurement. Furthermore, we present Raman spectroscopy results and highlight the extent of similarities to other disproportionated bismuthates despite the distinct crystal structure Ag₂BiO₃.

[1] C. B. M. Oberndorfer et al., Solid State Sciences 8, 267 (2006).
[2] J. He et al., Nature Communications 9, 492 (2018).
  

Analytic calculation of generalized Brillouin zone in non-Hermitian bands

In this talk, we introduce a systematic method to calculate the generalized Brillouin Zone (GBZ) analytically in one dimensional non-Hermitian systems. In general, a m-band non-Hermitian Hamiltonian is constituted by m distinct sub-GBZs, each of which is a piecewise analytic closed loop. All the analytic properties of the GBZ can be characterized by an algebraic equation, which is dubbed as auxiliary GBZ. As an application of our theory, we show a new kind of topological phase under open boundary condition, which is characterized by the non-zero energy winding number for each band.   

Materials database development for electromagnetic responses

The interplay between electromagnetic response theory and symmetry is crucial to understand the transport properties in quantum materials. It is critical to fully understand these physical properties and find materials that host strong electromagnetic response, which, have an extensive impact on the development of data storage, information processing, and energy conversion, etc. Experimentally, however, such large-scale screening is very impractical, as a quantitative determination of the electromagnetic responses by electrical and optical measurements requires integrating each material separately into a complex multicomponent mesoscopic transport device. Theoretically and computationally, the situation is in principle much more straightforward. Via high throughput numerical simulations, we developed the database for intrinsic spin Hall effect in nonmagnetic compounds, shift current in inversion symmetry Weyl semimetals, anomalous Hall effect and anomalous Nernst effect in magnetic Heusler compounds based on the known materials. Our database is helpful for the full understanding of the electronic properties of materials and selecting the correcting materials for further experimental studies.
  

Reentrant Defect Modes in a PT-Symmetric Circuit

Systems obeying PT-symmetry are a special case in non-Hermitian physics where real eigenvalue spectra can still emerge. They usually exhibit a phase diagram with different regimes of symmetry conservation or spontaneous symmetry breaking in their eigenstates. We examine a localized zero-energy defect mode within a PT-symmetric hopping model that disappears and re-emerges at different PT phase transitions and present an exhaustive explanation for this phenomenon. Our theoretical findings are confirmed by eigenstate measurements for different gain/loss profiles in an electrical circuit implementation.   

Distinct multiple fermionic states in a single topological metal

Among the quantum materials that have recently gained interest are the topological insulators, wherein symmetry-protected surface states cross in reciprocal space, and the Dirac nodal-line semimetals, where bulk bands touch along a line in momentum space. However, the existence of multiple fermion phases in a single material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, here we discuss a systematic study of the metallic ternary material discovering properties, which are unique in a single topological quantum material. We experimentally observe weak topological insulator surface states and our calculations suggest the existence of additional strong topological insulator surface states. Our first-principles calculations reveal a one-dimensional Dirac crossing—the surface Dirac-node arc—along a high-symmetry direction, which is confirmed by our ARPES and time-resolved ARPES measurements. Furthermore, we will present our recent results on the experimental observation of new topological quantum materials. These are topological superconductors and magnetic topological materials which were discovered through ARPES and time-resolved ARPES measurements with further support from first-principles calculations.
  

Anomalous quantum oscillations in a spin-3/2 topological semimetal: I. Experiment

Gapless spin-3/2 quasiparticles lead to an unprecedented class of high-spin topological superconductivity which hosts a Majorana fluid on the surface. The spin-3/2 Fermi surface can be realized in a crystal lattice with high symmetry. The RPtBi (R=rare earth) half-Heuslers are a family of promising candidates, in which strong spin-orbit interaction inverts the Bi p-orbital derived bands and Bi s-orbital derived bands. In this particular case, the low energy quasiparticles are adequately described by the four-band Luttinger–Kohn model. In this talk, we report compelling evidence for a spin-3/2 Fermi surface in YPtBi via studies of the angle-dependent Shubnikov-de Haas (SdH) effect uniquely explained by the anisotropic effect of Zeeman interaction on spin-3/2 quasiparticles, confirming the long-awaited high-spin nature of topological semimetal RPtBi compounds.   

Anomalous quantum oscillations in a spin-3/2 topological semimetal: II. Theory

Gapless spin-3/2 quasiparticles lead to an unprecedented class of high-spin topological superconductivity which hosts a Majorana fluid on the surface. The spin-3/2 Fermi surface can be realized in a crystal lattice with high symmetry. The RPtBi (R=rare earth) half-Heuslers are a family of promising candidates, in which strong spin-orbit interaction inverts the Bi p-orbital derived bands and Bi s-orbital derived bands. In this particular case, the low energy quasiparticles are adequately described by the four-band Luttinger–Kohn model. In this talk, we report compelling evidence for a spin-3/2 Fermi surface in YPtBi via studies of the angle-dependent Shubnikov-de Haas (SdH) effect uniquely explained by the anisotropic effect of Zeeman interaction on spin-3/2 quasiparticles, confirming the long-awaited high-spin nature of topological semimetal RPtBi compounds.   

Correspondence between winding numbers and skin modes in non-hermitian systems

We establish exact relations between the winding of “energy” (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of “skin modes” with open boundary condition in non-hermitian systems. This correspondence is exactly related to by our new understanding of generalized Brillouin zone, which is the curve defined on the complex plane and always surrounding the same number of zeros and poles of characteristic equation of the system. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the non-vanishing current through the system.