Session G60: Topological Materials: Semimetals and Higher Order States

Ultrathin epitaxial Na3Bi films for topological electronics

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

Polymerized triptycene as a candidate material of higher-order topological insulator

Higher-order topological insulators (HOTIs) have attracted growing attention as a novel class of topological state of matter, where boundary states, protected by topological natures of Bloch wave functions in a bulk, appear at boundaries with co-dimension larger than one. So far, various theoretical models for HOTIs have been proposed, and it is highly desirable to search suitable materials to realize the HOTIs.
In this presentation, we propose that a class of carbon-based materials called polymerized triptycene is a promising platform for a two-dimensional second-order topological insulator. The materials are composed of triptycene molecules and phenyl rings connecting the triptycene molecules. In this class of materials, the C₆ rings form a kagome-type network, which becomes a platform to realize the HOTI when introducing the ``breathing” structure. We show by the analysis of the tight-binding model that the corner states appear under the appropriate choice of the sample edges. We also demonstrate that the corner states are topologically protected by the bulk topological invariant, or the Z₃ Berry phase, that characterizes HOTIs.   

Apatite as a higher-order topological insulator with 2/3-filled hinge states

In our previous work we have shown that electrides are suitable for achieving various topological semimetal phases [1]. In our presentation, we show that the apatite A6B4(SiO4)6, one of the one-dimensional electrides, realizes a higher-order topological insulator with 2/3-filled one-dimensional metallic hinge states. This is considered to be in the class of C_n-protected higher-order topological insulators proposed by Benalcazar et al. [2], but the hinge charge is different from that naively expected from their theory. This difference comes from the difference in the fundamental units constituting the crystal; the apatite crystal consists of triangular units, unlike hexagonal units assumed in Ref. [2]. We show how this difference affects topological properties of the system via crystal terminations. [1] M.Hirayama, S. Matsuishi, H. Hosono, and S. Murakami, Phys. Rev. X 8, 031067 (2018). [2] W. A. Benalcazar, T. Li, T. L. Hughes, Phys. Rev.B 99, 245151 (2019).   

Evidence of Higher Order Topology in WTe2 from Josephson Coupling through Anisotropic Hinge States

The noncentrosymmetric Td-WTe₂, previously known as a Type-II Weyl semimetal, is expected to have higher order topological phases with topologically protected, helical one-dimensional (1D) hinge states when their scarcely separated Weyl points get annihilated. However, the detection of these hinge states is difficult in the presence of the semimetallic behaviour of the bulk. Here, we spatially resolved the hinge states by analysing the magnetic field interference of supercurrent in Nb-WTe₂-Nb proximity Josephson junctions. The Josephson current along the a-axis of the WTe₂ crystal, but not along the b-axis, showed sharp enhancements at the edges of the junction; the amount of enhanced Josephson current was comparable to the upper limits of a single 1D conduction channel. Furthermore, the Josephson effect under microwave radiation, shows voltage doubling of Shapiro steps when Josephson current flows along the a-axis of WTe₂ crystal, which implies 4π periodicity of current phase relationship. Our experimental observations provide evidence of the higher order topological phase in WTe₂ and its corresponding anisotropic topological hinge states, in good agreement with theoretical calculations.   

Higher order topological insulators in anti-perovskites

We prove that a family of anti-perovskite materials realize a higher order topological insulator (HOTI) phase, characterized by a previously introduced Z4 index. A tight binding model and a k.p model are used to capture the physics of the bulk, surface and hinge states of these anti-perovskites. A phase diagram of the Z4 index and weak topological invariant is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the lattice to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.   

Transport evidence of triply degenerate nodal semimetal YRh6Ge4

Triply-degenerate nodal semimetal (TDNS) represents a new topological quantum state [1,2]. In this talk, we report our magnetotransport studies on YRh₆Ge₄, which was recently predicted to be a TDNS[3]. We find it exhibits remarkable signatures of a chiral anomaly, manifested by large negative longitudinal magnetoresistance, quadratic field dependence of magnetoconductance and planar Hall effect [4]. Furthermore, we have also observed Shubnikov-de Haas (SdH) quantum oscillations, the analyses of which reveals two point-like Fermi surfaces consistent with the calculated band structure; these pockets host nearly massless three-component fermions. These results suggest YRh₆Ge₄ may serve as a model system to probe the exotic properties of three-component fermions and understand their underlying physics.

[1] Bradlyn, B., Cano, J., Wang, Z., Vergniory, M. G., Felser, C., Cava, R. J. & Bernevig, B. A.. Science 10, 1126, (2016).
[2] Zhu, Z., Winkler, G. W., Wu, Q., Li, J. & Soluyanov, A. A. Physical Review X 6, 031003, (2016).
[3] Guo, P.-J., Yang, H.-C., Liu, K. & Lu, Z.-Y. Phys. Rev. B 98, 045134, (2018).
[4] Nandy, S., Sharma, G., Taraphder, A. & Tewari, S. Phys. Rev. Lett 119, 176804, (2017).   

Cornering the zero mode: realization of an artificial electronic higher-order topological insulator

Quantum simulators are essential tools for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices have led the field so far, but the basis for electronic quantum simulators is now being developed. Here, we experimentally realize an electronic higher-order topological insulator (HOTI). More specifically, we create a breathing kagome lattice by manipulating carbon monoxide molecules on a Cu(111) surface using a scanning tunneling microscope [1]. We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, but is absent in the trivial one. Different from conventional topological insulators, the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, leading to a particular robustness against perturbations. Our versatile approach to designing artificial lattices holds promise for investigating novel quantum phases of matter.

[1] S. N. Kempkes & M. R. Slot et al., Robust zero-energy modes in an electronic higher-order topological insulator, Nature Materials (2019)   

Systematic investigation of physical properties of YbB6±x using the combinatorial approach

Rare-earth boride systems have gained tremendous interest for exploring exotic and novel physical phenomena such as mixed valence states, heavy fermion, strong correlation and superconductivity. Since samarium hexaboride (SmB₆) has turned out to be a topological insulator, ytterbium boride (YbB_x) systems have been intensively studied as another possible topological insulator. However, the existence of the topologically protected surface states of YbB₆ is yet to be confirmed, and the origin of the quantum oscillations in Kondo insulator YbB₁₂ remains unresolved. We are systematically investigating the physical properties of YbB_6±x depending on stoichiometry using the thin-film combinatorial approach. The composition spread YbB_6±x thin films were fabricated by the co-sputtering of YbB₆ and B targets. The composition mapping of the spread films is performed using wavelength dispersive X-ray spectroscopy (WDS), and synchrotron x-ray diffraction measurements are employed for structural mapping analysis. We will discuss the electrical behavior of YbB_6±x with the change in the valence state of Yb ion depending on the stoichiometry.   

The fate of topological properties in U-based materials

Recent reports on CeSbTe show that Weyl and Dirac topological states can be tuned by low magnetic fields, which provide a promising route for investigating the interplay between magnetism and topology [1]. Here we aim at increasing the degree of correlations in this system by replacing Ce with U atoms. Though USbTe has been investigated previously [2,3], little is known about its putative topological properties. In this talk, I will discuss the growth of USbTe single crystals and their physical properties characterization via thermodynamic and electrical transport measurements at ambient pressure and under applied pressure.

[1] L. M. Schoop et al, Science Advances 4, eaar2317 (2018).
[2] D. Kaczorowski et al, Journal of Magnetism and Magnetic Materials 140, 1431 (1995).
[3] D. Kaczorowski et al, Journal of Alloys and Compounds, 398, L1 (2005)
  

New kagome prototype materials: discovery of KV3Sb5, RbV3Sb5, CsV3Sb5

With its unique and elegant structure, the kagome lattice is a key platform for the study of condensed matter physics. From quantum spin liquid candidates, topologically nontrivial phases, and Weyl semi-metal candidates, these materials are poised at the frontier of material science. The kagome metals, in particular, offer unique opportunities due to the delocalization of electrons and renormalization of the electronic and magnetic ground state. Recently we discovered a new class of kagome metals: KV₃Sb₅, RbV₃Sb₅, and CsV₃Sb₅, all of which crystallize in the P6/mmm space group and exhibit a structurally perfect kagome lattice of vanadium. Our work has indicated that these materials are prime candidates for correlated electron phenomenon (anomalous Hall, heavy fermion transport, etc.). Furthermore, the Fermi level is in close proximity to Dirac features, and we can demonstrate Fermi level tuning through deintercalation of the alkali metal. Our work indicates that KV₃Sb₅ and its cogeners are fruitful candidates for the exploration of exotic transport phenomena.   

Tuning the Fermi level to access the flat bands in PbPd3

PbPd₃ has been reported to host an interesting band structure that includes a dispersionless branch along the Γ-X line that could result in a large DOS near the E_F and Dirac-like surface states.[1] Previous results on the Fermi surface topography of PbPd₃ suggest that the E_F is roughly 50 meV above the flat bands.[2] This results in the flat bands only having a weak effect on the bulk properties, while the impact of the Dirac cone at the Γ-point is limited due to it being several hundred meV above the E_F. In order to access the flat bands, we doped Au on the Pb site to lower the E_F. As a result, a significantly enhanced thermopower has been achieved. Furthermore, we performed magnetoresistance and torque magnetometry measurements in magnetic fields up to 45 T to reveal the change in the Fermi surface as a result of doping. We will discuss detailed results of the Fermi surface topology measurements on these doped series and prospects for tuning the E_F in the opposite direction to meet the Dirac cone.
[1] K. Ahn et al.,PRB 98,035130(2018).
[2] K. Wei et al.,PRM 3,041201(R)(2019).   

The Bulk boundary Correspondence in 3d non-Hermitian Semimetals

Recently, Both numerical and analytical methods are proposed
to calculate the generalized Brillouin zone (GBZ) and explore the bulk-coundary correspondence in
non-Hermitian systems. In this article, we apply these methods to the study of the bulk-boundary
correspondence of non-Hermitian semimetal model. Concretely, we take two non-Hermitian semimetal
models into account and assume open boundary condition in x, y and z directions. In each case, we
calculate the spectrums and GBZ with typical parameters and plot topological phase diagram with
unit-circle Brillouin zone. We nd that GBZ recover the manifest consistency between OBC and
PBC spectrums, and the topological phase diagram in x, y and z direction open boundary condition
is consistent with the projection of 3 dimensional (3d) topological phase diagram into corresponding
direction. Besides, we compare the topological phase diagrams calculated with unit-circle Brillouin
zone and GBZ, which clearly shows that GBZ recovers the bulk-boundary correspondence in non-
Hermitian systems. The GBZ phase diagrams in x-direction and y-direction open boundray cases,
there exist exceptional lines phases; and in z-direction open boundary case, we get the parameter
space for topological nontrivial phase with winding number w = 1.   

Phonon Hall effect in nonmagnetic insulators

Thermal Hall effect (THE), a phenomena in which the presence of magnetic field causes thermal current perpendicular to the temperature gradient, is a useful probe to detect current of charge-neutral particles in materials: excitation of spin or lattice motion. Recently, mechanisms of THE have been theoretically investigated to reveal how the charge-neutral particles are affected by magnetic moments or magnetic field. THE of phonons has been observed only in magnetic insulators [1], and previous studies have attributed the origin of THE to spin-phonon interaction, such as the Raman interaction [2] and magnon-phonon interaction [3].
In sharp contrast, our study shows that THE of phonon is possible even without magnetic moment. This is due to imperfect screening of magnetic field in crystals: negative charge of electrons and positive one of nuclei do not completely cancel each other when the correction beyond the adiabatic approximation is taken into account. For quantitative estimation, we calculated the THE in lattice models of band insulators.

[1] C. Strohm, et al., PRL 95, 155901 (2005)
[2] L. Sheng, et al., PRL 96, 155901 (2006)
[3] X. Zhang, et al., PRL 123, 167202 (2019)