Topology

Weyl and Dirac excitations

Ideas of topology have been widely applied to electronic band structures. We have been exploring the application these ideas to phonon and other excitations.

Figure 1: A cartoon of double Weyl phonons as we reported in Phys. Rev. Lett. 121, 035302 (2018).

References

2021

Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl₃

Haoxiang Li, T. T. Zhang, A. Said, G. Fabbris, D. G. Mazzone, J. Q. Yan, D. Mandrus, Gábor B. Halász, S. Okamoto, S. Murakami, M. P. M. Dean, H. N. Lee, and H. Miao

Nature Communications 12, 3513 (2021)

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The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl₃ using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK 8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl₃ and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.
Observation of a chiral wave function in the twofold-degenerate quadruple Weyl system BaPtGe

Haoxiang Li, Tiantian Zhang, A. Said, Y. Fu, G. Fabbris, D. G. Mazzone, J. Zhang, J. Lapano, H. N. Lee, H. C. Lei, M. P. M. Dean, S. Murakami, and H. Miao

Phys. Rev. B 103, 184301 (2021)

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Topological states in quantum materials are defined by bulk wave functions that possess nontrivial topological invariants. While edge modes are widely presented as signatures of nontrivial topology, how bulk wave functions can manifest explicitly topological properties remains unresolved. Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with first principles calculations, we report experimental signatures of chiral wave functions in the bulk phonon spectrum of BaPtGe, which we show to host a previously undiscovered twofold-degenerate quadruple Weyl node. The chirality of the degenerate phononic wave function yields a nontrivial phonon dynamical structure factor, S(Q,ω), along high-symmetry directions, that is in excellent agreement with numerical and model calculations. Our results establish IXS as a powerful tool to uncover topological wave functions, providing a key missing ingredient in the study of topological quantum matter.

2019

Phononic Helical Nodal Lines with PT Protection in MoB₂

T. T. Zhang, H. Miao, Q. Wang, J. Q. Lin, Y. Cao, G. Fabbris, A. H. Said, X. Liu, H. C. Lei, Z. Fang, H. M. Weng, and M. P. M. Dean

Phys. Rev. Lett. 123, 245302 (2019)

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While condensed matter systems host both fermionic and bosonic quasiparticles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such as phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine firstprinciples calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal symmetry protected helical nodal lines in the phonon spectrum of MoB₂. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

2018

Observation of double Weyl phonons in parity-breaking FeSi

Hu Miao, TT Zhang, Le Wang, Derek Meyers, AH Said, YL Wang, YG Shi, HM Weng, Zhong Fang, and MPM Dean

Phys. Rev. Lett. 121, 035302 (2018)

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[ANL Highlight]

Condensed matter systems have now become a fertile ground to discover emerging topological quasiparticles with symmetry protected modes. While many studies have focused on fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by Zhang et al.’s recent theoretical prediction of double Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)], we directly measure the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calculations, we make the first observation of double Weyl points in FeSi, which will be an ideal material to explore emerging bosonic excitations and its topologically nontrivial properties.