Topological Singularity Induced Chiral Kohn Anomaly in a Weyl Semimetal

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Topological Singularity Induced Chiral Kohn Anomaly in a Weyl Semimetal

Thanh Nguyen, Fei Han, Nina Andrejevic, Ricardo Pablo-Pedro, Anuj Apte, Yoichiro Tsurimaki, Zhiwei Ding, Kunyan Zhang, Ahmet Alatas, Ercan E. Alp, Songxue Chi, Jaime Fernandez-Baca, Masaaki Matsuda, David Alan Tennant, Yang Zhao, Zhijun Xu, Jeffrey W. Lynn, Shengxi Huang, and Mingda Li

Phys. Rev. Lett. 124, 236401 – Published 11 June 2020

Abstract

The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition, and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wave vector nests the Fermi surface of metals. Here we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide. Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of the Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials.

Received 23 March 2020
Accepted 13 May 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.236401

Physics Subject Headings (PhySH)

Weyl semimetal

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Thanh Nguyen^1,*, Fei Han^1,*, Nina Andrejevic^2,*, Ricardo Pablo-Pedro^1,*, Anuj Apte³, Yoichiro Tsurimaki⁴, Zhiwei Ding ², Kunyan Zhang⁵, Ahmet Alatas⁶, Ercan E. Alp⁶, Songxue Chi⁷, Jaime Fernandez-Baca⁷, Masaaki Matsuda⁷, David Alan Tennant ⁷, Yang Zhao^8,9, Zhijun Xu^8,9, Jeffrey W. Lynn ⁸, Shengxi Huang⁵, and Mingda Li ^1,†

¹Department of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, USA
²Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139, USA
³Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
⁴Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 02139, USA
⁵Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
⁶Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁷Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁸NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
⁹Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA

^*These authors contributed equally to this work.
^†Corresponding author. mingda@mit.edu

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Vol. 124, Iss. 23 — 12 June 2020

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Images

Figure 1
Field-theoretical calculations of topological Kohn anomaly. Density plots of the (a), real, and the (b), imaginary part of the polarization function $- Π (q^{'}, ν^{'})$ at $T = 1 K$ . (c) Constant-frequency line profile of $- Re [Π (q^{'}, ν_{0}^{'} = μ)]$ and $- Im [Π (q^{'}, ν_{0}^{'} = μ)]$ . (d) Constant-wave vector line profile of $- Re [Π (q_{0}^{'} = k_{F}, ν^{'})]$ and $- Im [Π (q_{0}^{'} = k_{F}, ν^{'})]$ . (e) Density plot of $- Re [Π (q_{x} - k_{{WP}_{x}}, q_{y} - k_{{WP}_{y}})]$ , which represents a realistic experimental setup scanning near the Weyl node. (f) Line cuts at different values of deviations away from a Weyl node. There is a noticeable dip at the Weyl node, yet even away from the Weyl nodes, softening can still exist due to the pointlike Weyl node and dynamic effect.
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Figure 2
Phonon dispersion of TaP. (a) Crystal structure of TaP with (b), corresponding Brillouin zone which features the locations and Berry curvature signs of paired Weyl nodes W1 (orange) and W2 (purple). (c) Schematic of relative energy location of W1 and W2 Weyl nodes. (d) Low-energy phonon dispersion of TaP, measured by IXS and INS at 300 K along the high-symmetry loop $Γ − Σ − Σ_{1} − Z − Γ$ . Points represent extracted phonon modes from measurements. The gray lines denote ab initio calculations showing excellent agreement, and the color map represents the spectra intensity.
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Figure 3
Topological Kohn anomaly at W2 Weyl node. (a) Location of the W2 Weyl node in energy and momentum space. (b) Phonon spectra near the W2 Weyl node, with central thicker line denoting the location of ${W 2}^{'}$ . Strong phonon softening at this Weyl node is observed. (c)–(f) Dispersion of two representative phonon modes near W2 at 18 and 300 K, along the $k_{x}$ and $k_{y}$ directions. Solid lines correspond to ab initio calculations without the EPI, where their discrepancy with experimental data further supports the strong softening near the W2 node. 2D (g) and 3D (h) showing the realization condition of Kohn anomaly, where a phonon $q = k_{W 2} - k_{W 1} \approx k_{W 2^{'}}$ connects two Weyl nodes $k_{W 1}$ and $k_{W 2}$ .
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Figure 4
Phonon characteristics at the W1 Weyl node and $Γ$ -point. (a) Location of the W1 Weyl node in energy and momentum space. Dispersions of two representative phonon modes obtained from IXS data near W1 at (b), 18 and (c), 300 K along the $k_{x}$ direction as well as (d) and (e), along the $k_{y}$ direction. Error bars represent 1 standard deviation. Experimental phonon dispersion agrees excellently with ab initio calculations (solid lines). (f) Schematic of the connection of two equivalent electronic states at $k_{W 2}$ and $k_{W 2^{'}}$ by the phonon $q = k_{W 2^{'}} - k_{W 2} \approx k_{W 1^{'}}$ , the W1 node near which IXS measurements were performed. (g) Schematic seen from the (001) plane of the connection between two equivalent electronic states at $k_{W 1^{'}}$ and $k_{\bar{W 1}}$ by the phonon momentum $q = k_{W 1^{'}} - k_{\bar{W 1}} \approx Γ$ .
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