Evidence for Dominant Phonon-Electron Scattering in Weyl Semimetal ${\mathrm{WP}}_2$

Topological semimetals have revealed a wide array of novel transport phenomena, including electron hydrodynamics, quantum field theoretic anomalies, and extreme magnetoresistances and mobilities. However, the scattering mechanisms central to the fundamental transport properties remain largely unexplored. Here, we reveal signatures of significant phonon-electron scattering in the type-II Weyl semimetal ${\mathrm{WP}}_2$ via temperature-dependent Raman spectroscopy. Over a large temperature range, we find that the decay rates of the lowest energy $A_1$ modes are dominated by phonon-electron rather than phonon-phonon scattering. In conjunction with first-principles calculations, a combined analysis of the momentum, energy, and symmetry-allowed decay paths indicates this results from finite momentum interband and intraband scattering of the electrons. The excellent agreement with theory further suggests that such results could be true for the acoustic modes. We thus provide evidence for the importance of phonons in the transport properties of topological semimetals and identify specific properties that may contribute to such behavior in other materials.

Popular Summary

Topological semimetals are a class of materials that display remarkable electronic transport properties, such as enormous changes in resistance under applied magnetic fields, and electrons moving with ultrahigh mobilities. Understanding the physical mechanisms that govern these behaviors is important for the development of novel materials. Through experimental and theoretical analysis of one topological semimetal, tungsten phosphide (WP2), we find that phonons—the fundamental quanta of lattice vibrations—play a key role in determining its electronic transport behavior.

The temperature dependence of a phonon’s linewidth can reveal the type of available decay paths it has. Through spectroscopic observations of WP2 over a wide range of temperatures, we observe that phonons of a specific symmetry decay primarily into electrons, rather than into other phonons. We address the energy and momentum conservation laws that allow this behavior, as well as the underlying material properties that permit this effect to be observed and for it to dominate over other forms of phonon decay.

We anticipate that future studies using experimental probes capable of accessing acoustic phonon modes will be valuable because of their larger predicted coupling strengths and more substantial contributions to the electronic transport properties.

Figure 1

(a) Room-temperature Raman spectra of an as-grown ${\mathrm{WP}}_2$ crystal surface in collinear XX and ${\mathrm{X}}^{\prime }{\mathrm{X}}^{\prime }$ polarization configurations. (b) Predicted phonon energies vs measured phonon energies. The solid line indicates ideal agreement.

Figure 2

(a) Temperature-dependent Raman spectra from 10 to 300 K. Spectra are vertically offset. (b) Percent difference of the phonon energies from the ${\omega }_0$ value at 10 K as a function of temperature. The lowest-energy $A_1$ mode changes by twice the percent of any other mode. (c) Linewidth temperature dependence of the $A_1(1)$ and $A_1(2)$ modes, which have energies 22.4 and 35.8 meV at 10 K, respectively. The $A_2(2)$ mode at 32.4 meV has an energy between that of the two $A_1$ modes. While both $A_1$ modes display an anomalous temperature dependence, the $A_2$ mode temperature dependence is that expected from anharmonic phonon decay. Fits in blue and red are those assuming decay into electron-hole pairs and acoustic phonons, respectively. (d) Three higher-energy $A_1$ modes, which also display the temperature dependence expected from anharmonic decay. (e) Schematic diagram showing the lowest-order anharmonic decay of an optical phonon with energy $\omega$ decay into two acoustic phonons with energy $\omega /2$.

Figure 3

(a) Schematic depicting interband (pink arrow) and intraband (blue arrow) transitions by optical phonons. An energy $\hslash {\omega }_a$ separates the initial electron state from the Fermi energy $E_F$. The electronic bands are labeled by irreducible representations ${\mathrm{\Gamma }}^i$ and ${\mathrm{\Gamma }}^j$, while the optical phonon of energy $\hslash {\omega }_{\mathrm{ph}}$ has the representation ${\mathrm{\Gamma }}^k$. (b) Calculated electronic band structure of ${\mathrm{WP}}_2$. The shaded regions indicate symmetry lines where scattering by $\mathrm{\Gamma }$-point optical phonons is allowed and energetically possible. (c) Weighted joint density of states for vertical ($q=0)$ transitions between states within $\pm 70\mathrm{meV}$ of $E_F$.

Figure 4

(a) Calculated phonon dispersion of ${\mathrm{WP}}_2$. The effective normalized phonon-electron matrix element is projected onto each phonon mode ($q$, $\omega$). The acoustic phonon modes have much stronger coupling than the optical modes. However, when comparing different optical modes, the lower-energy modes $A_1(1)$ and $A_1(2)$ show a significant enhancement of phonon-electron coupling compared to that of the higher-energy ones. (b) Close-up view of the phonon-electron coupling strength for small $q$ near $\mathrm{\Gamma }$, highlighting the largely enhanced coupling strength at finite $q$. Only the optical modes are colored according to coupling for clarification.