Non-Fermi-liquid signatures of quadratic band touching and phonon anomalies in metallic ${\text{Pr}}_{2}{\text{Ir}}_{2}{\text{O}}_{7}$

Non-Fermi-liquid signatures of quadratic band touching and phonon anomalies in metallic ${Pr}_{2} {Ir}_{2} O_{7}$

M. Rosalin, Prachi Telang, Surjeet Singh, D. V. S. Muthu, and A. K. Sood

Phys. Rev. B 108, 195144 – Published 27 November 2023

Abstract

A single Fermi node in $\Pr_{2} {Ir}_{2} O_{7}$ protected by time reversal and inversion symmetry resulting from an interplay between strong electronic correlations and spin-orbit coupling (SOC) has attracted significant attention. Here, we report a detailed temperature-dependent Raman study of the “quadratic band touching Luttinger semimetal” $\Pr_{2} {Ir}_{2} O_{7}$ . In addition to phonons, we observe an underlying flat electronic continuum due to electronic Raman scattering (ERS) that is dominant below a characteristic temperature $T_{Q}$ . The observed ERS is understood using the Raman susceptibility of a non-Fermi liquid expected in a quadratic band touching system. The phonon frequencies and linewidths show anomalous temperature dependence below $T_{Q} \sim 150$ K attributed to strong electron-phonon coupling (EPC) in a quadratic band touching (QBT) state. The Ir-O-Ir bending $E_{g}$ mode shows pronounced Fano asymmetry as well as anomalous linewidth broadening below $T_{Q}$ . Further, a Raman line at $\sim 460 {cm}^{- 1}$ involving crystal field transition couples strongly to the $T_{2 g}$ phonon at $\sim 350 {cm}^{- 1}$ . Our results establish the enhanced scale of electron-electron correlations and electron-phonon coupling in the QBT state of metallic $\Pr_{2} {Ir}_{2} O_{7}$ .

Received 30 July 2023
Revised 10 October 2023
Accepted 6 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.195144

Physics Subject Headings (PhySH)

Phonons

Pyrochlores Semimetals

Magnetization measurements Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Rosalin ¹, Prachi Telang², Surjeet Singh², D. V. S. Muthu ¹, and A. K. Sood ^1,*

¹Department of Physics, Indian Institute of Science, Bangalore 560012, India
²Department of Physics, Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India

^*asood@iisc.ac.in

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Vol. 108, Iss. 19 — 15 November 2023

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Figure 1
(a) Powder x-ray diffraction pattern of $\Pr_{2} {Ir}_{2} O_{7}$ . The vertical green bars below the diffraction pattern indicate the positions of the Bragg peaks of the pyrochlore phase. The fitted profile and difference plot is shown using red and blue color, respectively. [(b) and (c)] Temperature dependence of resistivity ( $ρ$ ) and inverse magnetic susceptibility, respectively for the $\Pr_{2} {Ir}_{2} O_{7}$ sample. The inset in (c) shows the measured magnetic susceptibility as a function of temperature. Solid red lines in both the main graph and inset indicate fit to the Curie-Weiss law and the dashed line in the inset is the extrapolated fit up to zero Kelvin.
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Figure 2
Temperature dependent Raman spectra of $\Pr_{2} {Ir}_{2} O_{7}$ ; upward vertical arrow indicates evolution of crystal field excitation $N_{1}$ .
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Figure 3
(a) 5 K Raman spectra of $\Pr_{2} {Ir}_{2} O_{7}$ ; shaded region indicates flat electronic continuum; red curve shows the fit to the NFL memory function formalism; inset shows the temperature dependence of the scaling factor Q of the NFL model; vertical black dashed line indicate the temperature scale of QBT denoted by $T_{Q}$ (b) Extracted $I_{ERS}$ of the electronic continuum from fitting the Raman spectra with memory function formalism at various measured temperatures; inset shows the low frequency region of the electronic continuum on an enlarged scale.
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Figure 4
The cumulative fit to the observed phonon and crystal field modes ( $E_{g}$ with BWF function and rest of the five modes with Lorentzian), top and bottom panels show 295 and 5 K, respectively. The green and magenta shaded regions indicate the $E_{g}$ and CFE modes, respectively (the background has been subtracted while fitting the phonons). The top inset shows the Pr ion environment surrounded by eight oxygen ions in the pyrochlore structure, and the bottom inset depicts the observed crystal field transition (energy levels shown are in ${cm}^{- 1}$ ) of the $\Pr^{3 +}$ .
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Figure 5
(a) 5 K Raman spectra of $\Pr_{2} {Ir}_{2} O_{7}$ ; shaded region indicates flat electronic continuum; red curve shows the fit to the NFL memory function formalism; inset shows the temperature dependence of the scaling factor Q of the NFL model; vertical black dashed line indicate the temperature scale of QBT denoted by $T_{Q}$ (b) The cumulative fit to the observed phonon and crystal field modes ( $E_{g}$ with BWF function and rest of the five modes with Lorentzian), top and bottom panels show 295 and 5 K, respectively. The green and magenta shaded regions indicate the $E_{g}$ and CFE modes, respectively (the background has been subtracted while fitting the phonons). The top inset shows the Pr ion environment surrounded by eight oxygen ions in the pyrochlore structure, and the bottom inset depicts the observed crystal field transition (energy levels shown are in ${cm}^{- 1}$ ) of the $\Pr^{3 +}$ .
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Figure 6
[(a) and (b)] Temperature variation of phonon frequencies and linewidths, respectively; two different color symbols indicate data from two independent sets of measurements; vertical black dashed line indicates the temperature scale of QBT denoted by $T_{Q}$ . Solid blue lines are fit to the anharmonic model (fitted to the combined set of data from both sets of measurements) and extended to zero Kelvin by dashed lines. Dark green line (in (b)) are fit to Eq. (7), whereas the yellow lines are guide to the eye. (c) The anharmonic corrected $Δ ω_{E P C}$ below $T_{Q}$ for different phonon modes. Solid green lines are fit to Eq. (8).
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Physical Review B

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Non-Fermi-liquid signatures of quadratic band touching and phonon anomalies in metallic ${Pr}_{2} {Ir}_{2} O_{7}$

M. Rosalin, Prachi Telang, Surjeet Singh, D. V. S. Muthu, and A. K. Sood

Phys. Rev. B 108, 195144 – Published 27 November 2023

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Non-Fermi-liquid signatures of quadratic band touching and phonon anomalies in metallic Pr2Ir2O7

M. Rosalin, Prachi Telang, Surjeet Singh, D. V. S. Muthu, and A. K. Sood

Phys. Rev. B 108, 195144 – Published 27 November 2023

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Non-Fermi-liquid signatures of quadratic band touching and phonon anomalies in metallic ${Pr}_{2} {Ir}_{2} O_{7}$