🔬 mesoscale physics

New plasmon-like mode in PdTe $_{2}$ : Raman scattering and memory function study

This study identifies a new plasmon-like mode in PdTe $_{2}$ below 100 K through temperature-dependent Raman scattering, confirming its electronic origin via congruent theoretical modeling and phenomenological analysis of the linear frequency dependence of the Raman relaxation rate.

Original authors: Bharathiganesh Devanarayanan, Sahil Rathi, Jalaja Pandya, Sonika, C. S. Yadav, Navinder Singh Bathinda, Satyendra Nath Gupta

Published 2026-06-29

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CC BY 4.0

Original authors: Bharathiganesh Devanarayanan, Sahil Rathi, Jalaja Pandya, Sonika, C. S. Yadav, Navinder Singh Bathinda, Satyendra Nath Gupta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Mystery in a "Superconductor" Material

Imagine you have a very special piece of material called PdTe₂ (Palladium Ditelluride). Scientists love this material because it’s a "Type II Dirac Semimetal." Think of it like a highway for electrons where they can zip around incredibly fast, almost without friction. It’s also a superconductor at very low temperatures, meaning electricity can flow through it with zero resistance.

The researchers wanted to understand how the atoms in this material vibrate and how the electrons behave. To do this, they used a technique called Raman Spectroscopy.

The Analogy: Imagine shining a flashlight on a drum. Most of the light bounces off unchanged. But a tiny bit of the light interacts with the drum’s vibrations, changing its color slightly. By analyzing that changed color, you can figure out exactly how the drum is vibrating. In this case, the "drum" is the crystal structure of PdTe₂, and the "vibrations" are the movements of its atoms and electrons.

The Mystery: A Ghost Note Appears

When the scientists shone their laser on PdTe₂ at room temperature, they heard two distinct "notes" (vibrations) from the material. These are called phonons, which are just bundles of vibrational energy. Let’s call them Note A and Note B.

But then, they cooled the material down to near absolute zero (10 Kelvin). Suddenly, a third note appeared! It was a broad, fuzzy sound centered around a specific frequency (250 cm⁻¹).

This was confusing. Why?

The Computer Check: They used supercomputers (Density Functional Theory) to simulate how the atoms in PdTe₂ should vibrate. The computer said, "There are only two notes possible: Note A and Note B."
The Magnetic Check: The material isn't magnetic, so this third note couldn't be coming from magnetic spins (magnons).

So, if it’s not an atom vibrating (phonon) and it’s not a magnetic spin (magnon), what is it?

The Solution: It’s an Electron Dance (Plasmon)

The scientists suspected the third note was a Plasmon.

The Analogy: Imagine a crowd of people (electrons) in a stadium. If one person pushes another, the push ripples through the crowd. That ripple is a collective movement of the crowd, not just one person moving. In physics, this collective ripple of electrons is called a plasmon.

The researchers argued that this third "note" wasn't an atom shaking, but rather the electrons in the material collectively sloshing back and forth.

How They Proved It: The "Fingerprint" Test

To prove this, they needed to find a unique "fingerprint" that distinguishes an electron ripple (plasmon) from an atom vibration (phonon). They used a mathematical tool called the Memory Function Formalism.

Think of this like analyzing how quickly a sound fades away (relaxation rate) in a room.

If it’s an atom vibration (Phonon): The sound fades in a specific, curvy way that eventually levels off (saturates) at high frequencies.
If it’s an electron ripple (Plasmon): The sound fades in a straight, linear line.

The Experiment:

Theory: The scientists built a simple mathematical model assuming the third note was a plasmon. The math predicted that if it were a plasmon, the "fade-out" rate would be a straight line.
Reality: They looked at their actual experimental data from the cold PdTe₂. They calculated the "fade-out" rate from the real measurements.

The Result: The real data matched the theory perfectly. Below 100 Kelvin, the "fade-out" rate was a straight line. Above 100 Kelvin, when the third note disappeared, the rate became curvy again (matching normal atom vibrations).

Summary of Findings

A New Discovery: PdTe₂ has a hidden mode that only shows up when it’s very cold (below 100 K).
Not an Atom: It is not caused by the atoms shaking.
It’s Electrons: It is caused by the collective movement of electrons (a plasmon-like mode).
The Proof: The way this mode interacts with light follows a linear pattern, which is the unique signature of plasmons, distinct from the curvy pattern of normal atomic vibrations.

Why Does This Matter?

While the paper doesn't list specific future gadgets, understanding these "plasmon-like" modes is crucial for physicists. It helps them understand how electrons behave in these exotic "Dirac" materials. This knowledge is a stepping stone for designing better electronic devices, sensors, or quantum materials in the future, because it reveals how energy moves through the material at a fundamental level.

Technical Summary: New plasmon-like mode in PdTe2: Raman scattering and memory function study

Problem Statement
Palladium ditelluride (PdTe $_2$ ) is a type II Dirac semimetal known for its tilted Dirac cones, nontrivial topological surface states, and superconductivity ( $T_c \approx 1.7$ K). While its electronic properties are well-studied, its lattice vibrations and electron-phonon coupling remain less explored. Previous Raman studies on similar Dirac materials, such as Cd $_3$ As $_2$ , have reported the emergence of a new Raman mode around 250 cm $^{-1}$ below a characteristic temperature of 100 K, but the origin of this mode has not been clearly established in the literature. This study aims to investigate the low-temperature Raman response of PdTe $_2$ to identify the nature of a newly observed spectral feature and to determine whether it arises from phononic, magnonic, or electronic (plasmonic) origins.

Methodology
The authors employed a multi-faceted approach combining experimental spectroscopy, first-principles calculations, and theoretical modeling:

Experimental Raman Spectroscopy: Single crystals of PdTe $_2$ were synthesized via solid-state reaction. Temperature-dependent Raman scattering measurements were performed in a backscattering configuration using a 532-nm laser, covering a temperature range from 10 K to 300 K. The spectra were fitted with Lorentzian line shapes to extract peak positions, full width at half maximum (FWHM), and intensities.
Density Functional Theory (DFT): First-principles calculations were performed using the QUANTUM ESPRESSO package within the Generalized Gradient Approximation (GGA) including spin-orbit coupling. Density Functional Perturbation Theory (DFPT) was used to calculate phonon dispersion and Raman-active modes to verify the phononic origin of observed peaks.
Microscopic Theoretical Model: To test the hypothesis that the new peak is plasmon-like, the authors constructed a microscopic model of electrons coupled to a single plasmon mode. Using the memory function formalism, they derived the imaginary part of the memory function, which corresponds to the Raman relaxation rate ( $\Gamma(\omega)$ ).
Phenomenological Analysis: The authors applied the memory function formalism to the experimental Raman spectra to phenomenologically extract the frequency-dependent Raman relaxation rate ( $\Gamma(\omega)$ ) and the mass enhancement factor ( $1 + \lambda(\omega)$ ). This involved calculating the correlation function from the measured spectra and applying Kramers-Kronig transforms.

Key Contributions and Results

Emergence of a New Mode: The experimental Raman spectra reveal two known phonon modes (assigned as $E_g$ at $\sim$ 85 cm $^{-1}$ and $A_{1g}$ at $\sim$ 128 cm $^{-1}$ based on DFT). Below 100 K, a third, broader peak emerges centered around 250 cm $^{-1}$ . This peak disappears completely at temperatures above 100 K.
Exclusion of Phononic and Magnonic Origins: DFT calculations confirm that PdTe $_2$ possesses only two Raman-active phonon modes ( $E_g$ and $A_{1g}$ ). Since the system is non-magnetic, the new peak cannot be a magnon. This suggests the peak originates from electronic excitations.
Anomalous Phonon Behavior: The two phonon modes follow a cubic anharmonicity model (where phonons decay into two equal-energy phonons) well below 100 K. Above 100 K, their frequencies and linewidths exhibit anomalous deviations from this model.
Linear Relaxation Rate Signature:
- Theoretical Prediction: The microscopic model of electron-plasmon coupling predicts that the Raman relaxation rate ( $\Gamma(\omega)$ ) exhibits a linear dependence on frequency (wavenumber) in the region of interest (100–1000 cm $^{-1}$ ) when the plasmon mode is present.
- Phenomenological Confirmation: Analysis of the experimental data shows that for temperatures below 100 K (where the new peak is present), the phenomenologically derived $\Gamma(\omega)$ is indeed linear with respect to frequency. Conversely, for temperatures above 100 K, $\Gamma(\omega)$ is non-linear and saturates near the Debye wavenumber ( $\sim$ 1408 cm $^{-1}$ ), consistent with phonon scattering.
- Mass Enhancement: The mass enhancement factor ( $1 + \lambda(\omega)$ ) decreases with frequency for all temperatures, asymptotically approaching 1. The drop is faster at higher temperatures (above 100 K) compared to lower temperatures.

Significance and Claims
The paper claims that the congruence between the theoretical prediction (linear relaxation rate from the microscopic plasmon model) and the phenomenological analysis of experimental data (linear relaxation rate below 100 K) provides decisive evidence that the new Raman mode observed in PdTe $_2$ below 100 K is a plasmon-like mode. This finding offers a microscopic understanding of a spectral feature previously observed in other Dirac materials like Cd $_3$ As $_2$ but not fully explained. The study highlights the utility of memory function formalism in distinguishing between phononic and electronic scattering mechanisms in Raman spectroscopy of topological materials.