Unveiling Novel Resonant Interband Contribution to Polarizability in three-dimensional systems

TL;DR

This work analyzes polarizability in three-dimensional Dirac nodal line semimetals within the random phase approximation, uncovering a novel interband contribution that explicitly depends on the chemical potential and exhibits a cubic-in-$q$ resonance in the long-wavelength limit. The authors show that in 3D DNLSMs, intraband processes dominate at low frequencies while interband transitions govern intermediate and high frequencies, with strong anisotropy introduced by out-of-plane momentum transfer $q_z$ and a mass term that can open a gap and induce metal–insulator transitions. The study provides detailed model calculations for Ca$_3$P$_2$ and ZrSiS, demonstrating significant tunability of both intraband and interband polarizability and suggesting potential tunable plasmonic and optoelectronic applications. These findings offer a new optical fingerprint for 3D nodal-line systems and extend dielectric-tuning concepts to three dimensions, with implications for experimental probing via spectroscopy and electron-energy-loss techniques.

Abstract

Polarizability plays an essential role in characterizing key phenomena, such as the screening effects, collective excitations, and dielectric functions present in the system. In three-dimensional materials, it typically comprises an intraband contribution, dependent on the chemical potential, and an interband contribution, largely independent of it. In this study, within the random phase approximation framework, we uncover a novel interband contribution that, unlike the conventional case, exhibits an explicit dependence on the chemical potential, which has no counterpart in two dimensions. In the long-wavelength limit, this term introduces a resonance feature with cubic wave-vector dependence when the chemical potential approaches the band edge, in contrast to the quadratic behavior characteristic of standard intraband and interband processes. Focusing on three-dimensional Dirac nodal line semimetals, we show that the polarizability is intraband-dominated at low frequencies, while interband processes prevail at intermediate and high frequencies, with the overall response being tunable via the chemical potential. Material-specific estimates for Ca$_3$P$_2$ and ZrSiS reveal a strong tunability of both contributions. These findings open new directions for probing frequency-dependent dielectric properties and hold promise for applications in tunable plasmonic and optoelectronic devices.

Figures (4)

• Figure 1: The schematic shows the different components of polarizability $\text{P}(\bm q, \omega)$, which consist of two main contributions: the interband part, $\sum\limits_{m\neq n}\text{P}^{mn}(\bm q, \omega)$, and the intraband part $\text{P}^{mm}(\bm q, \omega)\delta_{mn}$. Here, the wave vector is defined as $q=\sqrt{q_\rho^2+q_z^2}$, with $q_\rho = \sqrt{q_x^2 + q_y^2}$. Further, the interband polarizability comprises two parts, one is the $\mu$ independent and the other is the $\mu$ dependent part, which shows $q^2$ and $q_zq^2$ dependence, respectively. In contrast, the intraband part arises solely from $\mu$ dependent part.
• Figure 2: The plot illustrates the interband component of the polarizability as a function of the mass parameter $\tilde{M}$ for different values of the chemical potential $\tilde{\mu}$. Panels (a) and (b) correspond to $\text{P}^{+-}$ and $\text{P}^{-+}$, respectively. The quantities $\text{P}_1^{+-}$ and $\text{P}_1^{-+}$ denote the $\tilde{\mu}$-independent parts of the interband polarizability in the DNLSM. The inset in panel (b) depicts the full variation of $\text{P}_1^{-+}$ with $\tilde{M}$ at a fixed frequency. The parameters used in the calculation are $\tilde{\omega} = 0.5$, $\tilde{q}_{\rho} = 0.01$, $\tilde{q}_{z} = 0.01$, and $\gamma = 2.8$.
• Figure 3: The $\text{P}^{++}$ component of the intraband polarizability as a function of mass $\tilde{M}$ for different values of $\tilde{\mu}$ is depicted. Here, we fix $\tilde{\omega}=0.5$, $\tilde{q}_{\rho} =0.01$, $\tilde{q}_{z} = 0.01$ and $\gamma = 2.8$.
• Figure 4: Plot depicts the comparison between the intraband and the interband components of the polarizability with the frequency $\tilde{\omega}$ at fixed $\tilde{\mu} = 0.6$, $\tilde{M}=0.5$, $\tilde{q}_{\rho} =0.01$, $\tilde{q}_{z} = 0.01$ and $\gamma = 2.8$.