[Paper Review] Short-range excitonic phenomena in low-density metals

Jaakko Koskelo, Lucia Reining+1 more|arXiv (Cornell University)|Jan 1, 2023

Advanced Chemical Physics Studies6 citations

TL;DR

This paper demonstrates that short-range excitonic effects can emerge in low-density metals due to incomplete screening of electron-hole interactions at small distances, challenging the conventional view that excitons are suppressed in metals by macroscopic screening. Using the Bethe-Salpeter equation with a fermionic test-charge dielectric function, the authors identify low-energy, anisotropic electron-hole bound states and ghost modes—indicating excitonic character—while showing that even the simple ALDA-TDDFT approximation captures these phenomena due to short-distance physics.

ABSTRACT

Excitonic effects in metals are commonly supposed to be weak, because the Coulomb interaction is strongly screened. We investigate the low-density regime of the homogeneous electron gas, where low-energy collective excitations and ghost modes were anticipated. Using the Bethe-Salpeter equation (BSE), we show that both phenomena exist thanks to reduced screening at short distances. This is not captured by common approximations used in ab initio BSE calculations, but requires vertex corrections that take the fermionic nature of charges into account. The electron-hole wavefunction of the low-energy modes shows strong and very anisotropic electron-hole correlation, which speaks for an excitonic character of these modes. The fact that short-range physics is at the origin of these phenomena explains why, on the other hand, also the simple adiabatic local density approximation to time-dependent density functional theory can capture these effects.

Motivation & Objective

• To understand the origin of low-energy collective excitations and ghost modes in low-density metals, which contradict the conventional expectation of complete screening in metals.
• To determine whether these modes have an excitonic character, despite the strong screening typically suppressing excitons in metals.
• To assess the validity of standard approximations in ab initio methods (like BSE and TDDFT) in capturing these phenomena, particularly in the context of short-range electron-hole correlations.
• To clarify why simple TDDFT with ALDA can reproduce complex excitonic effects not captured by standard BSE approximations.

Proposed method

• Solving the Bethe-Salpeter equation (BSE) using a test-charge dielectric function that accounts for the fermionic nature of charges and excludes self-polarization, enabling accurate modeling of short-range electron-hole interactions.
• Employing a static, screened electron-hole interaction derived from the Tamm-Dancoff approximation with a test-charge dielectric function (st-GW TCTE), which captures vertex corrections essential for excitonic physics.
• Comparing results from the BSE with those from time-dependent density functional theory (TDDFT) in the adiabatic local density approximation (ALDA), to assess the predictive power of simpler functionals.
• Analyzing the electron-hole wavefunction and the inverse dielectric function to identify signatures of excitonic modes and ghost modes (imaginary poles) at low energies and large wavevectors.
• Using the static dielectric function to detect negative screening, a precursor to instabilities such as Wigner crystallization, and linking it to the emergence of excitonic modes.
• Validating the results by comparing the BSE and TDDFT-ALDA responses, focusing on spectral intensity and mode dispersion to assess consistency and physical origin.

Experimental results

Research questions

• RQ1 Can excitonic effects exist in low-density metals despite strong screening, and what is the physical origin of such effects?
• RQ2 What role does short-range screening play in enabling electron-hole binding and the formation of low-energy collective modes?
• RQ3 Why does the simple ALDA-TDDFT approximation capture these excitonic effects, while standard BSE approaches fail to do so?
• RQ4 How can ghost modes—imaginary poles in the inverse dielectric function—be linked to excitonic rather than plasmonic character?
• RQ5 What are the implications of these findings for the detection and potential application of excitonic phenomena in low-density electron systems?

Key findings

• The electron-hole wavefunction of the low-energy mode exhibits strong, anisotropic correlations, providing direct evidence for an excitonic character of the mode.
• Ghost modes—imaginary poles in the inverse dielectric function—appear at low energies and large wavevectors, signaling the presence of collective excitations with excitonic nature.
• The BSE with a fermionic test-charge dielectric function successfully captures both the ghost mode and low-energy excitonic state, while standard BSE approximations fail due to missing vertex corrections.
• Despite its known limitations in semiconductors, ALDA-TDDFT reproduces the key features of the excitonic mode, due to the dominance of short-range physics that is captured by the functional's structure.
• The static approximation used in the effective interaction is justified by strong dispersion in the mode, indicating significant dynamical cancellations, though dynamical corrections could further enhance the effect.
• Negative static screening (ε(q,ω=0) < 0) emerges at low densities (rs > 5.25), signaling a precursor to electronic instabilities and providing a necessary condition for the formation of these excitonic modes.