Correlation-Driven In-Gap Branch Achieves New Insights in Doped Excitonic Insulators

Scientists are increasingly focused on understanding the unusual electronic behaviour arising in correlated materials, and new research published today details a surprising discovery within doped excitonic insulators. Tatsuya Kaneko, Ryota Ueda, and Satoshi Ejima, from The University of Osaka and the Deutsches Zentrum f ur Luft- und Raumfahrt (DLR) respectively, demonstrate the emergence of a correlation-driven in-gap branch within the single-particle spectrum of a doped one-dimensional excitonic insulator , a phenomenon revealed through advanced matrix-product-state calculations. This finding is significant because it identifies a clear spectroscopic signature of excitonic correlations, potentially offering a novel method for detecting and characterising these subtle, yet crucial, electron-hole interactions in materials.

This decomposition of particle dynamics provides a detailed understanding of how doping influences the electronic structure of the excitonic insulator, moving beyond the simplistic rigid-band picture often applied to conventional band insulators. The team achieved these results using a one-dimensional correlated two-band model, meticulously calculated with a chain of 160 lattice sites and a maximum bond dimension of 2000, ensuring high accuracy and minimal truncation error. Researchers utilized the density-matrix renormalization group (DMRG) method to obtain the ground state of the system, building upon previous DMRG calculations and refining the analysis for doped excitonic insulators.

The time-evolving block decimation (TEBD) algorithm was then employed to evolve the system in real time, allowing for the computation of dynamical correlation functions essential for understanding the spectral properties. A time step of 0.01/th and a bond dimension of 1000 were used for time evolutions up to 40/th, with a damping factor of 0.125th applied to achieve accurate spectral functions. This work opens exciting possibilities for designing and identifying novel excitonic insulator materials with tailored properties, potentially leading to advancements in optoelectronics and quantum computing. The doping-induced in-gap branch, as demonstrated in this study, can serve as a sensitive probe for detecting and quantifying electron-hole correlations, offering a powerful tool for materials characterization. Furthermore, understanding the interplay between correlation effects and doping in excitonic insulators is crucial for developing a comprehensive theory of strongly correlated systems and unlocking their full potential for technological innovation.

Matrix-product-state analysis of doped excitonic insulator spectra reveals

This work pioneers a detailed examination of the propagation dynamics of a single particle, decomposing it to elucidate that the doping-induced branch arises from excitonic correlations. The study demonstrates that this newly observed branch can potentially serve as a crucial indicator of electron-hole correlations within the material. The model, expressed mathematically as H = − Σj Σα tα c†j,αcj+1,α + H. c. + D/2 Σj (nj,a −nj,b) + U Σj nj,anj,b,. Experiments revealed that the window function employed in the Fourier transformation was w(t) = [1 + cos(πt/tmax)]/2, designed to minimise artefacts arising from the finite-time cutoff at tmax.

The Fermi level, EF, was defined as EF = −[Emin(N −1) −E0(N)], where E0(N) represents the ground-state energy of N fermions and Emin(N −1) is the minimum energy when one fermion is removed, in the insulating state, EF corresponds to the lower edge of the band gap. The single-particle spectra of the nondoped state, at U = 3th, demonstrated a clear band gap opening due to Coulomb repulsion, consistent with previous studies. Spectral weight analysis showed the a orbital remaining below EF and the b orbital above EF, confirming the excitonic nature of the insulating state in this one-dimensional system. Data shows that doping to δ = 0.05 induced a downward shift of EF and a deformation of the spectral structure, invalidating a simple rigid-band picture.

Analysis of Aa(k, ω) revealed that this doping-induced branch stemmed from the a-orbital component and developed above EF, accompanied by a redistribution of spectral weight near EF. Tests prove that the real part of the optical conductivity, σ(ω), at U = 3th, exhibited a spectral weight above the single-particle gap for δ = 0, which altered with doping. Specifically, the team measured Ga(x, t) = −i ⟨ψ0|cj+x,a(t)c† j,a(0)|ψ0⟩, providing insights into the propagation of a created fermion.

Doping reveals excitonic correlation in-gap branch dispersion

This in-gap branch originates from excitonic correlations, as evidenced by decomposition of the single-particle dynamics, suggesting it functions as an indicator of electron-hole interactions. The study establishes a link between doping and the appearance of this in-gap branch, providing insight into the behaviour of excitonic insulators when perturbed from their pristine state. The authors acknowledge that their calculations are performed within finite-size systems, which may introduce limitations in accurately capturing the behaviour in the thermodynamic limit. Future work could explore the robustness of this in-gap branch to variations in model parameters and investigate its potential observability in real materials. These findings contribute to a deeper understanding of correlated electron systems and offer a potential pathway for identifying and characterizing excitonic correlations in condensed matter physics.