Correlation-driven branch in doped excitonic insulators

TL;DR

This work addresses how carrier doping reshapes the spectrum of a one-dimensional excitonic insulator and whether a doping-induced in-gap branch signals electron-hole correlations. Using matrix-product-state-based DMRG/TEBD, the authors compute the single-particle spectrum $A(k,\omega)$ and the optical conductivity $\sigma(\omega)$ in a correlated two-band model, and they dissect the origin of the in-gap branch by decomposing the $a$-orbital creation operator into singly-occupied and excitonic components, linking the branch to excitonic dynamics. The key finding is a robust doping-induced in-gap branch arising from the $a$-orbital sector, with spectral weight transfer toward $E_F$ and a growing Drude response; the in-gap feature is tied to excitonic correlations via an effective exchange scale $J\simeq \frac{4 t_a t_b}{U}$. This provides a concrete spectral signature of electron-hole correlations in doped excitonic insulators and offers guidance for interpreting experiments on materials such as Ta$_2$NiSe$_5$, while highlighting directions for incorporating lattice and spin degrees of freedom in future work.

Abstract

We investigate the spectral properties of a doped one-dimensional excitonic insulator. Employing matrix-product-state-based methods, we compute the single-particle spectrum and optical conductivity in a correlated two-band model. Our numerical calculation reveals the emergence of a correlation-driven in-gap branch in the doped state. The origin of the in-gap branch is examined by decomposing the propagation dynamics of a single particle, elucidating that the doping-induced branch is associated with excitonic correlations. Our demonstrations suggest that the doping-induced branch can serve as an indicator of electron-hole correlations.

Figures (5)

• Figure 1: Single-particle spectra for (a) $\delta=0$ (half filling) and (b) $\delta=0.05$ (hole doping), where $U=3t_{\rm h}$ and $D=1.95t_{\rm h}$. The left, middle, and right panels display $A(k,\omega)$ (total), $A_a(k,\omega)$ (orbital $a$), and $A_b(k,\omega)$ (orbital $b$), respectively. The horizontal lines represent the Fermi level $E_{\rm F}$.
• Figure 2: Densities of states for (a) $\delta=0$ (half filling) and (b) $\delta=0.05$ (hole doping), where $U=3t_{\rm h}$ and $D=1.95t_{\rm h}$. The energy of the horizontal axis is shifted by $U/2$, where the center of the gap is at zero in (a). The vertical dashed lines in (a) indicate the lower and upper edges of the band gap. The vertical dashed line in (b) represents the Fermi level $E_{\rm F}$.
• Figure 3: Real part of the optical conductivity $\sigma(\omega)$ for various $\delta$, where $U=3t_{\rm h}$ and $D=1.95t_{\rm h}$. The vertical dashed line represents the single-particle excitation gap of the nondoped insulator ($\delta=0$). Inset: Enlarged view of the spectra. Note that when $\delta=0$, the nonzero optical conductivity for $\omega$ below the gap is due to the broadening factor introduced in the numerical calculation.
• Figure 4: Absolute values of the space-time correlation functions $\mathcal{G}_a(x,t) = -i \braket{\psi_0 | \hat{\mathcal{O}}_{j+x,a}(t) \hat{\mathcal{O}}^{\dag}_{j,a}(0) | \psi_0}$ for (a) $\hat{\mathcal{O}}^{\dag}_{j,a} = \hat{c}^{\dag}_{j,a}$, (b) $\hat{\mathcal{O}}^{\dag}_{j,a} = \hat{s}^{\dag}_{j,a}=\hat{c}^{\dag}_{j,a} (1-\hat{n}_{j,b})$, and (c) $\hat{\mathcal{O}}^{\dag}_{j,a} = \hat{d}^{\dag}_{j,a}=\hat{c}^{\dag}_{j,a} \hat{n}_{j,b}$, where $U=8t_{\rm h}$, $D=0.92t_{\rm h}$, and $\delta=0.05$. The translucent red lines in (b) represent $x=\pm Jt$, where $J=4t_at_b/U$. (d) Single-particle spectrum $A_{a}(k,\omega)$ and (e) spectrum obtained by the Fourier transformation of $\mathcal{G}_a(x,t)$ for $\hat{s}^{\dag}_{j,a}$ in (b). Schematic figures of the operators (f) $\hat{s}^{\dag}_{j,a} = \hat{c}^{\dag}_{j,a} (1-\hat{n}_{j,b})$ and (g) $\hat{d}^{\dag}_{j,a} = \hat{c}^{\dag}_{j,a} \hat{n}_{j,b}$.
• Figure 5: (a) Schematic figure of the single-particle creation and the propagation of the created particle along the $a$-orbital chain. (b) Absolute value of the correlation function $\mathcal{G}_X(x,t) = -i \braket{\psi_0 | \hat{X}_{j+x}(t) \hat{X}^{\dag}_{j}(0) | \psi_0}$ for $\hat{X}^{\dag}_j = \hat{c}^{\dag}_{j,a} \hat{c}_{j,b}$, where $U=8t_{\rm h}$, $D=0.92t_{\rm h}$, and $\delta=0.05$. The translucent blue lines in (b) represent $x=\pm Jt$, where $J=4t_at_b/U$.