First-principles design of excitonic insulators: A review

Abstract

The excitonic insulator (EI) is a more than 60-year-old theoretical proposal that yet remains elusive. It is a purely quantum phenomenon involving the spontaneous generation of excitons in quantum mechanics and the spontaneous condensation of excitons in quantum statistics. At this point, the excitons represent the ground state rather than the conventional excited state. Thus, the scarcity of candidate materials is a key factor contributing to the lack of recognized EI to date. In this review, we begin with the birth of EI, presenting the current state of the field and the main challenges it faces. We then focus on recent advances in the discovery and design of EIs based on the first-principles Bethe-Salpeter scheme, in particular the dark-exciton rule guided screening of materials. It not only opens up new avenues for realizing excitonic instability in direct-gap and wide-gap semiconductors, but also leads to the discovery of novel quantum states of matter such as half-EIs and spin-triplet EIs. Finally, we will look ahead to possible research pathways leading to the first recognized EI, both computationally and theoretically.

Figures (7)

• Figure 1: (Color online) (a) A diagrammatic illustration of the correlation between $E_g$ and $E_b$. The larger the $E_g$, the weaker the screening effect, the stronger the exciton binding, the smaller the radius, and the higher the $E_b$. Conversely, the smaller the $E_g$, the stronger the screening, the weaker the exciton binding, the larger the radius, and the smaller the $E_b$. (b) The 1/4 linear scaling relationship between $E_b$ and $E_g$ in two-dimensional materials. Adapted from Ref. Jiang2017.
• Figure 2: (Color online) (a) Strain dependence of $E_g$ and two-dimensional polarizability $\alpha_{2D}$ for two-dimensional GaAs in the double-layer honeycomb structure. (b) Strain dependence of $E_g$ and $E_b$ with different calculation methods. Adapted from Ref. Jiang2018.
• Figure 3: (Color online) (a) Top row: Geometric structure of one-dimensional molecular wire MnCp$_\infty$. Bottom row: $E_g$, $E_b$ and oscillator strength of the lowest-energy exciton as a function of applied electric fields. On two sides of the critical electric field around 0.15 V/Å, the relative magnitudes of $E_g$ and $E_b$ turn over, signalling the existence of a phase transition between the band insulator and the EI. It should be emphasised that the oscillator strengths in the EI phase from the current first-principles BSE have no physical significance, and the difference is only at the time of the phase transition. (b) Top two rows: Illustration of $E_g$ narrowing due to the giant Stark effect. The valence band top originates from the Mn $d$-orbitals. They are localized and are almost unaffected by the electric field, as shown in the first row. Therefore, the energy change of the valence band maximum due to the electric field is small. In contrast, the conduction band bottom originates from delocalized $\pi$-orbitals. As shown in the second row, these electrons move in the opposite direction to the external electric field and accumulate on one side of the two C atoms. The charge redistribution reduces the system's potential energy, compensating for the loss of kinetic energy, resulting in a significant downward shift of the conduction band. As a consequence, the $E_g$ is notably reduced. Bottom two rows: Evolution of the real-space wave function of the lowest-energy exciton under a transverse electric field. The red dots mark the positions of the holes (fixed at central Mn atoms). Adapted from Ref. Liu2021.
• Figure 4: (Color online) Schematics of (a) the parity frustration in a topological EI, and (b) the evolution from atomic orbitals into a topological EI of Mo$_2$HfC$_2$O$_2$ at the $\Gamma$ point. Adapted from Ref. Dong2023.
• Figure 5: (Color online) (a) A schematic representation of three kinds of excitonic instability in magnetic materials as classified by spin-resolved $E_t$. When both spins have $E_t > 0$, it is a normal magnetic insulator. When both spins have $E_t < 0$, it is a normal magnetic EI. When one spin has $E_t > 0$ and the other has $E_t < 0$, it is a new state of matter, i.e., half-EI. (b) Characterized $d$-electron configurations in monolayer 1$T$-NiCl$_2$. (c) The low-energy exciton energies (vertical lines), superimposed on the imaginary part of the BSE dielectric function. $X_i$ and $D_i$ denote dark and bright excitons, respectively. (d) Reciprocal-space (top) and real-space (bottom) exciton wave functions modulus. The green dots denote the hole positions that are fixed at the central Ni atom. (e) The spontaneous formation of $X_1$-excitons makes the neighbouring Ni atoms no longer equivalent, with one behaving like an electron and the other like a hole, as shown in (d). Thus, they exhibit +1 and +3 valence, respectively. The appearance of this mixed valence implies a change in the long-range magnetic interaction of the system from a super-exchange to a double-exchange mechanism. Adapted from Ref. Jiang2019.