Zhang–Rice Exciton: Concepts & Spectroscopy

• Zhang–Rice exciton is a bound charge-transfer excitation arising from strong p–d hybridization and local Coulomb correlations, observable in diverse materials.
• Spectroscopic probes such as RIXS, optical absorption, and XPS detect narrow resonance features and distinctive energy shifts that reveal local charge and spin dynamics.
• Material studies show that ZR exciton behavior is sensitive to doping, pressure, and disorder, affecting magnetic order and charge-transfer energetics in many-body systems.

Searching arXiv for recent and foundational papers on Zhang–Rice excitons and related Zhang–Rice states. The Zhang–Rice exciton is a charge-transfer excitation built from a Zhang–Rice (ZR) state, namely a bound ligand-hole–transition-metal configuration generated by strong $p$–$d$ hybridization and local Coulomb correlations. In the canonical cuprate setting, the underlying object is the Zhang–Rice singlet on a CuO$_4$ plaquette; in other materials the relevant local manifold can instead be a generalized ZR state or a Zhang–Rice triplet–singlet pair. The term therefore covers a family of closely related many-body excitations: low-energy optical or RIXS-active charge-transfer excitons in cuprates, generalized ligand-hole resonances in correlated oxides such as UO$_2$, and optically bright magnetic excitons in layered van der Waals antiferromagnets such as NiPS$_3$ and NiI$_2$ (Liu et al., 10 Dec 2025, Huang et al., 2015, Belvin et al., 2021).

1. Canonical definition and microscopic construction

In the standard cuprate formulation, the ZR singlet is a local bound singlet formed between a Cu $3d_{x^2-y^2}$ hole and a ligand O $2p_\sigma$ hole on a CuO$_4$ plaquette. A convenient schematic form is

$$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$

where $d$0 creates the bonding combination of the surrounding O $d$1 holes with $d$2 symmetry. This local singlet is the basis for the familiar reduction of the three-band Emery model to a one-band Hubbard or $d$3–$d$4 description in much of cuprate theory (Liu et al., 10 Dec 2025).

The excitonic extension of this idea is material-dependent. In cuprates, the “Zhang–Rice exciton” typically denotes an optical or RIXS excitation in which one member of the electron–hole pair is ZR-derived, for example a ZRS $d$5 upper-Hubbard-band transition or a charge-transfer excitation that creates a ZR-like final state (Liu et al., 10 Dec 2025, Monney et al., 2016). In UO$d$6, the corresponding object is a generalized ZR-type bound state composed predominantly of U $d$7 and O $d$8 character, centered between $d$9 and $_4$0 eV, and built on a $_4$1 triplet local moment rather than a Cu-like spin-$_4$2 background (Huang et al., 2015). In NiPS$_4$3 and NiI$_4$4, the relevant local degrees of freedom are a Zhang–Rice triplet (ZRT) ground state and a Zhang–Rice singlet (ZRS) excited state; the observed exciton is then a triplet-to-singlet magnetic excitation of a Ni–ligand cluster (Kim et al., 2023, Son et al., 2021).

A recurrent point across these realizations is that the ZR exciton is not a simple weakly bound Wannier exciton. It is a local or quasi-local many-body excitation whose energy and symmetry are controlled by charge-transfer energetics, local multiplet structure, and spin or spin–orbit selection rules. This suggests that “Zhang–Rice exciton” is best understood as a correlated bound excitation built from a ZR local state, rather than as a single universal quasiparticle type.

2. Spectroscopic manifestations

ZR excitons and ZR-derived bound states are identified through a characteristic combination of resonance behavior, narrow spectral structure, and sensitivity to magnetic or local-moment backgrounds.

System	Probe	Representative signature
Li$_4$5CuO$_4$6	O $_4$7-edge RIXS	intrachain ZR singlet at $_4$8 eV; interchain ZR singlet at $_4$9 eV
MnO(001)	ARPES and Mn $_2$0 XPS	top valence ZR bound state; non-local $_2$1 screening channel
NiPS$_2$2	PL and optical/THz probes	magnetic exciton at $_2$3–$_2$4 eV with $_2$5 meV linewidth
NiI$_2$6	Optical absorption	ZRT $_2$7 ZRS exciton at $_2$8 eV

In cuprates, O $_2$9-edge XAS and RIXS remain central because they couple directly to ligand $_3$0 states. In overdoped LSCO, O $_3$1-edge feature A at $_3$2 eV is assigned to the ZRS band, feature B at $_3$3 eV to the upper Hubbard band, and optical features $_3$4 eV and $_3$5 eV are assigned to ZRS $_3$6 UHB and LHB $_3$7 UHB transitions, respectively (Liu et al., 10 Dec 2025). In Li$_3$8CuO$_3$9, O $_2$0-edge RIXS resolves both intra- and interchain ZR singlets and also identifies a ZR triplet excitation, which allows direct extraction of ZR binding energies and singlet–triplet splittings (Monney et al., 2016).

In binary oxides and actinides, the same physics appears in other spectroscopies. In MnO(001), the topmost valence band is a ZR bound state formed by Mn $_2$1 and O $_2$2 orbitals, while Mn $_2$3 XPS resolves a non-local screening channel $_2$4 tied directly to the ZR state (Kundu et al., 2023). In cubic UO$_2$5, DFT+DMFT identifies an isolated ZR-like resonance between $_2$6 and $_2$7 eV that is strongly hybridized between U $_2$8 and O $_2$9 and appears as an almost flat feature in the momentum-resolved spectral function (Huang et al., 2015).

In van der Waals magnets, the optical signatures are exceptionally sharp. NiPS$3d_{x^2-y^2}$0 exhibits a magnetic exciton near $3d_{x^2-y^2}$1–$3d_{x^2-y^2}$2 eV with a linewidth as small as $3d_{x^2-y^2}$3 meV, while Ni$3d_{x^2-y^2}$4P$3d_{x^2-y^2}$5S$3d_{x^2-y^2}$6 shows a ZR exciton near $3d_{x^2-y^2}$7 eV with distinct phonon sidebands spaced by about $3d_{x^2-y^2}$8 (Kim et al., 2023, Khan et al., 25 Jul 2025). Such sharpness is a hallmark of the local correlated character of these excitations.

3. Cuprate realizations

In cuprates, the ZR exciton is inseparable from the Zhang–Rice singlet itself. XAS across the doping range up to $3d_{x^2-y^2}$9 found that the integrated ZRS spectral weight $2p_\sigma$0 increases continuously with doping and shows no saturation, while deviating from simple linearity. This was interpreted as evidence that the ZRS picture remains intact across the most prominent doping regimes of high-$2p_\sigma$1 cuprates, even though the orbital composition evolves with doping (Chen et al., 2013). A first-principles study of the one-dimensional cuprate Ca$2p_\sigma$2Y$2p_\sigma$3Cu$2p_\sigma$4O$2p_\sigma$5 further showed that localized ZR singlets can emerge above a threshold doping near $2p_\sigma$6, with localized O $2p_\sigma$7 states appearing about $2p_\sigma$8 eV above the valence-band top (0803.0440).

Direct cuprate ZR excitons are especially clear in Li$2p_\sigma$9CuO$_4$0. O $_4$1-edge RIXS resolves an intrachain ZR singlet exciton at $_4$2 eV and an interchain ZR singlet exciton at $_4$3 eV; by combining these with a previously determined intrachain charge-transfer energy of $_4$4 eV, the ZR singlet binding energy was extracted as $_4$5 eV. The same analysis yielded a singlet–triplet splitting $_4$6 eV and identified ZR triplet excitations in the RIXS spectra (Monney et al., 2016). Because O $_4$7-edge RIXS conserves spin, the intensities of the singlet and triplet channels track nearest-neighbor spin correlations: the intrachain ZR singlet weakens on cooling as ferromagnetic intrachain order develops, whereas the interchain ZR singlet strengthens as interchain antiferromagnetic order grows (Monney et al., 2016).

The overdoped regime is more contested. TF-$_4$8SR and susceptibility data in LSCO showed that a Curie-like paramagnetic component grows beyond $_4$9, implying that doped holes do not neutralize all Cu spins through complete ZR singlet formation; the interpretation advanced there is that an increasing fraction of holes enters the Cu $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$0 orbital (Kaiser et al., 2012). A later broadband optical and XAS study of LSCO proposed that beyond $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$1 the canonical ZRS manifold reconstructs into ZR1 and ZR2 subbands, with a new low-energy shoulder A$$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$2 near $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$3 eV in XAS and a new optical feature $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$4 eV assigned to LHB $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$5 ZR1 transitions (Liu et al., 10 Dec 2025). Taken together, these works suggest that there is no single universal overdoped endpoint: some probes emphasize continuity of ZR spectral weight up to moderate overdoping, whereas others detect incomplete ZR formation or explicit reconstruction once the hole density becomes sufficiently large (Chen et al., 2013, Kaiser et al., 2012, Liu et al., 10 Dec 2025).

4. Generalized Zhang–Rice excitons beyond cuprates

The ZR concept extends beyond CuO$$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$6 plaquettes when ligand-hole binding survives in a different correlated background. In cubic UO$$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$7, DFT+DMFT identified a generalized ZR state as an isolated peak between $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$8 and $$\left|{\rm ZRS}\right\rangle \sim \frac{1}{\sqrt{2}}\Big( d^\dagger_{i\uparrow}\,\tilde p^\dagger_{i\downarrow} - d^\dagger_{i\downarrow}\,\tilde p^\dagger_{i\uparrow} \Big)\left|{\rm ref}\right\rangle,$$9 eV composed predominantly of U $d$00 and O $d$01 characters. Because the local U $d$02 ground state is a $d$03 triplet, this bound state is not a simple cuprate-like spin singlet; rather, it is a spin–orbit-entangled ligand-hole–plus–local-moment composite built mainly from the $d$04 manifold (Huang et al., 2015).

Pressure in UO$d$05 provides an unusually clean control parameter for the survival of that generalized ZR exciton. The Mott gap collapses at $d$06, corresponding to $d$07 GPa, where the $d$08 channel becomes metallic while $d$09 remains insulating up to about $d$10 GPa. In that metallic state the generalized ZR peak rapidly broadens and loses intensity; by $d$11, or about $d$12 GPa, it is almost smeared out (Huang et al., 2015). This establishes a general principle: local ZR-type bound states are stabilized by a Mott-insulating background with robust local moments and are destroyed when pressure-driven itinerancy washes those moments into a quasiparticle continuum.

MnO(001) provides a different extension of the same motif. There the topmost valence band is a ZR bound state formed by Mn $d$13 and O $d$14 orbitals, and antiferromagnetic order sharpens this state and folds it with the periodicity of the AFM unit cell. Embedded DMFT shows that the sharpening is spin-selective: the minority-spin Mn $d$15–O $d$16 hybridization peak becomes stronger and narrower in the AFM phase (Kundu et al., 2023). The same ZR state also controls Mn $d$17 core-level screening, where a $d$18 final state produces a distinct non-local screening peak. This core-hole-screened state is not named an exciton in the paper, but it is naturally interpreted as an excitonic configuration in which a core hole is screened through a ZR-derived valence channel (Kundu et al., 2023).

These non-cuprate examples broaden the meaning of the term. They show that the essential ingredient is not Cu specifically, but a bound ligand-hole configuration strongly entangled with a local correlated shell and rendered spectroscopically visible through photoemission, XPS, or optical selection rules.

5. Van der Waals magnetic excitons

Layered van der Waals antiferromagnets have turned the ZR exciton into a directly addressable optical object. In NiPS$d$19, the magnetic exciton is assigned to a transition between a ZRT ground state and a ZRS excited state on a NiS$d$20 cluster. Optical studies placed this exciton near $d$21–$d$22 eV with a linewidth around $d$23 meV, while $d$24S NMR later provided microscopic evidence that the ground state is indeed a spin-triplet $d$25–$d$26 hybridized ZRT with $d$27 K. The same NMR work found a power-law divergence $d$28 with $d$29 K, indicating critical charge fluctuations consistent with spin-nematic correlations (Kim et al., 2023, Kim et al., 9 Jun 2026).

The coherence of the NiPS$d$30 exciton is strikingly fragile to ligand or cation disorder. In Ni$d$31Cd$d$32PS$d$33, only a few percent Cd substitution drastically suppresses the exciton intensity while its linewidth broadens gradually, even though the antiferromagnetic ground state remains robust (Kim et al., 2023). In NiPS$d$34Se$d$35, Se substitution produces a secondary lower-energy peak $d$36 in addition to the primary $d$37; both retain the same polarization anisotropy, but their energies, linewidths, and thermal stability evolve differently with Se content, implicating local $d$38-orbital inhomogeneity as the key control knob (Kumar et al., 20 Apr 2025). Under resonant photoexcitation at $d$39 eV, these NiPS$d$40 ZR excitons can even drive a transient antiferromagnetic metal with a Drude response coexisting with a coherent long-wavelength magnon, a non-thermal phase not accessible by simple heating (Belvin et al., 2021).

NiI$d$41 realizes a multiferroic variant. Cluster CI calculations identify a ZRT ground state with strong $d$42 mixing and a ZRS excited state of $d$43 symmetry. Optical absorption then reveals an ultra-sharp magnetic exciton at $d$44 eV with a $d$45 meV linewidth at $d$46 K, but only below the lower magnetic transition $d$47 K where the proper-screw spiral and ferroelectric polarization break inversion symmetry. In that setting the otherwise dark ZRT $d$48 ZRS excitation becomes optically allowed (Son et al., 2021).

Ni$d$49P$d$50S$d$51 adds a phononic dimension. Its EA peak at $d$52 eV has a linewidth of about $d$53 meV at $d$54 K and is accompanied by phonon sidebands spaced by $d$55, close to an $d$56 Raman mode. The linear polarization degree reaches about $d$57 at $d$58 K, and the survival temperatures of both the ZR exciton and its sidebands fall rapidly as thickness is reduced from bulk to 10–15 nm flakes (Khan et al., 25 Jul 2025). This indicates that ZR exciton coherence in layered magnets is jointly limited by spin order, phonon coupling, and dimensionality.

6. Conceptual issues, controversies, and organizing principles

A first conceptual issue is terminology. In some papers the object is explicitly called a “Zhang–Rice exciton,” especially when it is optically bright or RIXS-active; in others it is called a ZR state, ZR bound state, or generalized ZRS. The difference is partly spectroscopic. Optical absorption, PL, and RIXS emphasize neutral excited states, whereas ARPES, XPS, and DMFT spectral functions emphasize charged final states or resonance features (Kundu et al., 2023, Huang et al., 2015). The common thread is the same: a low-energy ligand-hole configuration bound to a correlated metal site.

A second issue concerns the range of validity of the canonical one-band ZR reduction. The evidence up to moderate cuprate overdoping is mixed but not inconsistent. O $d$59-edge XAS found no saturation of ZRS spectral weight up to $d$60, supporting the continued usefulness of ZR-based descriptions in the main superconducting regime (Chen et al., 2013). By contrast, TF-$d$61SR in LSCO inferred incomplete ZR singlet formation beyond $d$62, and broadband optics plus DQMC proposed a ZR1/ZR2 reconstruction once $d$63 (Kaiser et al., 2012, Liu et al., 10 Dec 2025). The literature therefore supports a nuanced view: ZR physics remains central across a wide regime, but its simple single-band form becomes progressively less complete in the heavily overdoped state.

A third organizing principle is the balance between localization and itinerancy. Pressure in UO$d$64 destroys a generalized ZR state by driving an orbital-selective Mott transition (Huang et al., 2015). Ligand substitution in NiPS$d$65 rapidly suppresses ZR-exciton coherence without eliminating antiferromagnetism, showing that $d$66-orbital homogeneity is as important as spin order (Kumar et al., 20 Apr 2025). Dimensional reduction in Ni$d$67P$d$68S$d$69 lowers the temperature window where the ZR exciton survives (Khan et al., 25 Jul 2025). These examples collectively suggest that ZR excitons are strongest when local moments remain well defined, ligand–metal hybridization is strong but not fully itinerant, and disorder does not fragment the local charge-transfer manifold.

Recent theory has also extended the implications of localized ZR states back into cuprate magnetism. One proposal showed that a ZR singlet can nucleate a skyrmion-like topological spin texture in a single-hole-doped CuO$d$70 plane (Morinari, 2012). Another argued that spatially localized ZR singlets mediate emergent $d$71 and $d$72 superexchange pathways, producing magnetic frustration and a spin-glass phase on the hole-doped side (Wang et al., 18 May 2026). These works do not compute ZR excitons directly, but they indicate that the local ZR building block can reorganize the spin background around it, which is a plausible implication for the dynamics and dispersion of any ZR-derived excitonic excitation.

Across these settings, the ZR exciton emerges as an organizing concept for correlated charge-transfer spectroscopy: it links ligand holes, local multiplets, magnetic order, and strong hybridization in a single bound excitation. Its material-specific forms differ markedly—cuprate charge-transfer singlets, actinide generalized ZR resonances, MnO spin-selective ZR bound states, and triplet–singlet magnetic excitons in van der Waals magnets—but all instantiate the same underlying many-body motif.