Weyl-Mott Insulators

• Weyl-Mott insulators are 3D correlated electron phases defined by the coexistence of a bulk Mott gap and topologically invariant Weyl nodes that yield gapless spinon surface states.
• The phase emerges as strong on-site Coulomb interactions suppress quasiparticle weight, localizing charge while preserving underlying topological invariants via Green’s function zeros.
• Distinct experimental signatures such as ARPES-detected Fermi arcs and anomalous Hall effects differentiate WMIs from conventional Mott insulators and trivial band insulators.

A Weyl-Mott insulator (WMI) is a three-dimensional correlated electron phase characterized by the coexistence of a bulk Mott gap in the electronic charge sector and nontrivial topological features inherited from Weyl semimetals, notably surface Fermi arcs and robust bulk monopole charges. Unlike conventional Mott insulators, where all low-energy electronic and spin excitations are gapped and surface states are trivial or fully gapped, the WMI hosts neutral, gapless spinon or topological boundary modes with signatures directly connected to the underlying Weyl band topology. This intersection of strong correlation-driven localization and topologically protected phenomena yields a phase with unique experimental diagnostics and theoretical significance within strongly correlated quantum matter (López et al., 2023, Morimoto et al., 2015, Flores-Calderón et al., 2024).

1. Theoretical Foundations and Minimal Models

Weyl-Mott insulators are constructed by introducing strong local Coulomb interactions (e.g., Hubbard $U$) into a lattice system whose noninteracting limit is a Weyl semimetal. The canonical noninteracting Weyl model possesses pairs of Weyl nodes—band touching points with linear dispersion and definite chirality—whose projections onto certain surfaces are connected by open Fermi arcs. The crucial theoretical innovation underpinning the WMI is the demonstration that it is possible to open a charge gap at each Weyl node (thus localizing electrons and destroying charge conduction) without annihilating pairs of nodes of opposite chirality or erasing the underlying topological invariants (Morimoto et al., 2015).

A prototypical Hamiltonian for a WMI consists of a Weyl-like hopping term $H_0$ and an on-site Hubbard interaction $H_U$: $$H = H_0 + H_U,\quad H_0 = t \sum_{\langle ij \rangle_a} e^{i\varphi_a}\, c_{i\alpha}^\dagger \sigma^a_{\alpha\beta} c_{j\beta},\quad H_U = \frac{U}{2} \sum_i (n_i-1)^2,$$ with appropriate flux choices $\varphi_a$ to yield multiple Weyl nodes (López et al., 2023). Variants include the momentum-diagonal Hatsugai-Kohmoto interaction, which admits exact analytical treatment and isolates the effect of correlation-induced zeros in the single-particle Green’s function (the so-called “Weyl-Mott point”) (Flores-Calderón et al., 2024).

The combination of strong interaction and nontrivial band topology triggers dramatic changes in the single-particle and collective excitation spectra, as well as emergent quantum numbers encoded in the Green’s function rather than in the noninteracting band structure.

2. Mott Transition Mechanisms and Green’s Function Topology

Central to the WMI is the nature of the metal-insulator transition and the persistence of topological invariants upon gap opening. In the weak-coupling limit, electron quasiparticles are well-defined (quasiparticle residue $Z \simeq 1$), supporting Weyl cones and Fermi arcs. Increasing $U$ continuously suppresses the quasiparticle weight ($Z \rightarrow 0$) at a critical value $U_c$, culminating in the opening of a charge gap ($\Delta_X \sim U-U_c$) throughout the Brillouin zone (López et al., 2023).

The key conceptual advance is the realization that the zeros of the single-particle Green’s function at $H_0$0 (the “Weyl-Mott point”) inherit the topological charge formerly associated with the band crossing pole; that is, the monopole charge remains protected by analytical continuity in the space of Green’s functions (Morimoto et al., 2015, Flores-Calderón et al., 2024). Explicitly, the Chern number for a two-dimensional slice (for fixed $H_0$1) is given by the Volovik–Gurarie–Ishikawa–Matsuyama formula: $H_0$2 This invariant remains nontrivial in the WMI, distinguishing it from a featureless (trivial) Mott insulator (Morimoto et al., 2015, Flores-Calderón et al., 2024).

The phase diagram as a function of correlation strength and chemical potential reveals a window where the WMI is stabilized ($H_0$3): the spectrum has a full charge gap but a persistent Green’s function zero at the original Weyl momentum, accompanied by non-Fermi-liquid behavior at the boundaries $H_0$4 (Flores-Calderón et al., 2024).

3. Surface States: Fermi Arcs and Penetration Depth

Topological bulk-boundary correspondence ensures that, as long as the bulk Green’s function retains a nontrivial monopole charge, Fermi arc states persist at the surface. In the WMI, these arcs originate from neutral spinon modes or correlated boundary excitations, with remarkable consequences for the spatial structure of the surface state. The single-particle spectral function for the surface reveals gapless lines (Fermi arcs) along high-symmetry directions, where the surface electronic gap is suppressed to zero at special surface momenta $H_0$5 despite the existence of a full bulk Mott gap $H_0$6 (López et al., 2023, Morimoto et al., 2015).

The penetration depth $H_0$7 of the Fermi arc state diverges as the momentum approaches the projection of the Weyl node: $H_0$8 signifying the merging of the arc into a bulk-like mode at the Weyl-Mott point (Morimoto et al., 2015). This feature is fundamentally distinct from surface states in conventional Mott or trivial band insulators, where no such divergence occurs.

4. Experimental Diagnostics and Materials Realizations

The experimental identification of WMIs relies on the unique coexistence of a bulk Mott gap and anomalous gapless surface modes. Angle-resolved photoemission spectroscopy (ARPES) is the primary probe: a WMI exhibits a gapped bulk spectrum but surface states with spectral weight extending to zero energy along Fermi arcs—manifested as a suppression (not enhancement) of the Mott gap on certain surfaces (López et al., 2023). Optical conductivity measurements show a threshold at the Mott gap energy but retain correlation-induced features (e.g., intraband peaks at $H_0$9), which are absent in conventional Mott insulators (Morimoto et al., 2015).

Thermal transport yields a $H_U$0 dependence due to neutral spinon excitations. The anomalous Hall conductivity remains nonzero in the insulating phase, directly reflecting the persistent bulk topological charge (Morimoto et al., 2015).

Pyrochlore iridates $H_U$1 are the prototypical candidate materials, showing a progression from correlated Weyl semimetal, through a bad semimetal regime, to a correlated insulator with surface-metallic domain wall states (López et al., 2023, Morimoto et al., 2015, Imada et al., 2014). Pressure-controlled Mott transitions in compounds such as La$H_U$2O$H_U$3Fe$H_U$4Se$H_U$5 illustrate the potential for tuning between conventional and topological Mott phases, although a clean WMI phase with both a bulk gap and robust Fermi arcs is an experimental frontier (Yang et al., 2023).

5. Correlations, Topological Invariants, and Dynamical Mean-Field Theory

Dynamical mean-field theory (DMFT) provides a nonperturbative framework for studying Mott transitions in topological semimetal models. DMFT calculations demonstrate that, as $H_U$6 increases, the Chern numbers associated with Weyl nodes persist up to a critical interaction strength, above which both the quasiparticle weight and the Chern numbers collapse to zero—yielding a trivial Mott insulator in generic models without long-range coherence of the topological charge (Irsigler et al., 2020).

However, the presence, mobility, and topological assignment of “blind bands” (zeros of the Green’s function) are essential for distinguishing true WMIs from topologically trivial Mott states. In models and parameter regimes where blind bands are flat (i.e., $H_U$7-independent) and carry zero Chern number, no robust WMI emerges (Irsigler et al., 2020). The precise conditions for the persistence of the WMI phase are thus model-dependent, reliant on spatial correlations, topology of the zero loci, and interaction structure.

6. Extensions: Domain Walls, Polyacetylene Analogy, and Unconventional Criticality

Beyond bulk and surface physics, domain wall and defect structures in WMI candidate systems present novel metallic states even in the fully gapped regime. The paradigmatic case is the magnetic domain wall in the all-in–all-out antiferromagnetic phase of the pyrochlore lattice (Imada et al., 2014). Analytical mapping to a Jackiw–Rebbi (soliton) problem reveals that a sign change in the order parameter across a domain wall traps in-gap, quasi-1D chiral modes with Fermi surfaces—effectively embedding a metallic two-dimensional system in a bulk Mott insulator. This mechanism is analogous to the soliton-protected states in polyacetylene, protected by a chiral (sublattice) symmetry of the effective Dirac Hamiltonian.

The unconventional quantum criticality at the correlation-induced topological transition, violating the Landau-Ginzburg-Wilson paradigm (e.g., with critical exponents $H_U$8), reflects the intertwined order and Fermi surface topology in the emergence of WMIs (Imada et al., 2014).

7. Summary Table: Distinguishing Features of Competing Phases

Phase	Bulk Charge Gap	Surface States	Topological Invariant	Signature Response
Weyl semimetal (WSM)	No	Fermi arcs (electronic)	Chern number/monopole	ARPES gapless cones, anomalous Hall, Drude peak
Conventional Mott insulator	Yes	None/trivial	0	Fully gapped, enhanced surface gap
Weyl-Mott insulator (WMI)	Yes ($H_U$9)	Spinon Fermi arcs	Chern number/monopole	Bulk gap, surface gap suppression, nonzero $$H = H_0 + H_U,\quad H_0 = t \sum_{\langle ij \rangle_a} e^{i\varphi_a}\, c_{i\alpha}^\dagger \sigma^a_{\alpha\beta} c_{j\beta},\quad H_U = \frac{U}{2} \sum_i (n_i-1)^2,$$0

The WMI phase is uniquely identified by the coexistence of a bulk Mott gap, nontrivial topological charge localized at a Green’s function zero, and the existence of surface spinon Fermi arcs resulting in suppressed surface gaps. These features distinguish it sharply from canonical Mott or band insulators and weakly interacting Weyl semimetals (López et al., 2023, Morimoto et al., 2015, Flores-Calderón et al., 2024).