Mott Transition in Correlated Materials

• Mott transition is an interaction-driven change from a metallic to an insulating state due to strong electron-electron interactions that block charge fluctuations.
• It is characterized by spectral-weight transfer, pseudogap formation, and critical scaling behaviors captured by dynamical mean-field theory and cluster methods.
• Experimental realizations in transition-metal oxides, organic salts, and moiré superlattices highlight tunable parameters such as pressure, doping, and bandwidth that control the transition.

The Mott transition is an interaction-driven change in the electronic state of matter in which charge motion is suppressed or restored by correlations rather than by ordinary band-structure effects. In its canonical form, a half-filled band that would be metallic in one-electron theory becomes insulating because strong local Coulomb repulsion blocks charge fluctuations; conversely, tuning bandwidth, filling, pressure, temperature, or density can delocalize the carriers and recover metallic transport. In modern usage, the term also extends to charge-transfer systems, orbital-selective localization, density-driven dissociation of bound states such as excitons, and even nonequilibrium analogues such as current-driven vortex delocalization (Kohno, 2012, Szwed et al., 9 Apr 2025).

1. Definition, criteria, and basic observables

In correlated-electron systems, the minimal language of the Mott transition is set by the Hubbard competition between kinetic delocalization and on-site repulsion. A standard form is

$$H = -t \sum_{\langle i,j \rangle,\sigma} (c^{\dagger}_{i\sigma} c_{j\sigma} + \mathrm{h.c.}) + U \sum_i n_{i\uparrow} n_{i\downarrow} - \mu \sum_{i,\sigma} n_{i\sigma},$$

where increasing $U/W$ suppresses double occupancy and can drive a metal-insulator transition at or near half filling. In this setting, the quasiparticle weight

$$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$

diagnoses coherence, while the charge compressibility

$\kappa = \frac{\partial n}{\partial \mu}$

distinguishes metallic and incompressible insulating regimes (Lang et al., 2023, Zhao et al., 29 Oct 2025).

A central distinction is between a Mott transition and a band-insulator-to-metal transition. The former is interaction-driven, entails large spectral-weight transfer between low-energy states and Hubbard bands, and often produces non-Fermi-liquid behavior near the insulating phase. The latter is controlled primarily by band edges or structural shifts and does not require strong correlations. In charge-transfer systems, the relevant gap is not set purely by $U$ but by the competition between $U$ and the ligand-to-correlated-orbital level separation, so the insulating state may be charge-transfer rather than Mott-Hubbard in the strict Zaanen–Sawatzky–Allen sense (Lang et al., 2023, Yanagisawa et al., 2014).

The term “Mott transition” is also used more broadly for density-driven unbinding of composite charged states. In three dimensions, the canonical density criterion is $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$, while in two dimensions the natural scaling is $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$. Recent work on excitonic Bose polarons measured $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$ and $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,IX}} \sim 0.9$, emphasizing that the notion of a Mott threshold extends beyond electrons in crystalline bands (Szwed et al., 9 Apr 2025).

2. Microscopic descriptions and theoretical interpretations

Dynamical mean-field theory and its cluster extensions provide the standard finite-temperature description of the bandwidth-controlled Mott transition. In the half-filled two-dimensional Hubbard model, plaquette CDMFT finds a first-order transition between a paramagnetic metal and a paramagnetic Mott insulator, bounded by spinodals and terminating at a critical endpoint near $U/W$0 and $U/W$1 in units where $U/W$2. Within that framework, pressure, entropy, compressibility, kinetic energy, potential energy, free energy, local entropy, and total mutual information all exhibit distinct signatures across the coexistence region and along the Widom line (Walsh et al., 2018).

At the level of momentum-resolved spectra, cluster perturbation theory and projected-wavefunction studies support a different emphasis: the Mott transition need not be understood primarily as band flattening. In the two-dimensional Hubbard model, a low-energy dispersing single-particle mode retains a bandwidth of order $U/W$3 while its spectral weight at the Fermi level vanishes continuously as $U/W$4, so the transition is characterized as freezing of the charge degrees of freedom in a single-particle excitation that continuously evolves into the magnetic excitation of the Mott insulator (Kohno, 2012). Related work on the $U/W$5–$U/W$6 model with a Gutzwiller wavefunction reaches the same conclusion across chains, ladders, square lattices, and bilayers: the electron-addition mode remains dispersive but loses spectral weight, and in the small-doping limit follows the magnetic dispersion shifted by the Fermi momentum, $U/W$7 (Kohno, 2020).

A more radical reinterpretation casts the Mott transition as a topological phase transition. In infinite-dimensional DMFT for the half-filled one-band Hubbard model, the mid-gap pole in the self-energy of the Mott insulator can be represented as the boundary Green’s function of an auxiliary generalized SSH chain. In this construction, the metallic phase corresponds to a trivial auxiliary chain, the insulating phase to a topological one with a zero-energy boundary state, and the transition to dissociation of domain walls; the Mott gap is then associated with zeros of the physical Green’s function induced by the self-energy pole (Sen et al., 2020).

Recent exactly solvable HK and MMHK constructions propose yet another organizing principle: a momentum-space $U/W$8 symmetry whose breaking opens the Mott gap. In that formulation, the charge compressibility rather than double occupancy acts as the operative order parameter, vanishing in the insulator and remaining finite in the metal. The same framework yields a universal deep-insulating Widom-line scaling $U/W$9 and an inflection-point scale obeying $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$0 with $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$1 (Zhao et al., 29 Oct 2025).

3. Spectral, transport, thermodynamic, and magnetic signatures

The spectroscopic hallmark of Mottness is spectral-weight transfer between coherent low-energy states and incoherent Hubbard features. In the two-dimensional Hubbard model, this is accompanied by a pseudogap, Fermi-arc phenomenology, an antinodal flat band, kink and waterfall structures, and doping-induced states transferred from the upper to the lower Hubbard band, all tied to the proximity of the Mott transition rather than to additional one-electron parameters such as $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$2 (Kohno, 2012).

Thermodynamically, the finite-temperature first-order transition is marked by jumps in entropy, double occupancy, and energy densities, while the supercritical regime is organized by the Widom line. In plaquette CDMFT, the entropy of the metal exceeds that of the insulator across the first-order boundary, the latent heat is small, and the loci of extrema in double occupancy, entropy, and mutual information all track the same crossover emanating from the critical endpoint (Walsh et al., 2018).

Experiments near putative continuous or quasi-continuous Mott criticality display a different pattern. In the triangular-lattice organic $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$3-(ET)$$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$4Cu$$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$5(CN)$$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$6, fine pressure tuning reveals that the Fermi-liquid coherence temperature collapses to the kelvin scale near $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$7 MPa, the $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$8 resistivity coefficient follows $$Z = \left[1 - \left.\frac{\partial \Sigma(\omega)}{\partial \omega}\right|_{\omega=0}\right]^{-1}$$9, and the insulating charge gap obeys $\kappa = \frac{\partial n}{\partial \mu}$0 away from the immediate critical regime. Clausius–Clapeyron analysis indicates an extremely weak first-order transition, consistent with a quasi-continuous evolution between a Fermi liquid and a spin liquid with a spinon Fermi surface (Furukawa et al., 2017).

Semiconductor moiré superlattices provide a complementary bandwidth-tuned realization. In angle-aligned MoTe$\kappa = \frac{\partial n}{\partial \mu}$1/WSe$\kappa = \frac{\partial n}{\partial \mu}$2 at fixed filling $\kappa = \frac{\partial n}{\partial \mu}$3, the activation gap on the insulating side scales as $\kappa = \frac{\partial n}{\partial \mu}$4 with $\kappa = \frac{\partial n}{\partial \mu}$5, while on the metallic side the Fermi-liquid coefficient gives $\kappa = \frac{\partial n}{\partial \mu}$6, implying a diverging effective mass. The resistance exhibits quantum-critical scaling collapse, the magnetic susceptibility evolves smoothly across the transition, and no long-range magnetic order is observed down to approximately $\kappa = \frac{\partial n}{\partial \mu}$7 of the Curie–Weiss temperature (Li et al., 2021).

4. Material realizations and control parameters

Transition-metal oxides furnish the classic materials arena for the Mott transition, but the mechanisms differ sharply from compound to compound. In Ca$\kappa = \frac{\partial n}{\partial \mu}$8RuO$\kappa = \frac{\partial n}{\partial \mu}$9, LDA+DMFT shows that the temperature-induced transition is lattice-driven: the first-order structural change from L-Pbca to S-Pbca narrows all $U$0 bands, enhances the crystal-field splitting, and drives the system from a correlated metal to a paramagnetic Mott insulator with $U$1 eV. Orbital order follows the structural transition rather than causing it, and no orbital-selective Mott phase is found down to about $U$2 K in Ca$U$3Sr$U$4RuO$U$5 for $U$6 (Gorelov et al., 2010).

Chromium-doped V$U$7O$U$8 remains the prototypical finite-temperature Mott material. Spatially resolved spectroscopy shows that the temperature-driven paramagnetic metal in lightly doped $U$9 is microscopically phase separated into metallic domains within an insulating background, explaining its poor-metal character. Pressure suppresses this thermodynamic instability and drives a more homogeneous metallic state, underscoring that pressure and doping are inequivalent routes across the same nominal Mott boundary (Lupi et al., 2010).

Iron chalcogenides and pnictides highlight the importance of multiorbital physics and bandwidth control. In K$U$0Fe$U$1Se$U$2, LDA+DMFT finds that vacancy-ordered KFe$U$3Se$U$4 is not a simple band insulator but a Mott–Kondo insulator: most Fe $U$5 orbitals show Mott poles in $U$6 at $U$7, while the $U$8 orbital exhibits a Kondo-insulator-like gap. Electron doping drives this state into an orbital-selective non-Fermi-liquid metal in which only the $U$9 sector remains itinerant (Craco et al., 2011). In a complementary slave-rotor analysis of modulated vacancy-ordered lattices relevant to $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$0, ordered Fe vacancies reduce the electronic bandwidth and thereby lower the critical interaction for Mott localization, establishing vacancy-induced band narrowing as a direct route to the insulating parent state (Yu et al., 2011).

Cuprates realize a charge-transfer variant. In the three-band Cu–O model, variational Monte Carlo finds a transition from metal to charge-transfer insulator when the level difference $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$1 reaches $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$2 for realistic parameters. In the insulating regime, the energy gain relative to the large-$n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$3 limit obeys $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$4, and reproducing material-specific Fermi-surface curvature requires an additional next-nearest-neighbor Cu–Cu hopping $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$5 (Yanagisawa et al., 2014).

5. Multiorbital selectivity, Hund physics, and charge-transfer variants

In multiorbital systems, the Mott transition is shaped by orbital degeneracy, crystal fields, and Hund’s coupling. Slave-spin calculations for iron-pnictide models show that Hund’s coupling strongly reduces the critical interaction and qualitatively changes the character of the insulator. In a two-orbital model at two electrons per Fe, the transition is one-step and leads either to a high-spin spin-Mott insulator or to a low-spin orbital-Mott insulator depending on $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$6 and $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$7; in a four-orbital model with four electrons per Fe, the small-$n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$8 transition is orbitally selective in the sense that $n_{\mathrm{M}}^{1/3} a_{\mathrm{B}} \simeq 0.25$9 undergo Mott localization while $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$0 and $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$1 enter band-insulating or orbitally polarized sectors at the same critical coupling (Yu et al., 2010).

Finite-temperature multiorbital phase diagrams can be still more unusual. In the two-orbital Hubbard model with different bandwidths and Ising-type Hund’s coupling, DMFT+CTQMC finds a first-order transition between the orbital-selective Mott phase and the full Mott insulator whose slope is reversed relative to the conventional single-orbital case: as temperature increases, the coexistence region shifts to larger $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$2. The mechanism is entropic. The orbital-selective phase carries frozen local moments in the wide orbital and gains more finite-temperature entropy than the full Mott insulator, while increasing Hund’s coupling lowers the critical endpoint temperature and eventually turns the transition into a crossover (Kim et al., 2015).

Hybridized correlated systems impose a further constraint: integer occupancy of the correlated orbital alone is insufficient. In the generalized periodic Anderson model studied within DMFT, a genuine zero-temperature Mott transition requires integer total filling $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$3. At noninteger total filling, even an integer $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$4 leaves a correlated metal because the itinerant band supplies a delocalization channel. The insulating state can be Mott–Hubbard-like or charge-transfer-like depending on the charge-transfer energy, and the transition is interpreted as Mott localization of local singlets formed between itinerant and correlated electrons (Amaricci et al., 2016).

A recurring misconception is that long-range screening generically controls the order of the transition. In the charge-transfer regime of a cubic hydrogen lattice treated by charge self-consistent DFT+DMFT, the correlation-renormalized charge-transfer gap closes smoothly at $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$5 Å, with no appreciable hysteresis and only a negligible coexistence window. The analysis attributes the insulating state to local energy scales $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$6, $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$7, $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$8, $$n_{\mathrm{M}}^{1/2} a_{\mathrm{B}} = C_{2\mathrm{D}}$$9, and $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$0, implying that long-range screening is not essential in that prototypical case (Lang et al., 2023).

6. Nonequilibrium, mesoscopic, and generalized Mott transitions

The concept of a Mott transition extends naturally into nonequilibrium and mesoscopic settings. In two-dimensional superconducting proximity arrays, vortices trapped by a periodic pinning potential form a vortex Mott insulator at unity filling. A dc current then induces a dynamic Mott transition: the low-current differential resistance shows a dip at commensurate filling, but increasing drive reverses the dip into a peak, signaling current-driven vortex delocalization. Time-dependent Ginzburg–Landau simulations further reveal nonmonotonic $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$1 near the transition and connect the driven criticality to non-Hermitian descriptions of nonequilibrium processes (Glatz et al., 2020).

In excitonic Bose polarons, the quasiparticle itself rather than the bath constituents undergoes a Mott transition. In a GaAs/AlGaAs electron–hole bilayer, direct-exciton impurities form attractive and repulsive Bose polarons inside a two-dimensional gas of long-lived indirect excitons. With increasing bath density, the polaron absorption peaks vanish and the spectrum becomes a step-like continuum. The transition density is $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$2, with measured two-dimensional Mott parameters $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$3 and $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$4 (Szwed et al., 9 Apr 2025).

Granular aluminum realizes a mesoscopic Mott-like transition in which intergrain tunneling plays the role of bandwidth and the grain charging energy plays the role of interaction. As the grains are progressively decoupled, the effective Fermi energy inferred from spin-flip magnetoresistance scales as $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$5 and falls to the charging energy $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$6 meV at $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$7, exactly where transport identifies the metal-insulator transition. The approach to this point is accompanied by $n_{\mathrm{M}}^{1/2} a_{\mathrm{B,DX}} \sim 0.4$8 and heavy-fermion-like magnetoresistance, emphasizing that a Mott criterion can be realized in a granular array rather than an atomic lattice (Bachar et al., 2014).

These generalized cases are directly relevant to device physics. Reviews of vanadium oxides, ruthenates, nickelates, and layered chalcogenides emphasize that voltage- and light-induced Mott switching is inherently different from thermodynamic tuning: Landau–Zener-like breakdown, Joule heating, filament nucleation, percolation, and ultrafast nonthermal pathways coexist, while phase coexistence and spatial nanotexture become functional degrees of freedom for memories, transistors, and neuromorphic elements (Milloch et al., 2024). Such work does not dissolve the meaning of the Mott transition; it shows instead that Mottness is a broader organizing principle for correlation-driven localization and delocalization across equilibrium, driven, and composite-particle systems.