Orbital-Selective Mott Phase (OSMP)

• Orbital-Selective Mott Phase is a state where specific orbitals lose coherent charge dynamics (Z=0) while others stay itinerant, creating a mixed localized-itinerant regime.
• The phase emerges from key factors such as bandwidth asymmetry, crystal-field splitting, and Hund coupling that differentiate orbital behavior under strong correlations.
• OSMP underpins unconventional magnetism, non-Fermi-liquid transport, and emergent topological features, guiding research in iron-based superconductors, chalcogenides, and moiré systems.

The orbital-selective Mott phase (OSMP) is a correlation-driven state of a multiorbital system in which some orbitals become Mott localized while others remain itinerant. In the language repeatedly used across multiorbital Hubbard, slave-spin, DMFT, DMRG, and first-principles studies, the localized orbitals have vanishing coherent spectral weight, $Z_\alpha=0$, while the itinerant orbitals retain $Z_\beta>0$; equivalently, one subset of orbitals is pinned near an integer occupancy and develops a Mott gap, whereas the remaining subset stays metallic or bad-metallic (Yu et al., 2012). This places OSMP between a conventional metal, where all relevant orbitals remain itinerant, and a full Mott insulator, where all orbitals localize. The phase has become a central organizing concept for iron-based superconductors and chalcogenides, ruthenates, ladder compounds, moiré systems, and other correlated materials because it combines localized moments and mobile carriers within the same microscopic Hilbert space, allowing unconventional magnetism, non-Fermi-liquid transport, Kondo-like physics, and, in metallic settings, even topological structures encoded in Green’s-function zeros (Yu et al., 2017).

1. Definition and distinguishing characteristics

The defining content of an OSMP is orbital differentiation in the Mott transition itself. One or more orbitals become effectively Mott insulating, with nearly frozen integer occupancy and local moments, while the remaining orbitals stay itinerant and metallic. This criterion appears in several equivalent forms in the literature. In slave-spin formulations, the hallmark is orbital-resolved quasiparticle weight,

$Z_\alpha=0,\qquad Z_\beta>0,$

as in the five-orbital description of alkaline iron selenides, where the $3d\,xy$ orbital becomes Mott localized while the remaining Fe $3d$ orbitals remain itinerant (Yu et al., 2012). In one-dimensional multiorbital Hubbard studies, the same phase is diagnosed by orbital occupancies: for example, in the three-orbital chain at filling $n=4/3$, orbital $\gamma=2$ locks to

$n_2=1,$

while the other two orbitals remain near

$n_0\sim n_1\sim 1.5,$

showing that one orbital is localized and the others carry the mobile charge (Rincon et al., 2014). In cluster and DMFT-based Green’s-function analyses, the localized orbital is additionally characterized by a gap or strongly suppressed low-energy spectral function and a singular or pole-like self-energy, while the itinerant orbitals retain finite low-energy spectral weight (Li et al., 2016).

This selective localization sharply distinguishes OSMP from neighboring phases. It is not a full Mott insulator, because the system can remain metallic overall through the itinerant orbitals. It is not an ordinary correlated metal, because the localized orbital has already lost coherent charge dynamics. It is also not merely a coexistence regime in a trivial sense. DMRG work on one-dimensional three-orbital models emphasized that OSMP should not be viewed only as “one orbital localized, the others itinerant,” but as a correlated mixed localized-itinerant state with its own internal magnetic and dynamical structure (Rincon et al., 2014).

The same logic extends beyond literal orbital labels. In the spontaneous layer selective Mott phase of a bilayer Hubbard model, one layer is pinned near half-filling while the other remains itinerant; the paper explicitly frames this as a layer analog of OSMP, with the layer index playing the role of an orbital label (Pangburn et al., 2024). In cluster interpretations of the two-dimensional Hubbard model, momentum-selective Mottness is described as the counterpart of OSMP under a cluster-to-orbital mapping, so the concept can organize both orbital and momentum differentiation (Acharya et al., 2018).

2. Microscopic mechanisms and theoretical formulations

Several ingredients recur across the OSMP literature. The first is bandwidth asymmetry. Narrower orbitals have a larger effective $U/W$ and therefore localize first. This mechanism is explicit in the iron-selenide five-orbital slave-spin study, where the $Z_\beta>0$0 orbital is selected because its noninteracting DOS is narrower than that of $Z_\beta>0$1, with

$Z_\beta>0$2

and because it sits highest in the crystal-field scheme, making it easier to approach half-filling (Yu et al., 2012). The same structure appears in one-dimensional three-orbital models, where $Z_\beta>0$3 is much smaller than $Z_\beta>0$4, so orbital $Z_\beta>0$5 becomes the localized Mott orbital (Rincon et al., 2014).

The second ingredient is crystal-field splitting and orbital occupancy redistribution. In alkaline iron selenides, crystal-field effects place $Z_\beta>0$6 at the top of the local level scheme, favoring selective localization when interactions increase (Yu et al., 2012). In doped two-band DMFT with crystal-field splitting, the orbital energy offset $Z_\beta>0$7 acts as an orbital-dependent chemical potential and can tune either the narrow band or, at sufficiently strong interaction, even the wide band to the commensurate occupancy $Z_\beta>0$8. The resulting phase diagram contains both a conventional narrow-band OSMP and, for suitable negative crystal field, a wide-band OSMP (Jakobi et al., 2013). In FePS$Z_\beta>0$9, pressure-enhanced crystal-field splitting ultimately destroys the OSMP by driving a low-spin, more conventional Fermi-liquid metal at higher pressure, after an intermediate orbital-selective regime (Kim et al., 2021).

The third ingredient is Hund coupling. Across iron-based models, Hund’s coupling suppresses interorbital charge fluctuations, stabilizes high-spin local configurations, and dynamically decouples orbitals. In alkaline iron selenides, the threshold for the OSMP as an intermediate phase is approximately

$Z_\alpha=0,\qquad Z_\beta>0,$0

and in the strongly correlated metallic regime the effective moment reaches

$Z_\alpha=0,\qquad Z_\beta>0,$1

(Yu et al., 2012). In the one-dimensional three-orbital Hubbard model, the phase diagram is especially broad around

$Z_\alpha=0,\qquad Z_\beta>0,$2

where orbital $Z_\alpha=0,\qquad Z_\beta>0,$3 is pinned to $Z_\alpha=0,\qquad Z_\beta>0,$4 and the remaining orbitals stay itinerant (Rincon et al., 2014). In FePS$Z_\alpha=0,\qquad Z_\beta>0,$5, the intermediate-pressure OSMP is described as a bad metal with large fluctuating moments due to Hund’s coupling, with $Z_\alpha=0,\qquad Z_\beta>0,$6 states metallizing while $Z_\alpha=0,\qquad Z_\beta>0,$7 states remain gapped (Kim et al., 2021).

A major theoretical issue concerns hybridization between orbitals. In realistic iron-pnictide and iron-chalcogenide models, the orbitals are kinetically hybridized in the orbital basis, so one must explain how selective localization survives at all. A $Z_\alpha=0,\qquad Z_\beta>0,$8 slave-spin plus Landau analysis showed that, in the presence of orbital-level splittings, the coupling between orbital quasiparticle amplitudes is biquadratic rather than bilinear: $Z_\alpha=0,\qquad Z_\beta>0,$9 which permits a saddle point with one $3d\,xy$0 and the other finite (Yu et al., 2017). Microscopically, intersite spin correlations renormalize the effective interorbital hybridization to zero as one orbital approaches localization. By contrast, a single-site DMFT analysis with finite nonlocal interorbital hopping argued that, under fairly general circumstances, a zero-temperature OSMP is unstable against any finite interorbital hopping because it generates a finite local impurity hybridization,

$3d\,xy$1

which Kondo-screens the would-be localized orbital at sufficiently low energy (Kugler et al., 2021). This implies that with finite interorbital hopping the OSMP may survive to extremely low temperatures but becomes a coherence-incoherence crossover rather than a strict $3d\,xy$2 phase within paramagnetic single-site DMFT. A complementary DMFT study of explicit interorbital hopping showed that the sign of the hopping matters: negative $3d\,xy$3 enhances the usual OSMP by increasing the effective bandwidth ratio, while large enough positive $3d\,xy$4 can invert the effective wide and narrow orbitals and generate a different OSMP in which the formerly wide effective orbital localizes first (Ni et al., 2021). Taken together, these results show that hybridization does not admit a single universal conclusion; its effect depends strongly on the theoretical framework and on whether one emphasizes slave-spin self-consistency, local DMFT bath generation, or effective-band reorganization.

3. Magnetic order, nonlocal correlations, and non-Fermi-liquid behavior

Once OSMP forms, the localized orbital carries robust local moments and the itinerant orbitals remain mobile, producing a low-energy problem closely related to ferromagnetic Kondo-lattice or double-exchange models. In one-dimensional DMRG studies, this leads to unexpected magnetic textures. The localized orbital can order ferromagnetically, but it can also form “Block” states: ferromagnetic spin clusters coupled antiferromagnetically. In the canonical three-orbital chain at $3d\,xy$5, the dominant OSMP Block pattern is

$3d\,xy$6

with a peak in the localized-orbital spin structure factor at

$3d\,xy$7

(Rincon et al., 2014). The same model supports larger block or incommensurate patterns at other fillings, such as $3d\,xy$8 for $3d\,xy$9 and even longer-period structures at lower filling (Liu et al., 2016). These results established that OSMP is not magnetically featureless but can host nontrivial cluster magnetism.

The dynamical spin response of the block-OSMP is likewise distinctive. Dynamical DMRG found two dominant features in the spin structure factor: a low-energy dispersive acoustic branch extending up to

$3d$0

and a high-energy nearly dispersionless optical branch centered near

$3d$1

(1804.01959). The acoustic mode is interpreted as spin-wave-like dynamics of ferromagnetic block units and is well approximated by a frustrated $3d$2-$3d$3 spin model with effective exchange scale

$3d$4

The optical mode, by contrast, is not captured by a spin-only description; it is a local on-site interorbital spin excitation controlled by Hund coupling, with energy scaling linearly with $3d$5 (1804.01959). RIXS-based DMRG analysis of BaFe$3d$6Se$3d$7 extended this picture to charge and orbital excitations. In the block OSMP, the $3d$8 orbital is Mott localized with a single-particle gap

$3d$9

while $n=4/3$0 and $n=4/3$1 remain itinerant. The RIXS two-peak structure at $n=4/3$2 is then interpreted as inter-orbital excitations between the itinerant and Mott sectors, and among the phases compared in the same model only the block OSMP simultaneously reproduces both the orbital spectroscopy and the block magnetic order (Patel et al., 2018).

OSMP also reshapes itinerant-electron self-energies and can generate strong nonlocality. Determinant QMC and DMRG on a three-orbital chain found that in the OSMP the self-energy of the itinerant electrons is momentum dependent, varying by nearly $n=4/3$3 across the Brillouin zone for orbitals 1 and 2 at $n=4/3$4 and $n=4/3$5, whereas the localized orbital 3 varies only by about $n=4/3$6–$n=4/3$7 (Li et al., 2016). The same nonlocal correlations shift the relative positions of hole-like and electron-like bands, showing that the itinerant part of OSMP is not simply a local DMFT metal dressed by static moments.

At the level of zero-temperature quantum impurity physics, the metallic sector inside OSMP may cease to be a conventional Fermi liquid. In a two-orbital Hubbard model without interorbital hopping, DMFT+NRG showed that the narrow orbital can be Mott insulating while the wide orbital remains metallic, but for any nonzero Hund coupling $n=4/3$8 the localized and itinerant orbital spins bind into an effective spin-1 object. The resulting low-energy problem is an underscreened spin-1 Kondo model, producing divergent spin susceptibilities and a singular Fermi liquid with

$n=4/3$9

$\gamma=2$0

(Greger et al., 2013). A different DMFT study tied strange metallicity itself to an OSMP in a two-band Hubbard model, arguing that once one orbital is selectively Mott localized, the remaining metallic orbital develops branch-cut Green’s functions, fractional power laws, and $\gamma=2$1-scaled spin and charge responses. In that framework, the orbital-selective Mott regime appears beyond

$\gamma=2$2

and is presented as the parent state of strange metallicity rather than merely a coexistence phase (Acharya et al., 2018). These results do not collapse into a single universal low-energy fixed point, but they agree that the itinerant sector of OSMP is generically strongly dressed by the localized one.

4. Topological Green’s-function structures in metallic OSMP

A recent conceptual extension of OSMP concerns topology in a metallic strongly correlated setting. In a four-orbital cubic-lattice model with heavy and light orbitals, the heavy orbitals become Mott localized while the light orbitals remain itinerant. The onsite Hubbard interaction acts only on the heavy orbitals, and the transition is diagnosed by the heavy-orbital quasiparticle weight,

$\gamma=2$3

while the light orbitals retain $\gamma=2$4 (Chen et al., 2024). A central physical feature is correlation-driven dehybridization: the effective heavy-light hybridization is renormalized to

$\gamma=2$5

so it vanishes in the OSMP. The heavy sector is then Mott gapped but the system as a whole remains metallic because the light sector stays itinerant.

The paper showed that in this situation the heavy-electron Green’s function develops momentum-dependent zeros inside the Mott gap. A Green’s-function zero is identified by

$\gamma=2$6

the counterpart of a quasiparticle pole. Because the method goes beyond a purely local treatment through a cluster $\gamma=2$7 slave-spin approach, the heavy-sector incoherent Green’s function remains momentum dependent even when the coherent piece vanishes. Along the high-symmetry line $\gamma=2$8, corresponding to $\gamma=2$9, two branches of zeros merge at

$n_2=1,$0

and $n_2=1,$1, precisely where the noninteracting heavy orbital had Dirac nodes protected by time-reversal, inversion, and $n_2=1,$2 symmetry (Chen et al., 2024).

To characterize this crossing, the paper constructs a Hermitian Green’s-function combination,

$n_2=1,$3

solves

$n_2=1,$4

and defines a Green’s-function Berry curvature

$n_2=1,$5

over the $n_2=1,$6 sectors. The corresponding spin Chern number on a fixed-$n_2=1,$7 slice,

$n_2=1,$8

jumps discontinuously when the slice passes through the zero crossing. At $n_2=1,$9, the paper finds a jump by $n_0\sim n_1\sim 1.5,$0 between $n_0\sim n_1\sim 1.5,$1 and $n_0\sim n_1\sim 1.5,$2, and locally a jump of $n_0\sim n_1\sim 1.5,$3 across each crossing because there are two nodes in each $n_0\sim n_1\sim 1.5,$4 plane (Chen et al., 2024). This quantized Berry flux identifies the crossing as a “Dirac zero,” extending topological Green’s-function-zero concepts from Mott insulators to orbital-selective correlated metals. The broader implication is that topology in strongly correlated matter need not be tied only to coherent quasiparticle bands or globally insulating phases; in an OSMP, it can reside in the zero manifold of the Green’s function.

5. Materials platforms and experimental realizations

Iron-based systems remain the canonical materials arena for OSMP. In alkaline iron selenides $n_0\sim n_1\sim 1.5,$5, slave-spin calculations found that for sufficiently strong Hund coupling the metal-to-Mott-insulator transition proceeds through an intermediate OSMP in which the $n_0\sim n_1\sim 1.5,$6 orbital is Mott localized while the others remain itinerant, both with and without ordered Fe vacancies (Yu et al., 2012). Ordered vacancies reduce the critical interactions $n_0\sim n_1\sim 1.5,$7 and $n_0\sim n_1\sim 1.5,$8, and the OSMP survives at finite doping, motivating a unified phase diagram in which it links the vacancy-ordered Mott insulator to the metallic or superconducting compounds. In FePS$n_0\sim n_1\sim 1.5,$9, first-principles eDMFT found a pressure-induced OSMP only under non-hydrostatic loading, with $U/W$0 states becoming metallic while $U/W$1 states remain gapped. Representative pressures are $U/W$2 GPa for the Mott insulator, $U/W$3 GPa for the OSMP, and $U/W$4 GPa for the high-pressure Fermi liquid, with the phase sequence

$U/W$5

under increasing pressure (Kim et al., 2021).

Ladder and chain iron chalcogenides provide especially clear low-dimensional manifestations. BaFe$U/W$6Se$U/W$7 is interpreted as a block-ordered OSMP in DMRG studies, with one orbital Mott localized and two itinerant, yielding both the block magnetic order seen by neutron scattering and the two-peak RIXS structure (Patel et al., 2018). In Ca$U/W$8Sr$U/W$9RuO$Z_\beta>0$00, ARPES identified a spectral-weight transfer in the $Z_\beta>0$01 band, assigned to $Z_\beta>0$02, consistent with an OSMP in which the $Z_\beta>0$03 band becomes Mott localized while $Z_\beta>0$04 remains itinerant but shows additional Kondo-hybridization-like renormalization (Kim et al., 2021). The ARPES analysis emphasized a soft-gap scale of about $Z_\beta>0$05 eV and a collapse of the localized state under very slight electron doping by potassium deposition, supporting a Mott-like interpretation.

Moiré systems extend OSMP into a highly tunable regime. In electron-doped twisted TMDs, two nearly degenerate conduction-band species with different effective masses and binding energies form overlapping minibands. Slave-rotor mean-field theory found that one miniband can be pinned to

$Z_\beta>0$06

while the other remains itinerant over a broad range of fillings and twist angles, realizing the basic ingredients of a Kondo lattice model with localized moments coexisting with a metallic band (Dalal et al., 2021). In WS$Z_\beta>0$07/WSe$Z_\beta>0$08, the relevant filling is

$Z_\beta>0$09

and the OSM regime appears around $Z_\beta>0$10; in MoS$Z_\beta>0$11/MoSe$Z_\beta>0$12, where the two lowest minibands overlap directly, the corresponding range is

$Z_\beta>0$13

with orbital-selective behavior around $Z_\beta>0$14 (Dalal et al., 2021). These moiré realizations highlight that OSMP is fundamentally about component differentiation under strong correlations, not specifically about atomic $Z_\beta>0$15 orbitals.

Several studies also point to measurable consequences beyond spectroscopy. Green’s-function zeros in OSMP may influence the Luttinger volume, Hall effect, and even quantum oscillations (Chen et al., 2024). In the spontaneous layer-selective Mott phase of a bilayer Hubbard model, the Fermi surface volume jumps at the transition between the selective and layer-uniform phases, from a small Fermi surface with one layer near half-filling to a larger one where both layers contribute (Pangburn et al., 2024). Although the formalism there violates Luttinger’s theorem, the result reinforces a recurrent theme: selective localization reorganizes the low-energy Fermi volume in a physically detectable way.

6. Conceptual tensions and current directions

The OSMP literature contains several unresolved tensions, many of which arise because different methods emphasize different aspects of the same mixed localized-itinerant problem. One major question is whether a true $Z_\beta>0$16 OSMP survives generic interorbital hopping. Slave-spin and Landau analyses support robustness even in hybridized orbital bases, with effective hybridization renormalized to zero as one orbital approaches localization (Yu et al., 2017). Paramagnetic single-site DMFT, by contrast, argues that any finite interorbital hopping induces a local bath hybridization and therefore destabilizes the zero-temperature localized orbital, leaving only a very low-coherence metal with exponentially small coherence scale

$Z_\beta>0$17

(Kugler et al., 2021). A plausible implication is that the stability of OSMP depends sensitively on whether one allows nonlocal self-energies, spontaneous symmetry breaking, or strong enough correlation-driven dehybridization to suppress the bath that DMFT would otherwise generate.

A second issue concerns the internal structure of low-energy excitations. In a half-filled two-orbital DMFT study, the low-energy narrow-band in-gap peaks traditionally interpreted as holon-doublon bound states were reinterpreted as inter-band Kondo-like bound states, involving a doublon in the narrow band bound to a Kondo-like superposition state in the wide band (Wang et al., 2024). The same work found anomalous peaks in the metallic wide band at

$Z_\beta>0$18

when the two bandwidths become closer, suggesting that even in OSMP the “localized” and “metallic” orbitals remain dynamically intertwined at low energy (Wang et al., 2024). ARPES on Ca$Z_\beta>0$19Sr$Z_\beta>0$20RuO$Z_\beta>0$21 likewise pointed to a combined OSMP plus possible Kondo-hybridization scenario in a $Z_\beta>0$22 material (Kim et al., 2021). These studies suggest that OSMP can serve not only as a coexistence phase but as a parent state for Kondo-lattice-like or heavy-fermion-like behavior.

A third current direction concerns nontrivial metallic topology and strongly correlated quantum geometry. The discovery of symmetry-protected, Berry-flux-carrying Green’s-function zero crossings in OSMP demonstrates that the phase can host topological structures hidden from ordinary band spectroscopy (Chen et al., 2024). This suggests that future work on heavy-fermion metals, iron-based superconductors, moiré systems, and geometry-induced flat-band compounds should not restrict topological diagnostics to poles of the Green’s function or to insulating states alone.

Taken as a whole, the modern view of OSMP is considerably broader than the original picture of a narrow orbital localizing before a wide one. It now encompasses magnetic cluster order, Hund-governed optical spin modes, nonlocal itinerant self-energies, strange metallicity, Kondo-lattice mappings, topological Green’s-function zeros, and spontaneous component differentiation in degenerate systems. The recurring core remains unchanged: OSMP is the state in which one component of a correlated multiorbital system is pinned into Mottness while another remains itinerant. The broader body of work suggests that this selective Mottness is not a peripheral instability but a versatile organizing principle for mixed localized-itinerant quantum matter.