2Eg Band Nesting in 2D Semiconductors

• 2Eg band nesting is a kinematic regime in which nearly parallel conduction and valence band dispersions produce a nearly constant interband transition energy over extended k-space regions.
• The phenomenon is exemplified in monolayer MoS₂ and related TMDs where the nesting leads to pronounced optical C exciton resonances and amplifies the joint density of states.
• Strain, anisotropy, and layer coupling can tune the nesting conditions, thereby affecting exciton binding energies, optical conductivity, and quantum capacitance.

$2E_g$ band nesting denotes an interband kinematic regime in which the conduction- and valence-band dispersions remain nearly parallel over an extended region of the Brillouin zone, so that the transition energy $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$ is nearly constant. In monolayer MoS$_2$, the phrase is used for a high-energy saddle in $\Delta E(\mathbf{k})$ along K–Q–$\Gamma$, occurring at an energy around twice the fundamental gap and giving rise to a pronounced optical resonance identified with the C exciton (Bieniek et al., 2020). Closely related formulations appear across semiconducting transition-metal dichalcogenides, MoSe$_2$, strained PdS$_2$, Y-shaped Kekulé graphene, and anisotropic ditellurides, where nesting amplifies the joint density of states, optical conductivity, absorption, excitonic structure, quantum capacitance, or nonlinear optical response (Carvalho et al., 2013, Kumar et al., 27 Feb 2025, Wang et al., 4 Nov 2025, Mohammadi, 2022, Wang et al., 2020).

1. Definition and scope

Band nesting in semiconductors is defined by the near-flatness of the interband separation over a finite k-space region: $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$ Equivalent statements in the cited literature are that $E_c(\mathbf{k})$ and $E_v(\mathbf{k})$ run nearly parallel, or that the gradients of the two bands nearly coincide over an extended area of the Brillouin zone (Kumar et al., 27 Feb 2025, Carvalho et al., 2013, Wang et al., 4 Nov 2025). Physically, many k-points then contribute vertical optical transitions at nearly the same photon energy.

The qualifier $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$0 is material- and context-specific rather than universal. In monolayer MoS$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$1, the nesting saddle lies at an energy around twice the fundamental gap and is directly responsible for the pronounced C-peak in optical spectra (Bieniek et al., 2020). In Y-shaped Kekulé-patterned graphene, the same geometric principle appears as a “band nesting resonance” between two conduction branches $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$2 and $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$3, producing a sharp optical feature once the chemical potential places the transition in the Pauli-allowed window (Mohammadi, 2022).

A common source of confusion is the use of “nesting” in metals. There, nesting usually refers to superposition of Fermi-surface segments by a wavevector $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$4, with consequent enhancement of the Lindhard susceptibility and density-wave tendencies. That usage is formally related but distinct from $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$5 interband nesting, because the latter is governed by the geometry of $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$6 for vertical optical transitions rather than by parallel Fermi-surface sheets at the Fermi level (Gao et al., 5 Aug 2025, O'Leary et al., 2024).

2. Kinematic formulation and singular response

The central object in $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$7 band nesting is the joint density of states (JDOS),

$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$8

or, equivalently,

$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$9

Upon converting the Brillouin-zone integral to an integral over a constant-$_2$0 contour, the JDOS acquires the factor $_2$1. Consequently, whenever $_2$2, the JDOS shows a large peak and in two dimensions can exhibit a logarithmic divergence for a true saddle point (Carvalho et al., 2013, Wang et al., 4 Nov 2025).

This enhancement feeds directly into optical response. In the dipole approximation, the optical conductivity or absorption coefficient contains the same $_2$3 constraint, weighted by interband matrix elements. The semiconducting-TMD literature therefore treats the large absorption peaks of atomically thin layers as JDOS-driven consequences of band nesting, often reinforced by van Hove singularities in the individual bands (Carvalho et al., 2013). In MoSe$_2$4, the same framework is expressed in terms of the absorption coefficient

$_2$5

with the “C” excitonic peak dominated by nested transitions (Kumar et al., 27 Feb 2025).

The singularity need not be identical in every realization. For a true saddle in two dimensions, the JDOS diverges logarithmically. For an extended nesting region where the gradients match while the second derivatives differ only weakly, the literature also notes a weaker square-root-like divergence,

$_2$6

which still produces a pronounced optical resonance (Kumar et al., 27 Feb 2025).

3. Canonical realizations in two-dimensional semiconductors

Monolayer MoS$_2$7 provides the clearest $_2$8 example in the supplied literature. An ab initio–based six-orbital tight-binding model places the relevant nesting region along K–Q–$_2$9, where the Mo $\Delta E(\mathbf{k})$0-orbital content of the conduction and valence bands evolves in a way that makes the bands nearly parallel. The resulting saddle in $\Delta E(\mathbf{k})$1 lies at an energy around twice the fundamental gap and is directly responsible for the C exciton; in the minimal 6-band tight-binding model, the associated nested-band resonance is described as occurring at $\Delta E(\mathbf{k})$2 eV in MoS$\Delta E(\mathbf{k})$3 (Bieniek et al., 2020, Bieniek et al., 2017).

The same band geometry strongly affects the exciton problem. A full Bethe–Salpeter treatment including K and Q valleys shows that nesting around Q increases the average reduced mass and raises the 1s exciton binding to $\Delta E(\mathbf{k})$4 meV, bends the excited $\Delta E(\mathbf{k})$5-series away from the textbook $\Delta E(\mathbf{k})$6 behavior toward a more $\Delta E(\mathbf{k})$7-like pattern, generates a Berry-curvature-induced $\Delta E(\mathbf{k})$8 splitting of $\Delta E(\mathbf{k})$9 meV, and places the A-exciton ground state in the spin-forbidden manifold, $\Gamma$0–$\Gamma$1 meV below the bright line (Bieniek et al., 2020).

MoSe$\Gamma$2 exhibits the same mechanism in a layer-dependent setting. First-principles DFT and $\Gamma$3BSE calculations identify nested transitions along the $\Gamma$4–Q and M–$\Gamma$5 directions, with the monolayer C-excitonic peak at $\Gamma$6 eV and the strongest oscillator strength. The density of states rises sharply near $\Gamma$7 eV, and the calculated quantum capacitance at $\Gamma$8 eV is $\Gamma$9 nF/cm$_2$0 for the monolayer, $_2$1F/cm$_2$2 for the bilayer, and $_2$3F/cm$_2$4 for the trilayer (Kumar et al., 27 Feb 2025).

A broader first-principles survey of semiconducting TMDs established that large optical response is a class property rather than a MoS$_2$5-specific anomaly. Using fully relativistic GGA-DFT, the optical conductivity peaks were tied to the total area satisfying $_2$6 eV/$_2$7, with representative values including WS$_2$8 at $_2$9 eV and $_2$0, TiS$_2$1 at $_2$2 eV and $_2$3, and ZrS$_2$4 with peaks at $_2$5 and $_2$6 eV and total $_2$7 (Carvalho et al., 2013).

System	Nested energy/condition	Principal consequence
MoS$_2$8	around $_2$9; C exciton at $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$0 eV	strong high-energy optical resonance
MoSe$$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$1 monolayer	C exciton at $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$2 eV	enhanced absorption and quantum capacitance
PdS$$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$3 monolayer	JDOS peak at $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$4 eV, shifting to $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$5 eV at 4% strain	continuous redshift of main absorption peak
Y-shaped Kekulé graphene	$$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$6 set by $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$7 hot-spot ring	sharp band-nesting resonance in $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$8

These systems show that $$\nabla_{\mathbf{k}}\bigl[E_c(\mathbf{k})-E_v(\mathbf{k})\bigr]\simeq 0.$$9 band nesting is not merely a band-structure curiosity. It controls the location, amplitude, and layer or strain dependence of high-energy optical resonances across several 2D semiconductors.

4. Model Hamiltonians and analytically tractable cases

In Y-shaped Kekulé-patterned graphene, the low-energy four-band Hamiltonian around the folded $E_c(\mathbf{k})$0 point yields two massless bands,

$E_c(\mathbf{k})$1

and two gapped bands,

$E_c(\mathbf{k})$2

The dominant nesting occurs between $E_c(\mathbf{k})$3 and $E_c(\mathbf{k})$4, and the hot-spot radius $E_c(\mathbf{k})$5 follows from the equality of the band gradients: $E_c(\mathbf{k})$6 At this ring, the resonant energy is

$E_c(\mathbf{k})$7

The real part of the optical conductivity is then enhanced through the contour-integral form of the Kubo formula, where the integrand contains the same $E_c(\mathbf{k})$8 factor that governs the JDOS (Mohammadi, 2022).

This graphene realization makes two points explicit. First, band nesting can be formulated as a purely geometric resonance condition even in a system not usually discussed in terms of a conventional semiconductor C exciton. Second, the resonance is tunable by the chemical potential, the on-site shift $E_c(\mathbf{k})$9, and the hopping deviation $E_v(\mathbf{k})$0; the supplied analysis states that the extra peak remains resolvable up to and beyond $E_v(\mathbf{k})$1 K so long as $E_v(\mathbf{k})$2 (Mohammadi, 2022).

A more general nonlinear-optical extension appears in electrically biased bilayer SnS. There the relevant object is not a pair but a triplet of nested bands satisfying

$E_v(\mathbf{k})$3

over an extended k-space region. At the double-resonance bias $E_v(\mathbf{k})$4 V, the three bands near the Y point become nearly equidistant with $E_v(\mathbf{k})$5 eV, and the maximum sheet susceptibility reaches $E_v(\mathbf{k})$6 pm$E_v(\mathbf{k})$7/V, or $E_v(\mathbf{k})$8 pm/V in bulk-equivalent units (Biswas et al., 2021). This is not a $E_v(\mathbf{k})$9 case in the narrow two-band sense, but it is a direct generalization of the same nesting geometry.

5. Strain, anisotropy, and device-level manifestations

Strain can preserve nesting while shifting its energy scale. In monolayer PdS$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$00, the highest valence and lowest conduction bands remain nearly parallel over wide Brillouin-zone paths. The unstrained system shows a JDOS peak at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$01 eV and a main absorption peak at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$02 eV. Under 4% biaxial tensile strain, the $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$03 plateau moves down by $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$04 eV, the JDOS peak shifts to $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$05 eV, and the main absorption peak shifts continuously to $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$06 eV, while the nesting condition remains valid to within $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$07 eV over the same region (Wang et al., 4 Nov 2025).

Anisotropy can turn the same mechanism into a dielectric-topology effect. In monolayer $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$08-WTe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$09, first-principles calculations show that the lowest conduction and highest valence bands run almost perfectly parallel along $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$10–Y, with $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$11 eV over a finite segment. Because the dipole matrix element is large along one in-plane axis and symmetry-suppressed along the other, the nesting-enhanced JDOS produces a sharp peak in $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$12 near $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$13 eV, while $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$14 remains small. The resulting Kramers–Kronig response yields $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$15 in the hyperbolic window $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$16–$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$17 eV (Wang et al., 2020).

The same paper shows that MoTe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$18, which is elliptic in the pristine state, can be driven into an elliptic-to-hyperbolic transition by $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$19 biaxial tensile strain. Under strain, the valence band flattens by $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$20 eV over the nested window while the conduction band shifts by $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$21 eV, producing a narrow resonance in $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$22 at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$23 eV and a hyperbolic window at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$24–$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$25 eV (Wang et al., 2020).

MoSe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$26 demonstrates a more electrochemical manifestation. In a three-electrode setup in $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$27 M H$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$28SO$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$29, multilayer APCVD-grown MoSe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$30 shows dark areal capacitance $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$31 and light areal capacitance $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$32 at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$33. The accompanying interpretation is that illumination accesses density-of-states regions enriched by van Hove singularities and nested transitions, thereby increasing the quantum-capacitance component of the interfacial response (Kumar et al., 27 Feb 2025).

6. Relation to Fermi-surface and $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$34-orbital nesting

Interband $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$35 nesting should be distinguished from metallic nesting instabilities even though both enhance response functions. In Fe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$36GeTe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$37, high-resolution ARPES identifies a $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$38 charge order with band folding confined to the $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$39 meV window below $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$40 where flat bands reside. The nesting vector is $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$41, and model Lindhard calculations show that flat bands at both $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$42 and K make the peak at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$43–K overwhelmingly dominant (Gao et al., 5 Aug 2025). This is an electronically driven low-energy reconstruction, not a vertical-transition resonance near $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$44.

A separate line of work concerns nesting involving $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$45-derived metallic bands. In Ba$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$46CuO$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$47, the low-energy manifold comprises the $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$48 and $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$49 orbitals, and for $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$50 the Fermi surface contains both quasi-1D sheets and a 2D barrel. The 1D sheets support perfect nesting at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$51, while the 2D barrel shows imperfect nesting near $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$52 (Jin et al., 2021). In LaSb$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$53, two La-$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$54 $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$55-derived bands near $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$56 produce a saddle point at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$57 eV at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$58, and the calculated bare susceptibility peaks at $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$59 and $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$60 (O'Leary et al., 2024).

The formal resemblance is the role of singular phase-space enhancement. In metallic nesting, the relevant susceptibility is

$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$61

and the ordering vector is finite $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$62. In $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$63 band nesting, the dominant object is the JDOS for $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$64 interband transitions, and the optical anomaly appears at a photon energy rather than as a density-wave wavevector (Gao et al., 5 Aug 2025, Carvalho et al., 2013). A plausible implication is that the two notions are best regarded as parallel manifestations of band-geometry enhancement rather than as interchangeable terms.

7. Scientific significance and unresolved issues

The literature converges on a geometric interpretation: nesting is controlled by the shape of the relevant dispersions, while many-body physics determines how the singular phase space is dressed into observable optical peaks, excitons, capacitances, or ordered states. In TMDs, DFT-based single-particle pictures already predict strong optical peaks and their relative material dependence, but $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$65, BSE, screening, and excitonic effects shift energies and redistribute oscillator strength (Carvalho et al., 2013, Kumar et al., 27 Feb 2025). In MoS$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$66, the full BSE treatment shows that the excitonic consequences of $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$67 nesting are qualitatively richer than any simple parabolic or massive-Dirac model (Bieniek et al., 2020).

Several open technical issues remain explicit in the supplied sources. One is robustness under perturbations: PdS$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$68 shows that biaxial strain can preserve the nesting geometry while translating it in energy, whereas MoTe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$69 demonstrates that strain can create a qualitatively new optical regime by improving nesting quality (Wang et al., 4 Nov 2025, Wang et al., 2020). Another is the role of dimensionality and layer coupling: in MoSe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$70, interlayer hybridization broadens and weakens the nesting peak, with Davydov splitting of A/B excitons by $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$71 meV in the bilayer and $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$72 meV in the trilayer (Kumar et al., 27 Feb 2025). A further issue is terminology itself: “band nesting” in optical semiconductors, “flat-band nesting” in Fe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$73GeTe$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$74, and “$$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$75-band nesting” in oxide or intermetallic metals all invoke related geometry but refer to different observables and different response functions (Gao et al., 5 Aug 2025, Jin et al., 2021, O'Leary et al., 2024).

Taken together, these results establish $$\Delta E(\mathbf{k})=E_c(\mathbf{k})-E_v(\mathbf{k})$$76 band nesting as a specific high-energy interband phenomenon of major importance in two-dimensional materials. It is the mechanism behind the C-exciton scale in several TMDs, a driver of unusual exciton spectra, a route to strain-tunable and anisotropic optical response, and a useful organizing principle for distinguishing optical JDOS resonances from Fermi-surface-driven ordering phenomena (Bieniek et al., 2020, Carvalho et al., 2013).