Kinetic-Energy-Driven Superconductivity

• Kinetic-energy-driven superconductivity is defined by a reversal in energy contributions, where the superconducting state is stabilized by a reduction in kinetic energy rather than the conventional potential energy decrease.
• It is examined through various models such as Hubbard, t–J, and correlated hopping, which reveal that pairing mechanisms and pseudogap boundaries are closely linked to changes in electronic mobility.
• Practical insights include optical spectral weight shifts and kinematic spin fluctuations, guiding experimental exploration of unconventional superconductivity in strongly correlated materials.

Searching arXiv for recent and foundational papers on kinetic-energy-driven superconductivity to ground the article. Kinetic-energy-driven superconductivity denotes a class of superconducting mechanisms in which the superconducting state is stabilized primarily by changes in electronic motion rather than by a conventional reduction of interaction energy. In the most literal usage, the superconducting transition is accompanied by a lowering of the electronic kinetic energy and a raising of the interaction or potential energy, opposite to the weak-coupling BCS pattern. In a broader usage, the term also refers to theories in which the pairing kernel itself arises from the kinetic term of a strongly correlated Hamiltonian, even if the energetic bookkeeping is not always presented in the same way. Across Hubbard, $t$–$J$, correlated-hopping, and projected-hopping models, the topic sits at the intersection of Mott physics, pseudogap phenomenology, spin fluctuations, and unconventional pairing [(Gull et al., 2012); (Feng et al., 2015); (Hirsch et al., 2014)].

1. Definition and scope of the concept

The most direct energetic definition compares superconducting and normal states at identical microscopic parameters through

$$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$

In the weak-coupling BCS case, superconductivity is potential-energy-driven, with $\Delta V<0$ and $\Delta K>0$. By contrast, kinetic-energy-driven superconductivity refers to the reversed pattern, $\Delta K<0$ and $\Delta V>0$, with the net condensation energy still negative because the kinetic-energy gain outweighs the potential-energy cost (Gull et al., 2012).

Taken together, these papers suggest that the term is used in at least three non-identical senses. First, it can mean an actual sign reversal in the condensation-energy decomposition, as in cluster and variational studies of the Hubbard model. Second, it can mean that the pairing interaction is generated by the kinetic term after imposing strong-correlation constraints, as in fermion–spin treatments of the $t$–$J$ model and in the kinematic spin-fluctuation mechanism [(Feng et al., 2015); (Plakida et al., 2014)]. Third, it can mean that correlated hopping or projected hopping makes paired carriers more mobile than isolated carriers, so that pairing lowers band kinetic energy even without a net attractive interaction [(Hirsch et al., 2014); (Oh et al., 2024)].

This multiplicity of usage is central to the subject. It explains why papers using the same phrase may differ in what is being computed: some compare $K_S$ and $J$0 directly, some derive an effective attraction from the kinetic operator, and some emphasize projected or constrained motion as the origin of pairing.

2. Hubbard-model energetics and the pseudogap boundary

A controlled formulation of the energetic question was given for the two-dimensional repulsive Hubbard model on a square lattice,

$J$1

using the eight-site dynamical cluster approximation with CT-AUX impurity solving and Nambu formalism for $J$2 superconductivity. In this framework the total energy is decomposed into

$J$3

The central result is a sharp distinction between two regimes. In a weak-coupling or larger-doping regime, where the normal state is a Fermi liquid, superconductivity is BCS-like: potential energy decreases and kinetic energy increases. In a strong-coupling or low-doping regime, where the normal state exhibits a pseudogap, the pattern reverses: superconductivity lowers kinetic energy and raises potential energy. The crossover coincides with the boundary of the normal-state pseudogap, and the total condensation energy remains of order $J$4 per site while $J$5 and $J$6 can be much larger and nearly cancel (Gull et al., 2012).

This result is important for two reasons. First, it shows that both BCS-like and kinetic-energy-driven superconductivity can occur in the same microscopic model, depending on coupling and doping. Second, it ties the sign change in superconducting energetics to pseudogap formation rather than to superconductivity alone. In the pseudogap regime, lowering temperature in the normal state increases the kinetic energy, reflecting localization tendencies; the onset of superconductivity reverses that trend and restores some coherence. The same study also tested an RVB-like interpretation by applying a pairing field and measuring the induced anomalous expectation value. On the weak-coupling side the response was strongly nonlinear, consistent with proximity to a superconducting instability, whereas on the strong-coupling pseudogap side the response was essentially linear, leading the authors to emphasize the “absence of discernibly nonlinear response” and to argue that RVB physics is not the origin of the kinetic-energy-driven superconductivity they found (Gull et al., 2012).

A variational Monte Carlo study reached a closely related conclusion from a different angle. In the standard Gutzwiller-BCS state $J$7, superconductivity is potential-energy-driven: the Coulomb energy decreases and the kinetic energy increases. In the improved correlated state

$J$8

the behavior reverses in the strongly correlated regime: at $J$9 and $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$0, the kinetic energy decreases and the Coulomb energy increases as the superconducting gap develops. The kinetic contribution becomes dominant for $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$1–$$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$2, and its magnitude diminishes with increasing hole doping (Yanagisawa, 2021).

3. Projected motion, kinetic frustration, and purely kinetic pairing

A different route to kinetic-energy-driven pairing arises when constraints or lattice geometry suppress single-particle motion more strongly than paired motion. In a repulsive Hubbard model on weakly coupled tetrahedra, with intra-plaquette frustration tuned to $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$3, single-hole kinetic energy is “optimally frustrated” in the $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$4 limit. At the same point, two holes on one plaquette acquire a positive binding energy, and second-order perturbation theory in interplaquette hopping yields an effective hard-core boson model whose condensed phase is a $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$5-wave superconductor. The mechanism is non-BCS because the bare interaction is purely repulsive and pairing survives at arbitrarily large $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$6; the energetic gain comes from coherent pair motion in a background where single-particle kinetic energy is frustrated (Isaev et al., 2010).

A more radical example is the projected-hopping model analyzed in “High-temperature superconductivity from kinetic energy” (Oh et al., 2024). There the effective low-energy ESD Hamiltonian contains only projected nearest-neighbor hopping and an onsite term $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$7. By tuning the parent double Kondo lattice model so that $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$8, the authors construct a model with no net attractive interaction in the low-energy theory. DMRG on cylinders up to $$\Delta K = K_S - K_N,\quad \Delta V = V_S - V_N,\quad \Delta E = \Delta K + \Delta V.$$9 nevertheless finds a superconducting ground state, with “pairing gaps, determined from spin and single-electron charge gaps, exceeding $\Delta V<0$0,” a phase stiffness that increases with doping, and an estimated “potential for high critical temperatures ($\Delta V<0$1) approaching $\Delta V<0$2” (Oh et al., 2024). In this setting the essential objects are empty states, singlons, and doublons, and the decisive kinetic processes are pair-conversion terms that make paired motion more favorable than isolated motion.

These studies support a broader inference: kinetic-energy-driven superconductivity need not require an explicit attractive potential if the constrained Hilbert space itself reorganizes mobility in favor of pairs.

4. Correlated hopping, dynamic Hubbard models, and hole superconductivity

In Hirsch’s correlated-hopping and dynamic-Hubbard framework, the mechanism is built directly into the hopping operator. For holes moving on negatively charged anions, the effective Hamiltonian is

$\Delta V<0$3

When another hole is nearby, hopping is enhanced; pairing therefore lowers kinetic energy by “undressing” heavily dressed hole carriers. In this language the relevant materials are those with holes in nearly full bands built from negatively charged anion orbitals, and higher $\Delta V<0$4 is favored when pressure enhances direct anion–anion overlap and correlated hopping. This program was applied to pressurized $\Delta V<0$5, where superconductivity was proposed to arise from holes in a nearly full sulfur $\Delta V<0$6-band, with pressure increasing $\Delta V<0$7 and $\Delta V<0$8, and to infinite-layer nickelates, where the same mechanism was proposed for holes in oxygen $\Delta V<0$9 orbitals [(Hirsch et al., 2014); (Hirsch et al., 2019)].

The dynamic Hubbard model generalizes this by introducing an explicit orbital-relaxation degree of freedom so that local orbitals expand when doubly occupied. After a Lang–Firsov transformation, one obtains occupancy-dependent hopping and correlated hopping. In this framework the model predicts kinetic-energy-driven charge expulsion from the interior to the surface, large sensitivity to disorder-induced charge inhomogeneity, positively charged quasiparticles, and tunneling asymmetry. These are presented as consequences of the same kinetic mechanism that produces superconductivity in nearly full bands (Hirsch, 2013).

A more speculative extension argues that superconductivity and superfluidity are both driven by kinetic-energy lowering associated with orbit expansion, and that the Meissner effect itself requires such a mechanism. In that proposal superconductors expel negative charge to the surface, support a ground-state spin current, and share with superfluid $\Delta K>0$0 a common origin in rotational zero-point motion. These claims are explicitly advanced as an alternative interpretation rather than as a settled consensus [(Hirsch, 2012); (Hirsch, 2011)].

5. Spin excitations generated by kinetic energy in doped Mott insulators

In the fermion–spin formulation of the $\Delta K>0$1–$\Delta K>0$2 model, the kinetic term becomes an interaction between charge carriers and the spin background once double occupancy is eliminated. The resulting charge-carrier pairing interaction arises “directly from the kinetic energy by the exchange of spin excitations,” and the same interaction generates the normal-state pseudogap in the particle–hole channel. Within this framework the superconducting state is controlled by both the $\Delta K>0$3-wave gap and the quasiparticle coherent weight, producing a maximal $\Delta K>0$4 around optimal doping and a pseudogap crossover temperature $\Delta K>0$5 that decreases monotonically with doping and disappears together with superconductivity at the end of the dome (Feng et al., 2015).

The same conceptual structure has been extended to other lattices. On the honeycomb lattice, within the $\Delta K>0$6–$\Delta K>0$7 model and charge–spin separation, the pairing kernel generated by the kinetic term favors chiral $\Delta K>0$8 symmetry. The charge-carrier pair gap displays a dome-like dependence on doping, with onset at $\Delta K>0$9, a maximum around $\Delta K<0$0, and suppression at high doping; it also decreases as $\Delta K<0$1 increases, indicating that sufficiently strong antiferromagnetic exchange destroys superconductivity (Lan et al., 2023). In the anisotropic square-lattice $\Delta K<0$2–$\Delta K<0$3 model with nematicity, the same kinetic-energy-driven formalism links the nematic characteristic energy to the enhancement of superconductivity: both the nematic characteristic energy and $\Delta K<0$4 show a dome-like dependence on the nematic strength, with a common optimal anisotropy (Cao et al., 2021).

A related strong-correlation formulation in terms of Hubbard operators yields what is explicitly called a “kinematic spin-fluctuation mechanism.” There the noncanonical algebra of Hubbard operators produces an effective spin-fluctuation coupling of order the bandwidth, $\Delta K<0$5, much larger than the superexchange scale $\Delta K<0$6. The resulting $\Delta K<0$7-wave pairing can survive sizable intersite Coulomb repulsion as long as $\Delta K<0$8, because the dominant pairing scale is set by the kinetic-energy scale rather than by $\Delta K<0$9 alone (Plakida et al., 2014).

DMRG studies of doped triangular-lattice Mott insulators also highlight the role of charge kinetic energy. With finite $\Delta V>0$0 and specific hopping-sign combinations $\Delta V>0$1, quasi-long-range superconductivity appears regardless of whether the parent spin background is $\Delta V>0$2 antiferromagnetic, quantum spin liquid, or stripy antiferromagnetic. The superconducting phases are characterized by short-ranged spin correlations and two charges per stripe, while flipping hopping signs can turn them into stripe phases without strong pairing or pseudogap-like phases without Cooper-pair phase coherence (Zhu et al., 2022).

6. Experimental signatures, material realizations, and controversies

One experimental route into the subject uses optical sum rules. In a single-band tight-binding picture, the low-frequency optical spectral weight is approximately related to $\Delta V>0$3, so a superconductivity-induced decrease of kinetic energy should appear as an increase of intraband optical spectral weight. The Hubbard-model study described above explicitly connected its strong-coupling pseudogap regime to underdoped-cuprate optical anomalies, while also cautioning that multiband effects, interband transitions, and cutoff dependence complicate the interpretation (Gull et al., 2012).

A different experimental observable is the field-induced kinetic energy density of the condensate, extracted from magnetization through

$\Delta V>0$4

In Bi$\Delta V>0$5Sr$\Delta V>0$6CaCu$\Delta V>0$7O$\Delta V>0$8, this quantity and the superfluid density peak near $\Delta V>0$9, where the pseudogap is argued to close and a van Hove singularity appears. That work concludes that $t$0 and $t$1 are related to the pseudogap energy scale and interprets the result as evidence for coexistence between superconductivity and the pseudogap. It also states explicitly that the measured $t$2 is the field-induced kinetic energy of the supercurrents in the mixed state, not a direct measurement of the total normal-to-superconducting kinetic-energy difference; accordingly, it does not by itself establish kinetic-energy-driven pairing in the strict condensation-energy sense (Lopes et al., 2020).

Material proposals span several distinct settings. The two-dimensional Hubbard model is used as a microscopic proxy for cuprates [(Gull et al., 2012); (Yanagisawa, 2021)]. The correlated-hopping and hole-superconductivity program has been applied to pressurized sulfides, infinite-layer nickelates, and, more generally, systems with holes on negatively charged anion networks [(Hirsch et al., 2014); (Hirsch et al., 2019)]. The double Kondo lattice construction underlying the projected-hopping ESD model has been proposed as relevant to bilayer nickelates, particularly when out-of-plane lattice constants are reduced (Oh et al., 2024).

The main controversy is therefore not whether the phrase exists, but what it denotes in a given paper. In one strand it names a measured or computed energetic sign reversal, $t$3 and $t$4. In another it names a pairing mechanism in which the kinetic term generates the effective interaction through spin excitations. In a third it describes constrained or correlated hopping that enhances the mobility of paired carriers. These usages are related but not interchangeable. The most controlled energetic evidence in the supplied literature comes from cluster and variational studies of the Hubbard model, especially in the pseudogap regime [(Gull et al., 2012); (Yanagisawa, 2021)]. The most expansive claims, involving charge expulsion, spin currents, or rotational zero-point motion, remain proposals within particular theoretical programs rather than universally accepted consequences of superconductivity [(Hirsch, 2013); (Hirsch, 2012); (Hirsch, 2011)].

In that sense, kinetic-energy-driven superconductivity is best regarded not as a single doctrine but as a family of strongly correlated scenarios in which superconductivity gains access to lower-energy charge motion that is blocked, frustrated, or incoherent in the normal state.