Starting from the spin-fermion model or Hertz-Millis theory describing electrons coupled to anti-ferromagnetic spin fluctuations we develop a theory to describe the transition from a fractionalized Fermi liquid into a $d_{x^2-y^2}$ superconductor. We focus on small electron doping on top of the half-filled state. The doped electrons enter the system as spinon-chargon bound states, which form a small, reconstructed Fermi surface. The bound states are neutral under the emergent U(1) gauge symmetry of the fractionalized Fermi liquid, but interact via a dipolar two-body potential. We show that because of the projective action of translation symmetry on the spinons and chargons, the Fourier components of this repulsive dipolar interaction are peaked at the anti-ferromagnetic wave vector, thereby providing a robust microscopic mechanism for $d_{x^2-y^2}$ pairing in a fractionalized metal.Starting from the spin-fermion model or Hertz-Millis theory describing electrons coupled to anti-ferromagnetic spin fluctuations we develop a theory to describe the transition from a fractionalized Fermi liquid into a $d_{x^2-y^2}$ superconductor. We focus on small electron doping on top of the half-filled state. The doped electrons enter the system as spinon-chargon bound states, which form a small, reconstructed Fermi surface. The bound states are neutral under the emergent U(1) gauge symmetry of the fractionalized Fermi liquid, but interact via a dipolar two-body potential. We show that because of the projective action of translation symmetry on the spinons and chargons, the Fourier components of this repulsive dipolar interaction are peaked at the anti-ferromagnetic wave vector, thereby providing a robust microscopic mechanism for $d_{x^2-y^2}$ pairing in a fractionalized metal.

arXiv:2606.17159Jun 15, 20260 citations

Fermi Liquid Superconductivity

Matthias Eschrig, James A. Sauls, Hubert Burkhardt +1 more

Springer eBooksJan 1, 20011 citation

Spin-Charge Bound States and Emerging Fermions in a Quantum Spin Liquid

Jens H. Nyhegn, K. Knakkergaard Nielsen, Leon Balents +1 more

The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t - J model where the background spins form a Z 2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t - J model where the background spins form a Z 2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.

arXiv:2507.02508PRX QuantumOct 24, 20253 citations

Roton Fermi liquid: A metallic phase of two-dimensional electrons

Leon Balents, Matthew P. A. Fisher

We introduce and analyze a metallic phase of two-dimensional $(2\mathrm{D})$ electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of $2\mathrm{D}$ electrons consisting of fermionic quasiparticles and $hc∕2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$ , but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.We introduce and analyze a metallic phase of two-dimensional $(2\mathrm{D})$ electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of $2\mathrm{D}$ electrons consisting of fermionic quasiparticles and $hc∕2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature $(T=0)$, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.

arXiv:cond-mat/0307446Physical Review BFeb 28, 200513 citations

Theory of a superfluid Fermi liquid

Alexander I. Akhiezer, Красильников Владимир Владимирович, S.V. Peletminskii +1 more

Uspekhi Fizicheskih NaukJan 1, 199315 citations

d_{x^2-y^2}

superconductor. We focus on small electron doping on top of the half-filled state. The doped electrons enter the system as spinon-chargon bound states, which form a small, reconstructed Fermi surface. The bound states are neutral under the emergent U(1) gauge symmetry of the fractionalized Fermi liquid, but interact via a dipolar two-body potential. We show that because of the projective action of translation symmetry on the spinons and chargons, the Fourier components of this repulsive dipolar interaction are peaked at the anti-ferromagnetic wave vector, thereby providing a robust microscopic mechanism for

d_{x^2-y^2}

pairing in a fractionalized metal.

We introduce and analyze a metallic phase of two-dimensional

(2\mathrm{D})

electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of

2\mathrm{D}

electrons consisting of fermionic quasiparticles and

hc∕2e

vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature

(T=0)

, but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.