Pairing of spinless fermions in two dimensions

We study the real-space pairing instability of spinless fermions on a two-dimensional square lattice with short-range attractive interactions. Various symmetries of the pairing order parameter are considered. It is found that in both nonflux and flux phases the most stable pairing state is chiral and anisotropic. It breaks both the parity and the time-reversal symmetries. The quasiparticle excitation has a minimum gap which could be much smaller than its average over the Fermi surface. The temperature dependence of the order parameter and the critical magnetic field are found to be similar to those of the classical BCS solutions. A possible connection with the high-temperature superconductivity is discussed.We study the real-space pairing instability of spinless fermions on a two-dimensional square lattice with short-range attractive interactions. Various symmetries of the pairing order parameter are considered. It is found that in both nonflux and flux phases the most stable pairing state is chiral and anisotropic. It breaks both the parity and the time-reversal symmetries. The quasiparticle excitation has a minimum gap which could be much smaller than its average over the Fermi surface. The temperature dependence of the order parameter and the critical magnetic field are found to be similar to those of the classical BCS solutions. A possible connection with the high-temperature superconductivity is discussed.

Physical review. B, Condensed matterSep 1, 19915 citations

Phases of attractive spin-imbalanced fermions in square lattices

Simone Chiesa, Shiwei Zhang

We determine the relative stability of different ground-state phases of spin-imbalanced populations of attractive fermions in square lattices. The ground state is determined within Hartree-Fock-Bogoliubov theory, with care taken to remove finite-size effects. The phases are systematically characterized by the symmetry of the order parameter and their real- and momentum-space structures. For quarter- to half-filled lattices, where the Fermi surfaces are most distorted from their spherical counterpart in the continuum, we predominantly find unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase exists when the ordering wave vector is diagonally directed. Charge and pairing order coexist, rather than compete, and are responsible for the opening of the gap on different portions of the Fermi surface. A variational determination of the correct pair momentum of the Larkin-Ovchinikov phases shows that phase separation does not occur in the considered regime of density and magnetization.We determine the relative stability of different ground-state phases of spin-imbalanced populations of attractive fermions in square lattices. The ground state is determined within Hartree-Fock-Bogoliubov theory, with care taken to remove finite-size effects. The phases are systematically characterized by the symmetry of the order parameter and their real- and momentum-space structures. For quarter- to half-filled lattices, where the Fermi surfaces are most distorted from their spherical counterpart in the continuum, we predominantly find unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase exists when the ordering wave vector is diagonally directed. Charge and pairing order coexist, rather than compete, and are responsible for the opening of the gap on different portions of the Fermi surface. A variational determination of the correct pair momentum of the Larkin-Ovchinikov phases shows that phase separation does not occur in the considered regime of density and magnetization.

arXiv:1303.3812Physical Review AOct 17, 201315 citations

Two-dimensional fermionic superfluids, pairing instability, and vortex liquids in the absence of time reversal symmetry

Predrag Nikolić

We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultracold-atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high-temperature superconductors.We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultracold-atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high-temperature superconductors.

arXiv:0901.2576Physical Review BApr 7, 20097 citations

High-Temperature Superconductivity from Finite-Range Attractive Interaction

Dmitry Miserev, Joel Hutchinson, Herbert Schoeller +2 more

In this letter we consider $D$ -dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range $R_s$ that is much greater than the Fermi wavelength $λ_F$ breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature $T_c$ versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal $T_c^* \sim 0.1 E_F$ on the interaction range at $R_s \gg λ_F$ , $E_F$ is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.In this letter we consider $D$-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range $R_s$ that is much greater than the Fermi wavelength $λ_F$ breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature $T_c$ versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal $T_c^* \sim 0.1 E_F$ on the interaction range at $R_s \gg λ_F$, $E_F$ is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.

arXiv:2502.11624Feb 17, 20250 citations

Unconventional superconducting phases for the two-dimensional extended Hubbard model on a square lattice

Wen-Min Huang, Chen-Yen Lai, Chuntai Shi +1 more

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site ( $U$ ) and nearest-neighbor ( $V$ ) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when $4V>U$ gives way to a ${d}_{xy}$ -wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive $V$ and a range of on-site repulsive interaction $U$ . In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking $({p}_{x}+i{p}_{y})$ -wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the $({p}_{x}+i{p}_{y})$ -wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while ${d}_{xy}$ pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site ($U$) and nearest-neighbor ($V$) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when $4V>U$ gives way to a ${d}_{xy}$-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive $V$ and a range of on-site repulsive interaction $U$. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking $({p}_{x}+i{p}_{y})$-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the $({p}_{x}+i{p}_{y})$-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while ${d}_{xy}$ pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.

arXiv:1303.7468Physical Review BAug 12, 201323 citations

Strongly interacting two-dimensional Dirac fermions

Lih-King Lim, Achilleas Lazarides, A. Hemmerich +1 more

We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s -wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s -wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.

arXiv:0905.1281Europhysics Letters (EPL)Nov 1, 200930 citations

In this letter we consider

D

-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range

R_s

that is much greater than the Fermi wavelength

λ_F

breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature

T_c

versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal

T_c^* \sim 0.1 E_F

on the interaction range at

R_s \gg λ_F

E_F

is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (

U

) and nearest-neighbor (

V

) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when

4V>U

gives way to a

{d}_{xy}

-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive

V

and a range of on-site repulsive interaction

U

. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking

({p}_{x}+i{p}_{y})

-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the

({p}_{x}+i{p}_{y})

-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while

{d}_{xy}

pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.