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 versus 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 versus doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.

May 8, 20090 citations

Engineering superfluidity in Bose-Fermi mixtures of ultracold atoms

Daw-Wei Wang, Mikhail D. Lukin, Eugene Demler

We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with $s$ -, $p$ -, and $d$ -wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with $s$-, $p$-, and $d$-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.

arXiv:cond-mat/0410494Physical Review ANov 17, 200560 citations

Unconventional pairing symmetry of interacting Dirac fermions on a π-flux lattice

Huaiming Guo

The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s*- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds*-wave phase consisting of alternating stripes of s*- and d-wave phases. A complementary mean-field analysis shows that while the s*- and d-wave symmetries individually have nodes in the energy spectrum, the ds* channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s*- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds*-wave phase consisting of alternating stripes of s*- and d-wave phases. A complementary mean-field analysis shows that while the s*- and d-wave symmetries individually have nodes in the energy spectrum, the ds* channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

APS March Meeting AbstractsJan 1, 20190 citations

Unconventional pairing symmetry of interacting Dirac fermions on a π -flux lattice

Huaiming Guo, Ehsan Khatami, Yao Wang +3 more

The pairing symmetry of interacting Dirac fermions on the $\ensuremath{\pi}$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The ${s}^{*}$ - (i.e., extended $s$ -) and $d$ -wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional $d{s}^{*}$ -wave phase consisting of alternating stripes of ${s}^{*}$ - and $d$ -wave phases. A complementary mean-field analysis shows that while the ${s}^{*}$ - and $d$ -wave symmetries individually have nodes in the energy spectrum, the $d{s}^{*}$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral $d$ -wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.The pairing symmetry of interacting Dirac fermions on the $\ensuremath{\pi}$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The ${s}^{*}$- (i.e., extended $s$-) and $d$-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional $d{s}^{*}$-wave phase consisting of alternating stripes of ${s}^{*}$- and $d$-wave phases. A complementary mean-field analysis shows that while the ${s}^{*}$- and $d$-wave symmetries individually have nodes in the energy spectrum, the $d{s}^{*}$ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral $d$-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

arXiv:1708.07256Physical review. B./Physical review. BApr 20, 201814 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

Vortex-Antivortex Lattice in Ultracold Fermionic Gases

Sergio S. Botelho, C. A. R. Sá de Melo

We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.

arXiv:cond-mat/0509387Physical Review LettersFeb 3, 200696 citations

s

p

-, and

d

-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.

The pairing symmetry of interacting Dirac fermions on the $\ensuremath{\pi}$-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The

{s}^{*}

- (i.e., extended

s

-) and

d

-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional

d{s}^{*}

-wave phase consisting of alternating stripes of

{s}^{*}

- and

d

-wave phases. A complementary mean-field analysis shows that while the

{s}^{*}

- and

d

-wave symmetries individually have nodes in the energy spectrum, the

d{s}^{*}

channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral

d

-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

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.