Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1407.2914 · Physical Review B

Chiral d -wave superconductivity on the honeycomb lattice close to the Mott state

Annica M. Black‐Schaffer, Wéi Wú, Karyn Le Hur

Published Aug 27, 2014• 50 citations
arXivHTMLPDF

Abstract

We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral $d+i{d}^{\ensuremath{'}}$-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the $t\ensuremath{-}J$ model and quantum Monte Carlo calculations of the Hubbard-$U$ model we show that the $d+i{d}^{\ensuremath{'}}$-wave state is the favored superconducting state for a wide range of on-site repulsion $U$, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality $d$-wave state, where the overall chirality cancels. We find that a state with $d+i{d}^{\ensuremath{'}}$-wave symmetry in one valley but $d\ensuremath{-}i{d}^{\ensuremath{'}}$-wave symmetry in the other valley is not possible in the $t\ensuremath{-}J$ model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekul\'e distortion, we find no energetically favorable $d$-wave solution with an overall zero chirality within the restriction of the $t\ensuremath{-}J$ model.

DOI
10.1103/physrevb.90.054521

Related papers

Correlated Dirac particles and superconductivity on the honeycomb lattice

Wéi Wú, Michael M. Scherer, Carsten Honerkamp A +1 more

We investigate the properties of the nearest-neighbor singlet pairing and the emergence of $d$-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of $d$-wave superconductivity, in agreement with earlier works. We show that a small but finite ${J}_{2}$ spin coupling between next-nearest neighbors stabilizes $d$-wave symmetry compared to the extended$s$-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a $d+id$ singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral $d+id$ symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In${}_{3}$Cu${}_{2}$VO${}_{9}$. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.

arXiv:1301.1267•Physical Review B•Mar 29, 2013•60 citations

Extended Hubbard model on a honeycomb lattice

Welberth Kennedy, Sebastião dos Anjos Sousa-Júnior, Natanael C. Costa +1 more

We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling $U$. However, the inclusion of a repulsive extended interaction $V$ between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with $d$-wave symmetry, i.e., only $s$-wave pairing is allowed.

arXiv:2411.07429•Physical review. B./Physical review. B•Apr 11, 2025•4 citations

Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Stephan Heßelmann, Daniel D. Scherer, Michael M. Scherer +1 more

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

arXiv:1805.02490•Physical review. B./Physical review. B•Jul 31, 2018•10 citations

Weak coupling model for s*- and d-wave superconductivity

D. van der Marel

The phase diagram of the unconstrained $t-J$ model is calculated using the random phase approximation. It is found that the extended $s$ and the $d_{x^2-y^2}$-channels are {\em not} degenerate near half filling. Extended $s$-pairing with a low $T_c$ occurs only for a band containing less then 0.4 electrons or holes per unit cell, whereas in a large region around half-filling $d$-wave pairing is the only stable superconducting solution. At half filling superconductivity is suppressed due to the formation of the anti-ferromagnetic Mott-Hubbard insulating state. By extending the analysis to the unconstrained $t-t'-J$ model, it is proven that, if a Fermi surface is assumed similar to the one that is known to exist in cuprous oxide superconductors, the highest superconducting $T_c$ is reached for about $0.7$ electron per site, whereas the anti-ferromagnetic solution still occurs for $1$ electron per site. It is shown, that the maximum $d$-wave superconducting mean field transition temperature is half the maximum value that the Neèl temperature can have in the Mott-insulating state.

arXiv:cond-mat/9309003•Sep 2, 1993•0 citations

Unconventional Chiral d-wave Superconductivity in the t-J-U Model on a Honeycomb Lattice

Lianjun Zou, Feng Xu

Abstract We investigate chiral d -wave superconductivity in the honeycomb-lattice t-J - U model within Renormalized Mean-Field Theory (RMFT). By incorporating Gutzwiller renormalization factors, the effects of strong correlations and the suppression of double occupancy are treated self-consistently. In the nearest-neighbor chiral d + id pairing state of the honeycomb lattice, we analyzed the evolution of the pairing amplitude, the quasiparticle spectrum, and the superfluid weight with respect to the doping concentration, the local Coulomb repulsion energy ( U ), and the antiferromagnetic exchange interaction ( J ). The pairing amplitude exhibits a dome-like doping dependence. As U increases, the dome broadens and the optimal doping shifts toward higher carrier concentration due to the renormalization of the effective kinetic energy. We further determine the critical exchange interaction required to obtain a self-consistent pairing solution and show that strong correlations reduce this threshold over a wide doping range. Finally, from the calculated superfluid weight, we estimate the phase-ordering temperature scale associated with the self-consistent chiral d-wave solution.Our research results have clarified how the correlation effect influences the chirality d-wave pairing and the superfluid weight in the honeycomb lattice system.

Chinese Physics B•May 19, 2026•0 citations

Competing orders in the honeycomb lattice t−J model

Zheng-Tao Xu, Zheng‐Cheng Gu, Shuo Yang

We study the honeycomb lattice $t\text{\ensuremath{-}}J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\ensuremath{\delta}<0.05$, we find almost degenerate uniform $d$-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\ensuremath{\delta}>0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\ensuremath{\delta}$. Furthermore, the stripe states with the lowest variational energy always display ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators.

arXiv:2208.13681•Physical review. B./Physical review. B•Jul 24, 2023•14 citations
We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral d+id\ensuremath′d+i{d}^{\ensuremath{'}}d+id\ensuremath′-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model and quantum Monte Carlo calculations of the Hubbard-UUU model we show that the d+id\ensuremath′d+i{d}^{\ensuremath{'}}d+id\ensuremath′-wave state is the favored superconducting state for a wide range of on-site repulsion UUU, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality ddd-wave state, where the overall chirality cancels. We find that a state with d+id\ensuremath′d+i{d}^{\ensuremath{'}}d+id\ensuremath′-wave symmetry in one valley but d\ensuremath−id\ensuremath′d\ensuremath{-}i{d}^{\ensuremath{'}}d\ensuremath−id\ensuremath′-wave symmetry in the other valley is not possible in the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekul'e distortion, we find no energetically favorable ddd-wave solution with an overall zero chirality within the restriction of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model.
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of ddd-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of ddd-wave superconductivity, in agreement with earlier works. We show that a small but finite J2{J}_{2}J2​ spin coupling between next-nearest neighbors stabilizes ddd-wave symmetry compared to the extendedsss-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a d+idd+idd+id singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral d+idd+idd+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In3{}_{3}3​Cu2{}_{2}2​VO9{}_{9}9​. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling UUU. However, the inclusion of a repulsive extended interaction VVV between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with ddd-wave symmetry, i.e., only sss-wave pairing is allowed.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
The phase diagram of the unconstrained t−Jt-Jt−J model is calculated using the random phase approximation. It is found that the extended sss and the dx2−y2d_{x^2-y^2}dx2−y2​-channels are {\em not} degenerate near half filling. Extended sss-pairing with a low TcT_cTc​ occurs only for a band containing less then 0.4 electrons or holes per unit cell, whereas in a large region around half-filling ddd-wave pairing is the only stable superconducting solution. At half filling superconductivity is suppressed due to the formation of the anti-ferromagnetic Mott-Hubbard insulating state. By extending the analysis to the unconstrained t−t′−Jt-t'-Jt−t′−J model, it is proven that, if a Fermi surface is assumed similar to the one that is known to exist in cuprous oxide superconductors, the highest superconducting TcT_cTc​ is reached for about 0.70.70.7 electron per site, whereas the anti-ferromagnetic solution still occurs for 111 electron per site. It is shown, that the maximum ddd-wave superconducting mean field transition temperature is half the maximum value that the Neèl temperature can have in the Mott-insulating state.
Abstract We investigate chiral d -wave superconductivity in the honeycomb-lattice t-J - U model within Renormalized Mean-Field Theory (RMFT). By incorporating Gutzwiller renormalization factors, the effects of strong correlations and the suppression of double occupancy are treated self-consistently. In the nearest-neighbor chiral d + id pairing state of the honeycomb lattice, we analyzed the evolution of the pairing amplitude, the quasiparticle spectrum, and the superfluid weight with respect to the doping concentration, the local Coulomb repulsion energy ( U ), and the antiferromagnetic exchange interaction ( J ). The pairing amplitude exhibits a dome-like doping dependence. As U increases, the dome broadens and the optimal doping shifts toward higher carrier concentration due to the renormalization of the effective kinetic energy. We further determine the critical exchange interaction required to obtain a self-consistent pairing solution and show that strong correlations reduce this threshold over a wide doping range. Finally, from the calculated superfluid weight, we estimate the phase-ordering temperature scale associated with the self-consistent chiral d-wave solution.Our research results have clarified how the correlation effect influences the chirality d-wave pairing and the superfluid weight in the honeycomb lattice system.
We study the honeycomb lattice $t\text{\ensuremath{-}}J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\ensuremath{\delta}<0.05$, we find almost degenerate uniform ddd-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\ensuremath{\delta}>0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\ensuremath{\delta}$. Furthermore, the stripe states with the lowest variational energy always display ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators.