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arXiv:1301.1267 · Physical Review B

Correlated Dirac particles and superconductivity on the honeycomb lattice

Wéi Wú, Michael M. Scherer, Carsten Honerkamp A, Karyn Le Hur

Published Mar 29, 2013• 60 citations
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Abstract

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.

DOI
10.1103/physrevb.87.094521

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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−J1\ensuremath−J2t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}t\ensuremath−J1​\ensuremath−J2​ 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−idd\ensuremath{-}idd\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 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-UUU model we show that the $d+i{d}^{\ensuremath{'}}$-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 $d+i{d}^{\ensuremath{'}}$-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 ddd-wave solution with an overall zero chirality within the restriction of the $t\ensuremath{-}J$ model.
We study the ground state of the doped Hubbard model on the honeycomb lattice in the small-doping and strongly interacting region. The nature of the ground state after doping holes into antiferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous effort has been spent investigating this challenging problem. In this work, we employ two complementary, state-of-the-art, many-body computational methods: constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) with self-consistent constraint and density matrix renormalization group (DMRG) methods. Systematic and detailed cross validations are performed between these two methods for narrow systems for which DMRG can produce reliable results. AFQMC is then utilized to study wider systems to investigate the thermodynamic limit properties. The ground state is found to be a half-filled stripe state in the small-doping and strongly interacting region. The pairing correlation shows ddd-wave symmetry locally but decays exponentially with the distance between two pairs.
In view of quite recent experimental activities on magnetic and superconducting properties of honeycomb and hexagonal lattice based materials, in this thesis we have used field-theoretic and many-body methods to investigate magnetic and superconducting properties of the large-U Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the (quantum) magnetic and superconducting phases at half-filling and in the hole-doped regime. At half-filling, we deal with the underlying spin degrees of freedom of the quantum antiferromagnetic (AF) Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear σ-model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. In the challenging hole-doped regime, our approach allows the derivation of a t-J Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations. In addition, we have performed an extensive study of the electronic structure of the doped system for each competing phase: AF, ferromagnetic (FM), and (spin-singlet pairing) s-, dx₂₋ʏ₂ – and idxʏ -wave superconducting (SC) state induced by purely electronic effects. In this context, an energetic analysis of the ground state of these phases reveal that the AF order prevails for low hole doping, while a dominantly chiral dx₂₋ʏ₂ + idxʏ superconducting state was found in the vicinity of the Van Hove singularity (high hole doping). We also stress that a thermodynamic analysis of the superconducting phase shows that the critical temperature is directly related to the exchange constant J = 4t²/U, in which t denotes the hopping amplitude and U the on-site Coulomb repulsion of the Hubbard model (purely electronic origin). Remarkably, the competition between the AF and dx₂₋ʏ₂ + idxʏ SC phases takes place by the occurrence of a first-order transition accompanied by a spatial phase separation of the referred phases.
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.
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.
Superconductivity and competing orders in honeycomb ttt-JJJ model: interplay of lattice geometry and next-nearest-neighbor hopping
We investigate the extended ttt-JJJ model on honeycomb lattices with next-nearest-neighbor (NNN) electron hopping t′t't′ and superexchange coupling J′=(t′/t)2JJ'=(t'/t)^2 JJ′=(t′/t)2J using large-scale density-matrix renormalization group (DMRG) simulations and slave-boson mean-field theory (SBMFT). By systematically varying t′t't′ and cylinder geometries, our DMRG results reveal several competing phases with distinct charge and superconducting (SC) properties. On YC4-0 cylinders possessing bonds lying along e⃗y\vec{e}_yey​ direction, the ground state of doped models exhibits pronounced quasi-long-range ddd-wave SC with coexisting armchair-oriented stripes (a-stripe) across a broad range of t′t't′. Notably, the SC Luttinger exponent has a non-monotonic dependence on t′t't′, showing an optimal top′∼0.4t'_{op}\sim0.4top′​∼0.4 for dominant SC. Conversely, XC cylinders host a competing long-range zigzag stripes phase without SC for t′>0.5t'>0.5t′>0.5, highlighting the role of boundary geometry in stabilizing distinct competing phases in DMRG. To elucidate the stability of all these competing phases in 2D limit, we employ SBMFT and identify the a-stripe as the stable configuration across most of phase diagram, with a transition to uniform nematic ddd-wave SC at large t′t't′ for δ=1/8δ=1/8δ=1/8. The combined results from two complementary approaches suggest a robust t′t't′-induced SC phase that might remain stable in doped extended ttt-JJJ model on the honeycomb lattice.