Pair-density wave (PDW) is a long-sought exotic state with oscillating superconducting order without external magnetic field. So far it has been rare in establishing a 2D microscopic model with PDW long-range order in its ground state. Here, we propose to study PDW superconductivity in a minimal model of spinless fermions (or spin-polarized electrons) on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interaction V_{1} and V_{2}, respectively. By performing a state-of-the-art density-matrix renormalization group study of this t-V_{1}-V_{2} model at finite doping on six-leg and eight-leg honeycomb cylinders, we show that the ground state exhibits PDW ordering (namely quasi-long-range order with a divergent PDW susceptibility). Remarkably this PDW state persists on the wider cylinder with 2D-like Fermi surfaces. To the best of our knowledge, this is probably the first controlled numerical evidence of PDW in systems with 2D-like Fermi surfaces.
Pair-density wave (PDW) is a long-sought exotic state with oscillating superconducting order without external magnetic field. So far it has been rare in establishing a 2D microscopic model with PDW long-range order in its ground state. Here, we propose to study PDW superconductivity in a minimal model of spinless fermions (or spin-polarized electrons) on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interaction V_{1} and V_{2}, respectively. By performing a state-of-the-art density-matrix renormalization group study of this t-V_{1}-V_{2} model at finite doping on six-leg and eight-leg honeycomb cylinders, we show that the ground state exhibits PDW ordering (namely quasi-long-range order with a divergent PDW susceptibility). Remarkably this PDW state persists on the wider cylinder with 2D-like Fermi surfaces. To the best of our knowledge, this is probably the first controlled numerical evidence of PDW in systems with 2D-like Fermi surfaces.
Abstract A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effective t-J-V model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the K and K′ K ′ points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge c ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.
A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with d-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive Vpd interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive Vpd, the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.
Pair-density-wave (PDW) superconductivity is a state in which the superconducting order parameter modulates at a finite wavevector. Using large-scale density matrix renormalization group, we study the doped altermagnetic Mott insulator in the checkerboard t-J model, where altermagnetic exchange anisotropy is encoded microscopically through anisotropic ferromagnetic next-nearest-neighbor exchange. By mapping the ground-state phase diagram as a function of doping and altermagnetic anisotropy, mainly on six-leg cylinders, we identify a transition from a uniform d-wave superconducting regime with charge modulation to a PDW regime coexisting with stripe order. In the PDW regime, we report an unconventional wave-vector locking QPDW≈2QStripe along the cylinder direction, in contrast to the conventional relation. Pair correlations reveal a two-scale structure, consisting of short-distance local d-wave pairing and long-distance finite-momentum PDW correlations. A symmetry-based Ginzburg--Landau analysis is presented for the observed locking. Our results identify altermagnetism as a strong-coupling, microscopically grounded route to finite-momentum superconductivity in doped Mott insulators.
Abstract We study the effects of doping the Kitaev model on the honeycomb lattice where the spins interact via the bond-directional interaction JK, which is known to have a quantum spin liquid as its exact ground state. The effect of hole doping is studied within the t-JK model on a three-leg cylinder using density-matrix renormalization group. Upon light doping, we find that the ground state of the system has a dominant quasi-long-range charge-density-wave correlations but short-range single-particle correlations. In the pairing channel, the even-parity superconducting correlation is dominant with d-wave-like symmetry, which oscillates in sign as a function of separation with a period equal to that of the spin-density wave and two times the charge-density wave. Although these correlations fall rapidly (possibly exponentially) at long distances, this is never-the-less the example where a pair-density wave is the leading instability in the pairing channel on the honeycomb lattice.
The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.
Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing (px,py) or (dxz,dyz) orbitals on the square lattice. For minimal interorbital t-J or t-V on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate dxy pair density wave (d-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal dxy pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-2 PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in p-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.