Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

Abstract

We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where d-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

“…Recently cluster DMFT calculations that included the possibility of AFM order, d-wave superconductivity and the striped phase simultaneously were performed. The results show coexistence of the d-wave superconductor and striped phases for a large doping region and a smaller area of a uniform d-wave superfluid [95]. Existence of the striped phase for one value of doping was also recently shown by a study combining several different numerical approaches [96], and for a Lieb-lattice geometry [97].…”

Period 4 stripe in the extended two-dimensional Hubbard model

“…Meanwhile, the two-dimensional (2D) Hubbard model [33] -which has been suggested as the most elementary microscopic model that may reproduce the essential features of the cuprates' phase diagram -has been a prominent subject of intense theoretical and numerical investigations. Much attention has been given especially on the underdoped region in the strongly correlated regime, where several low-energy states are very closely competing, including a uniform d-wave superconducting (SC) state [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] and various stripe states [20][21][22][23][52][53][54][55][56][57][58][59][60][61] with or without coexisting superconducting order. A similar competition can also be found for the t − J model -the effective model in the strong coupling limit [62][63][64][65][66][67][68][69][70][71].…”

Magnetization, d -wave superconductivity, and non-Fermi-liquid behavior in a crossover from dispersive to flat bands

“…We use exact diagonalization (ED) and continuous time quantum Monte Carlo (CT-INT) as impurity solvers at zero temperature and finite temperature, respectively. [27,50]. We define the local magnetization, m i = n i,↑ − n i,↓ , where n i,σ = G i,σ (τ → 0 − ) is the density of spin-σ particles for a given site of the unit cell.…”

“…In our case the cluster is a four site (2 × 2) plaquette as shown in Fig. 1, which has been used to study the dSC order in the canonical square lattice Hubbard model [27,53,54]. The local cluster Green's function of the lattice system is given by the matrix equation…”

“…Although there is no direct mathematical foundation for such an interpretation, we have previously reported presence of spatially non-uniform magnetic and charge order coexisting with dSC using an extended plaquette DMFT approximation for the canonical 2D Hubbard model. In that case calculations were carried out for unit cells with a large number of sites by taking one-dimensional slices of the lattice [27]. There, incommensurate orders coexisting with dSC were reported, such as the spin density wave coexisting with inhomogeneous dSC of wavelength 12 plaquettes which was found to have the lowest energy for µ = 1.40 and U = 6.0.…”