In view of cuprate superconductors, effects of point-type repulsive impurity potential ( V ) on partially filled antiferromagnetic (AF) states are studied for a strongly correlated square-lattice Hubbard model ( U/t = 12) with a diagonal transfer ( t ' = −0.3 t ), using a variational Monte Carlo method. To simplify interpretation, here we focus on the case of δ imp = δ, where δ imp and δ are densities of impurity sites and doped holes, respectively, with δ = 0.04 − 0.20. As a result, a filling-control-type Mott transition occurs at V = V M ( ∼ 2 t ) irrespective of δ ; a partially filled AF state becomes Mott insulating for V > V M . Such impurity-induced Mott transitions extensively appear beyond the above parameter settings.
In view of cuprate superconductors, effects of point-type repulsive impurity potential ( V ) on partially filled antiferromagnetic (AF) states are studied for a strongly correlated square-lattice Hubbard model ( U/t = 12) with a diagonal transfer ( t ' = −0.3 t ), using a variational Monte Carlo method. To simplify interpretation, here we focus on the case of δ imp = δ, where δ imp and δ are densities of impurity sites and doped holes, respectively, with δ = 0.04 − 0.20. As a result, a filling-control-type Mott transition occurs at V = V M ( ∼ 2 t ) irrespective of δ ; a partially filled AF state becomes Mott insulating for V > V M . Such impurity-induced Mott transitions extensively appear beyond the above parameter settings.
Abstract In view of cuprate superconductors, effects of point-type impurity potential (V) on half-filled antiferromagnetic and paramagnetic states are studied for a strongly correlated square-lattice Hubbard model (U/t = 12) with a diagonal transfer (t′), using a variational Monte Carlo method. In the trial states, we introduce a Rice-Brinkman-type one-body projector for V, which enables us to treat the whole range of V (− ∞ < V/t < ∞) with small statistical errors. Filling-control-type Mott (insulator-to-metal) transitions are found to occur at <?CDATA V=VU(±)?> V = V U ( ± ) (∼ ±U). In the metallic states <?CDATA (∣V∣>VU(±))?> ( | V | > | V U ( ± ) | ) , charge carriers are holes (electrons) in the case of attractive (repulsive) potential. The mechanism of the transitions is intuitively understood.
Abstract With cuprate superconductors in mind, we study the effects of point-type impurity potential (V) on a d x 2−y 2 -wave superconducting (d-SC) state in a strongly correlated squarelattice Hubbard model (U/t = 12) with a diagonal transfer (t′), using a variational Monte Carlo method. At half filling, insulator-to-conductor (filling-control-type Mott) transitions occur at <?CDATA V=VU(±)∼±U?> V = V U ( ± ) ∼ ± U . The phase realized for <?CDATA V<VU(−)?> V < V U ( − ) is robust d-SC and the charge carriers are holes, whereas for <?CDATA V>VU(+)?> V > V U ( + ) a metallic (or weak d-SC) state appears with charge carriers of electrons. For a partially-filled case where the impurity density is equal to the doping rate, a d-SC-to-insulator transition arises at V ≡ V M ∼ 4t. In the weak-|V| phases, the impurity effects in the electron distribution are smeared out by the screening effect, whereas in the strong-|V| phases, the electron distribution directly depend on the impurity configurations.
Recent numerical studies have shown that antiferromagnetism (AF) prevails widely near half filling in the two-dimensional Hubbard ( t - t '- U ) model, contrary to the experiments on cuprate superconductors. In cuprates, disorders owing to the dopants, which are usually disregarded in theory, are possibly intrinsic and considerable. Thus, as a first step, we consider the effects of point-type impurity potentials, which are randomly distributed on the lattice sites, on the stability of AF. It is found that a moderate impurity potential does not modify the stability of AF, but a sufficiently strong attractive potential V ( V ≲ − U ) appreciably weakens an antiferromagnetic state owing to an insufficient screening of V .
We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half-filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U, we can identify a hidden critical point UMott, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of U), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMott has crucial consequences when doping the system: We observe a tendency for phase separation into hole-rich and hole-poor regions only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMott, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMott shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.
In connection with recent experiments on excitation in which Mott insulators change to conductors, we study the properties of excited states beyond the Mott gap as quasi-stationary states for a two-dimensional Hubbard (t-t'-U) model at half filling. A variational Monte Carlo method is used with trial wave functions for paramagnetic or normal (PM), superconducting with dx2-y2-wave (d-SC), isotropic s-wave, and extended s-wave symmetries, and antiferromagnetic (AF) states. The excited states are generated by imposing a minimum number of doubly occupied sites (doublons) D_L on the lowest-energy states. For U>W (W: band width), d_L=D_L/Ns (Ns: number of sites) corresponds to the excitation intensity. It is found that the AF state is the most stable among the states we treated for d_L<0.14 and insulating. The PM and d-SC states become conductive over a threshold d_Lc, and the conduction is caused by unbound doublons and holons (empty sites). The PM state arises for d_L>0.14, but the d-SC state is always hidden by the AF state. The s-wave-type superconducting states are not stabilized for any parameter set.