Pair Hopping Research Articles

EFFECT OF CORRELATED-HOPPING INTERACTION ON A ONE-DIMENSIONAL EXTENDED HUBBARD MODEL WITH SPIN-EXCHANGE INTERACTION

By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO2 planes

The influence of interlayer hoppings on the superconducting transition temperature (T c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t ⊥(k) = t ⊥(cos(k x ) − cos(k y ))2 and treated as a small perturbation for the states of two CuO2 planes described by the t-t′-t″-J* model. In the generalized mean field approximation for \({d_{{x^2} - {y^2}}}\) symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO2 layers provides an additional mechanism of Cooper pair formation or an increase in T c. In the concentration dependence of T c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.

Absence of orderings in Hubbard models

In this paper, an absence of certain orderings in multiparameter family of Hubbard models is proved. A technical tool is a reflection positivity, which allows to establish upper bounds on certain susceptibilities. These bounds in turn imply an absence of magnetic, charge, and superconducting orderings. The models considered are extended Hubbard models with charge and spin interactions, correlation hopping, and pair hopping.

Emergence of non-equilibrium superconductivity originated from repulsive interaction: Demonstration using optical lattices and implication to solid-state matter system

We study the dynamical properties of ultracold fermions in one-dimensional optical superlattices by using the adaptive time-dependent density matrix renormalization group method. The system is repulsive Hubbard model with an two-site periodic superlattice potential. Owing to superlattice structure, the ground-state states become the Mott-type insulating state at quarter-filling and band-type insulating state at half-filling, respectively. We clarify the dynamical properties of time evolution when the system is non-adiabatically changed to another lattice structure (i.e., the superlattice potential is suddenly changed to a normal one). In the case of Mott-type insulating state at quarter-filling, the time evolution exhibits a profile similar to that expected for single atom. On the other hand, we clarify the dynamical properties of a band-type insulating state at half-filling. The strongly-correlated interaction an unusual pairing of fermions induced the pair hopping process. We further address the robustness of pair hopping process and possibility of superconductivity by using sudden change from superlattice structure to normal one.

Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling

We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.

Featureless Mott insulators

A family of the pair hopping models exhibiting the incompressible quantum liquid at fractional filling $1/m^D$ is constructed in $D$ dimensional lattice. Except in one dimension, the lattice is the generalized edge-shared triangular lattice, for example the triangular lattice in two dimensions and tetrahedral lattice in three dimensions. They obey the new symmetry, conservation of the center-of-mass position proposed by Seidel et al..\cite{Seidel2005} The uniqueness of the ground state is proved rigorously in the open boundary condition. The finiteness of the excitation energy is calculated by the single mode approximation.

Charge-spin-orbital dynamics of one-dimensional two-orbital Hubbard model

We study the real-time evolution of a charge-excited state in a one-dimensional eg-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the z direction, electrons hop between adjacent 3z2−r2 orbitals, while x2−y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2−r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2−r2 orbital and x2−y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.

Pair-Hopping Mechanism for Layered Superconductors

We propose a possible charge fluctuation effect expected in layered superconducting materials. In the multireference density functional theory, relevant fluctuation channels for the Josephson coupling between superconducting layers include the interlayer pair hopping derived from the Coulomb repulsion. When interlayer single-electron tunneling processes are irrelevant in the Kohn–Sham electronic band structure calculation, the two-body effective interactions stabilize a superconducting phase. This state is also regarded as a valence-bond solid in a bulk electronic state. The hidden order parameters coexist with the superconducting order parameter when the charging effect of a layer is comparable to the pair hopping. Relevant material structures favorable for the pair-hopping mechanism are discussed.

Functional renormalization-group study of the doping dependence of pairing symmetry in the iron pnictide superconductors

We use the functional renormalization group to analyze the phase diagram of a four-band model for the iron pnictides subject to band interactions with certain ${A}_{1g}$ momentum dependence. We determine the parameter regimes where an extended $s$-wave pairing instability with and without nodes emerges. For electron doping, the parameter regime in which a nodal gap appears is in correspondence to recent predictions [A. Chubukov et al., arXiv:0903.5547 (unpublished)], however, at very low ${T}_{c}$. Upon hole doping, the $s$-wave gap never becomes nodal: above a critical strength of the intraband repulsion, the system favors an exotic extended $d$-wave instability on the enlarged hole pockets. At half filling, we find that a strong momentum dependence of interband pair hopping yields an extended $s$-wave instability instead of spin-density wave ordering. These results demonstrate that an interaction anisotropy around the Fermi surfaces generally leads to a pronounced sensitivity of the pairing state on the system parameters.

Pair tunneling of bosonic atoms in an optical lattice

We show that atom-molecule coupling with large detuning can cause effective hopping of pairs of bosonic atoms in a state-dependent optical lattice. Taking advantage of the high controllability of all relevant parameters in such systems, we discuss the pair-superfluid (PSF) to Mott insulator (MI) transition using the effective model within mean-field theory. In the presence of on-site disorder, simultaneous tunneling of bosonic atoms can result in a compressible weak Mott insulating phase. We have also investigated the coexistence of superfluid (SF) and PSF in the lattice, and found that the competition between the two hopping mechanisms can cause a first-order PSF(SF)-MI transition.

The Fulde–Ferrell–Larkin–Ovchinnikov phase in the presence of pair hoppinginteraction

The recent experimental support for the presence of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO)phase in CeCoIn5 directed attention towards the mechanisms responsible for this type of superconductivity.We investigate the FFLO state in a model where on-site/inter-site pairingcoexists with the repulsive pair hopping interaction. The latter interactionis interesting in that it leads to pairing with non-zero momentum of theCooper pairs even in the absence of the external magnetic field (the so-calledη pairing). It turns out that, depending on the strength of the pair hopping interaction, themagnetic field can induce one of two types of the FFLO phase with different spatialmodulations of the order parameter. It is argued that the properties of the FFLO phase maygive information about the magnitude of the pair hopping interaction. We also show thatη pairing and d-wave superconductivity may coexist in the FFLO state. It holds true also forsuperconductors which, in the absence of magnetic field, are of pure d-wave type.

Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0, 0) and ( π, π) in the folded Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is A 1 g in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.

Metastable Superfluidity of Repulsive Fermionic Atoms in Optical Lattices

In the fermionic Hubbard model, doubly occupied states have an exponentially large lifetime for strong repulsive interactions U. We show that this property can be used to prepare a metastable s-wave superfluid state for fermionic atoms in optical lattices described by a large-U Hubbard model. When an initial band-insulating state is expanded, the doubly occupied sites Bose condense. A mapping to the ferromagnetic Heisenberg model in an external field allows for a reliable solution of the problem. Nearest-neighbor repulsion and pair hopping are important in stabilizing superfluidity.

Electronic Correlations within Fermionic Lattice Models

We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J (parallel spins), J (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V ). As a first step we find the eigenvalues Eα and eigenvectors |Eα〉 of the dimer and we represent each partial Hamiltonian Eα|Eα〉〈Eα| (α = 1, 2, . . . , 16) in the second quantization with the use of the Hubbard and spin operators. Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons. A typical feature is the appearance of two generalized t−J interactions ascribed to two different energy levels which do not vanish even for U = J = J = V = 0 and their coupling constants are equal to ±t in this case. In the large U -limit for J = J = V = 0 there is only one t−J interaction with coupling constant equal to 4t2/|U | as in the case of a real lattice. The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U = J = J = V = 0 and t 6= 0. The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels. It qualitatively explains the origin of the phase diagram of the model. We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.

Cooperative transport in a potassium ion channel

Our current understanding of ion permeation through the selectivity filter of the KcsA potassium channel is based on the concept of a multi-ion transport mechanism. The details of this concerted movement, however, are not well understood. In the present paper we report on molecular dynamics simulations which provides new insights. It is shown that ion translocation is based on the collective hopping of ions and water molecules which is mediated by the flexible charged carbonyl groups lining the backbone of the pore. In particular, there is strong evidence for pairwise translocations where one ion and one water molecule form a bound state. We suggest a physical explanation of the observed phenomena employing a simple lattice model. It is argued that the water molecules can act as rectifiers during the hopping of ion-water pairs.

Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models

A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem.

Unusual properties of icosahedral boron-rich solids

Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the “self-healing” that underlies these materials’ extraordinary radiation tolerance. Furthermore, boron carbides, a group of icosahedral boron-rich solids, possess unusual electronic, magnetic and thermal properties. For example, the charge carriers, holes, localize as singlet pairs on icosahedra. The unusual origin of this localization is indicated by the absence of a concomitant photo-ionization. The thermally assisted hopping of singlet pairs between icosahedra produces Seebeck coefficients that are unexpectedly large and only weakly dependent on carrier concentration. These properties are exploited in devices: (1) long-lived high-power high-capacity beta-voltaic cells, (2) very high temperature thermoelectrics and (3) solid-state neutron detectors.

Holliday junction dynamics and branch migration: Single-molecule analysis

The Holliday junction (HJ) is a central intermediate in various genetic processes including homologous and site-specific recombination and DNA replication. Branch migration allows the exchange between homologous DNA regions, but the detailed mechanism for this key step of DNA recombination is unidentified. Here, we report direct real-time detection of branch migration in individual molecules. Using appropriately designed HJ constructs we were able to follow junction branch migration at the single-molecule level. Branch migration is detected as a stepwise random process with the overall kinetics dependent on Mg2+ concentration. We developed a theoretical approach to analyze the mechanism of HJ branch migration. The data show steps in which the junction flips between conformations favorable to branch migration and conformations unfavorable to it. In the favorable conformation (the extended HJ geometry), the branch can migrate over several base pairs detected, usually as a single large step. Mg2+ cations stabilize folded conformations and stall branch migration for a period considerably longer than the hopping step. The conformational flip and the variable base pair hopping step provide insights into the regulatory mechanism of genetic processes involving HJs.

Enhancement of pairing in a boson-fermion model for coupled ladders

Motivated by the presence of various charge inhomogeneities in strongly correlated systems of coupled ladders, a model of spatially separated bosonic and fermionic degrees of freedom is numerically studied. In this model, bosonic chains are connected to fermionic chains by two types of generalized Andreev couplings. It is shown that for both types of couplings the long-distance pairing correlations are enhanced. Near quarter filling, this effect is much larger for the splitting of a pair in electrons which go to the two neighboring fermionic chains than for a pair hopping process. It is argued that the pairing enhancement is a result of the nearest neighbor Coulomb repulsion which tunes the competition between pairing and charge ordering.

Effective low-energy theory of superconductivity in carbon nanotube ropes

We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature ${T}_{c}$ below the mean-field value, and a temperature-dependent resistance below ${T}_{c}$. We compare our theoretical results to recent experimental data of Kasumov et al. [Phys. Rev. B 68, 214521 (2003)] for the sub-${T}_{c}$ resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit.