Nearest-neighbor Coulomb Interaction Research Articles

Topological Phase Diagram of an Interacting Kitaev Chain: Mean Field versus DMRG Study

In this work, we study the topological phase transitions of a Kitaev chain generalized by the addition of nearest-neighbor Coulomb interaction. We show the presence of a robust topological phase as a function of the interaction strength and of the on-site energy with associated non-zero energy Majorana states localized at the chain edges. We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. Temperature robustness within a physically relevant threshold has also been demonstrated. These findings shed light on an entire class of topological interacting one-dimensional systems in which the effects of residual Coulomb interactions play a relevant role.

Superconductivity from repulsive interactions on the kagome lattice

The discovery of superconductivity in layered vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) has added a new family of materials to the growing class of possible unconventional superconductors. However, the nature of the superconducting pairing in these materials remains elusive. We present a microscopic theoretical study of the leading superconducting instabilities on the kagome lattice based on spin- and charge-fluctuation mediated Cooper pairing. The applied methodology includes effects of both on-site and nearest-neighbor repulsive Coulomb interactions. Near the upper van Hove filling -- relevant for the $A$V$_3$Sb$_5$ materials -- we find a rich phase diagram with several pairing symmetries being nearly degenerate. In particular, while a substantial fraction of the phase diagram is occupied by a spin-singlet order parameter transforming as a two-dimensional irreducible representation of the point group, several nodal spin-triplet pairing states remain competitive. We compute the band and interaction parameter-dependence of the hierarchy of the leading superconducting instabilities, and determine the detailed momentum dependence of the resulting preferred gap structures. Crucially, for moderate values of the interaction parameters, the individual pairing states depend strongly on momentum and exhibit multiple nodes on the Fermi surface. We discuss the properties of these superconducting gap structures in light of recent experimental developments of the $A$V$_3$Sb$_5$ materials.

Topological superconductivity in Sn/Si(111) driven by nonlocal Coulomb interactions

Superconductivity was recently observed in boron-doped $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{Sn}/\mathrm{Si}(111)$. The material can be described by an extended Hubbard model on a triangular lattice. Here, we use the random-phase approximation to investigate the charge and spin fluctuations as well as the superconducting properties of the system with respect to filling and the relative strength of the extended versus the on-site Hubbard interactions. Our calculations reveal that near half-filling and weak extended Hubbard interactions, the superconducting ground state exhibits chiral $d$-wave pairing. Far from half filling and for stronger nearest-neighbor Coulomb interactions, the system shows chiral $p$-wave (hole-doping) and $f$-wave (electron-doping) pairings. The dependence of the pairing symmetry on the extended Hubbard interactions suggests that charge fluctuations play an important role in the formation of Cooper pairs. Finally, the temperature dependence of the Knight shift is calculated for all observed superconducting textures and put forward as an experimental method to examine the symmetry of the superconducting gap function.

Required nearest-neighbor Coulomb interactions for a charge-ordered phase transition in (TMTTF)2MF6 with inversion symmetry breaking in crystal

We examined the charge-ordered phase transition in (TMTTF)2MF6 systems by exact diagonalization of an extended Hubbard model Hamiltonian whose parameters were referred from quantum chemical calculations with periodic boundary conditions along with inversion symmetry breaking in the crystal. We showed that a nearest-neighbor Coulomb interactions for the charge-ordered phase transition should be twice as much as those previously obtained by fitting for conductivities with a minute inversion symmetry breaking of the crystal (∼0.01 Å) which was confirmed by a recent experimental study.

Dynamical cluster approximation study of electron localization in the extended Hubbard model

We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\times 2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes "screening" effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$. We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes and document the different correlation aspects of charge order and Mott states.

Interorbital nematicity and the origin of a single electron Fermi pocket in FeSe

The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the $Y$ point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. Here, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of interorbital ${d}_{xz}\text{\ensuremath{-}}{d}_{xy}$ and ${d}_{yz}\text{\ensuremath{-}}{d}_{xy}$ character, with spontaneously broken amplitudes for these two components. This interorbital nematic order naturally leads to distinct hybridization gaps at the $X$ and $Y$ points of the 1-Fe Brillouin zone, and may thereby produce highly anisotropic Fermi surfaces with only a single electron pocket at one of these momentum-space locations. The associated superconducting gap structure obtained with the generated low-energy electronic band structure from spin-fluctuation mediated pairing agrees well with that measured experimentally. Finally, from a comparison of the computed spin susceptibility to available neutron scattering data, we discuss the necessity of additional self-energy effects, and explore the role of orbital-dependent quasiparticle weights as a minimal means to include them.

DMRG study of exciton condensation in the extended Falicov-Kimball model

The formation and condensation of excitonic bound states of conduction-band electrons and valence-band holes surely belongs to one of the most exciting ideas of contemporary solid state physics. In this short review we present the latest progress in this field reached by the density-matrix-renormalization-group (DMRG) calculations within various extensions of the Falicov-Kimball model. Particular attention is paid to a description of crucial mechanisms (interactions) that affect the stability of the excitonic phase, and namely: (i) the interband $d$-$f$ Coulomb interaction, (ii) the $f$-electron hopping, (iii) the nonlocal hybridization with odd and even parity, (iv) combined effects of the local and nonlocal hybridization, (v) the nearest-neighbor Coulomb interaction between $d$ and $f$ electrons and (vi) the correlated hopping. The relevance of numerical results obtained within different extensions of the Falicov-Kimball model for a description of the real $d$-$f$ materials is widely discussed.

Quantum Monte Carlo study of magnetic ordering and superconducting pairing symmetry in twisted bilayer graphene

To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard $U$ is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the $d+id$ symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction $V$ results in a suppression of the $d+id$ superconductivity, but it can survive in the small $V$ regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.

Maximized electron interactions at the magic angle in twisted bilayer graphene

The electronic properties of heterostructures of atomically thin van der Waals crystals can be modified substantially by moiré superlattice potentials from an interlayer twist between crystals1,2. Moirétuning of the band structure has led to the recent discovery of superconductivity3,4 and correlated insulating phases5 in twisted bilayer graphene (TBG) near the 'magic angle' of twist of about 1.1 degrees, with a phase diagram reminiscent of high-transition-temperature superconductors. Here we directly map the atomic-scale structural and electronic properties of TBG near the magic angle using scanning tunnelling microscopy and spectroscopy. We observe two distinct van Hove singularities (VHSs) in the local density of states around the magic angle, with an energy separation of 57millielectronvolts that drops to 40millielectronvolts with high electron/hole doping. Unexpectedly, the VHS energy separation continues to decrease with decreasing twist angle, with a lowest value of 7 to 13 millielectronvolts at a magic angle of 0.79 degrees. More crucial to the correlated behaviour of this material, we find that at the magic angle, the ratio of the Coulomb interaction to the bandwidth of each individual VHS (U/t) is maximized, which is optimal for electronic Cooper pairing mechanisms. When doped near the half-moiré-band filling, a correlation-induced gap splits the conduction VHS with a maximum size of 6.5 millielectronvolts at 1.15 degrees, dropping to 4 millielectronvolts at 0.79 degrees. We capture the doping-dependent and angle-dependent spectroscopy results using a Hartree-Fock model, which allows us to extract the on-site and nearest-neighbour Coulomb interactions. This analysis yields a U/t of order unity indicating that magic-angle TBG is moderately correlated. In addition, scanning tunnelling spectroscopy maps reveal an energy- and doping-dependent three-fold rotational-symmetry breaking of the local density of states in TBG, with the strongest symmetry breaking near the Fermi level and further enhanced when doped to the correlated gap regime. This indicates the presence of a strong electronic nematic susceptibility or even nematic order in TBG in regions of the phase diagram where superconductivity is observed.

Competing superconducting phases in the interacting two-dimensional electron gas with strong Rashba spin-orbit coupling

In this work we study interacting electrons on square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consider the repulsive onsite Hubbard and nearest-neighbor coulomb interactions, the so called extended Hubbard model. To examine the superconducting instability we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings, and found that while the $d_{xy}$ and $d_{x^2-y^2}$ symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instability. The possibility of topological superconductivity and triplet pairing is also discussed.

Quantum phase transitions in the dimerized extended Bose-Hubbard model

We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that the phase boundaries of the Haldane phase to Mott insulator and density-wave states belong to the Gaussian and Ising universality classes with central charges $c=1$ and $c=1/2$, respectively, and merge in a tricritical point. Interestingly we can demonstrate a direct Ising quantum phase transition between the dimerized Mott and density-wave phases above the tricritical point. The corresponding transition line terminates at a critical end point that belongs to the universality class of the dilute Ising model with $c=7/10$. At even stronger Coulomb interactions the transition becomes first order.

Microwave signatures of the Z2 and Z4 fractional Josephson effects

We present a many-body exact diagonalization study of the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements.

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like critical phase for the charge degrees of freedom in the intermediate-temperature regime between the charge-ordered and disordered phases in two-dimensional systems with competing short-range Coulomb repulsion. As the simplest example, we investigate the extended Hubbard model with on-site and nearest-neighbor Coulomb interactions on a triangular lattice at half filling in the atomic limit by using a classical Monte Carlo method, and find a critical phase, characterized by algebraic decay of the charge correlation function, belonging to the universality class of the two-dimensional XY model with a $\mathbb{Z}_6$ anisotropy. Based on the results, we discuss possible conditions for the critical phase in materials.

Microscopic tight-binding study of the interplay between on-site and inter-site Coulomb interactions in Graphene

It is realized that the Coulomb interaction plays a vital role in describing the magnetic properties of graphene-on-substrate. We attempt here to study the competition between on-site and inter-site repulsive Coulomb interactions, with impurities at both the sub-lattices in graphene-on-substrate .The Hamiltonian describes the electron hopping up to third-nearest-neighbors within tight-binding approximation. Due to substrate effect, A-sub lattice is raised by energy and B-sub lattice acquired energy , besides impurity effects at both the sub lattices. The model consists of on-site repulsive Coulomb interaction at two sublattices with same on-site Coulomb energy U and nearest-neighbor inter-site Coulomb interactions between A and B sub lattice with inter site Coulomb energy . The Coulomb interaction is considered within Hartree-Fock type mean-field approximation. The Hamiltonian is solved by Zubarev's Green's function technique and an expression for temperature dependent difference in electron occupancies between two sub-lattices is calculated and solved self-consistency. Finally the charge gap and hence modified substrate induced gap is computed numerically by varying different physical parameters of the system like on-site and inter-site Coulomb interactions and substrate induced gap, impurity concentration and electron occupancy. It is observed that inter-site Coulomb interaction is smaller than on-site Coulomb interaction and plays an important role in describing the properties of graphene.

Charge-Density-Excitation Spectrum in the t–t′–J–V Model

We study the density-density correlation function in a large-N scheme of the t-t'-J-V model. When the nearest-neighbor Coulomb interaction V is zero, our model exhibits phase separation in a wide doping region and we obtain large spectral weight near momentum q=(0,0) at low energy, which originates from the proximity to phase separation. These features are much stronger for electron doping than for hole doping. However, once phase separation is suppressed by including a finite V, the low-energy spectral weight around q=(0,0) is substantially suppressed. Instead a sharp zero-sound mode is stabilized above the particle-hole continuum. We discuss that the presence of a moderate value of V, which is frequently neglected in the t-J model, is important to understand low-energy charge excitations especially close to q=(0,0) for electron doping. This insight should be taken into account in a future study of x-ray scattering measurements.

Polaron and bipolaron stability on paraphenylene polymers.

Polyparaphenylene is the prototypical conjugated polymer containing phenyl rings and its properties are good references for a family of derived polymers. We investigate the structure, stability, and dynamics of polarons and bipolarons in polyparaphenylene chains under an applied electric field. To do this, we use a bidimensional SSH Hamiltonian model with the Hubbard extension, i.e., with local and nearest-neighbor Coulomb interaction, which has been designed to work with general hexagonal lattices, from which polyparaphenylene can be seen as a prominent case. Using the time-dependent Hartree-Fock approximation, we calculate the structural characteristics, the maximum field strength, supported before polarons and bipolarons gets unstable, and the maximum velocity achieved by these charge carriers. We obtained the polaron and bipolaron terminal velocity to be 0.51 Å/fs and 1.15 Å/fs, respectively. The maximum field strength determined by our calculations is 0.54 mV/Å and 0.80 mV/Å, respectively. Our results are in good agreement with other theoretical methods and experiments.

Correlation Effects on Charge Order and Zero-Gap State in the Organic Conductor α-(BEDT-TTF)2I3

The effects of electron correlation in the quasi-two-dimensional organic conductor \alpha-(BEDT-TTF)2I3 are investigated theoretically by using an extended Hubbard model with on-site and nearest-neighbor Coulomb interactions. A variational Monte Carlo method is applied to study its ground-state properties. We show that there appears a nonmagnetic horizontal-stripe charge order in which nearest-neighbor correlation functions indicate a tendency toward a spin-singlet formation on the bonds with large transfer integrals along the charge-rich stripe. Under uniaxial pressure, a first-order transition from the nonmagnetic charge order to a zero-gap state occurs. Our results on a spin correlation length in the charge-ordered state suggest that a spin gap is almost unaffected by the uniaxial pressure in spite of the suppression of the charge disproportionation. The relevance of these contrasting behaviors in spin and charge degrees of freedom to recent experimental observations is discussed.

Metal–insulator transition in an one-dimensional half-filled interacting mesoscopic ring with spinless fermions: Exact results

We calculate persistent current of one-dimensional rings of fermions neglecting the spin degrees of freedom considering only nearest-neighbor Coulomb interactions with different electron fillings in both ordered and disordered cases. We treat the interaction exactly and find eigenenergies by exact diagonalization of many-body Hamiltonian and compute persistent current by numerical derivative method. We also determine Drude weight to estimate the conducting nature of the system. From our numerical results, we obtain a metal–insulator transition in half-filled case with increasing correlation strength U but away from half-filling no such transition is observed even for large U.

Criticality at the Haldane-insulator charge-density-wave quantum phase transition

Exploiting the entanglement concept within a matrix-product-state based infinite density-matrix renormalization group approach, we show that the spin-density-wave and bond-order-wave ground states of the one-dimensional half-filled extended Hubbard model give way to a symmetry-protected topological Haldane state in case an additional alternating ferromagnetic spin interaction is added. In the Haldane insulator the lowest entanglement level features a characteristic twofold degeneracy. Increasing the ratio between nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the entanglement entropy, the variation of the charge, spin and neutral gaps, and the dynamical spin/density response signal a quantum phase transition to a charge-ordered state. Below a critical point, which belongs to the universality class of the tricritical Ising model with central charge 7/10, the model is critical with $c=1/2$ along the transition line. Above this point, the transition between the Haldane insulator and charge-density-wave phases becomes first order.

Emergent topological mirror insulator int2g-orbital systems

Motivated by the itinerant band structure of high-${T}_{c}$ iron pnictides, which exhibit four Dirac cones in the bulk, we demonstrate the prospect of pnictides with transition elements to be topological insulators in two dimensions. In this report, we explore interaction-induced topological phases, in contrast to the spin-orbit-coupling interaction, as the crucial mechanism for tuning Dirac metals into ${Z}_{2}$-topological insulators protected by time reversal and mirror symmetries. We find spontaneous orbital currents generated through nearest-neighbor interorbital Coulomb interaction in the ${t}_{2g}$ manifold of the $d$ orbitals. When spin degrees of freedom are incorporated, spontaneous orbital currents lead to two stable topological phases of the ground state. The first topological insulator is an anomalous orbital Hall phase, characterized by an even Chern number, while the second topological insulator is realized by protected mirror symmetries with a ${Z}_{2}$ index.