arXiv subjects

Douglas J. Scalapino

Publications and source records attributed to Douglas J. Scalapino.

At least 19 recordsLinked to original sources

arXiv2023

Density-matrix-renormalization-group-based downfolding of the three-band Hubbard model: the importance of density-assisted hopping

Typical Wannier-function downfolding starts with a mean-field or density functional set of bands to construct the Wannier functions. Here we carry out a controlled approach, using DMRG-computed natural orbital bands, to downfold the three-band Hubbard model to an effective single band model. A sharp drop-off in the natural orbital occupancy at the edge of the first band provides a clear justification for a single-band model. Constructing Wannier functions from the first band, we compute all possible two-particle terms and retain those with significant magnitude. The resulting single-band model includes two-site density-assisted hopping terms with $t_n \sim 0.6 t$. These terms lead to a reduction of the ratio $U/t_{\rm eff}$, and are important in capturing the doping-asymmetric carrier mobility, as well as in enhancing the pairing in a single-band model for the hole-doped cuprates.

cond-mat.str-el↗

arXiv2022

Pairing Properties of the $t$-$t'$-$t''$-$J$ model

We study the pairing properties of the two-dimensional $t$-$t'$-$t''$-$J$ model, where $t'$ and $t''$ are second and third neighbor hoppings, at a doping level $x\approx0.1$. Recent studies of the $t$-$t'$-$J$ model find strong pairing for $t'>0$, associated with electron doping, but an absence of pairing for $t'<0$ associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parameterizations for the cuprates estimate a $t''$ comparable to $t'$, which, in principle, might fix this discrepancy. However, we find that it does not; we observe a suppression of pairing for the hole-doped system ($t'<0, t''>0$) while for the electron-doped system ($t'>0, t''<0$) $d$-wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band $t$-$t'$-$J$ model capable of describing the pairing in the hole doped system.

cond-mat.supr-con↗

arXiv2021

Ground State Phase Diagram of the $t$-$t'$-$J$ model

We report results of large scale ground state density matrix renormalization group(DMRG) calculations on $t$-$t'$-$J$ cylinders with circumferences 6 and 8. We determine a rough phase diagram which appears to approximate the 2D system. While for many properties, positive and negative $t'$ values ($t'/t = \pm 0.2$) appear to correspond to electron and hole doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The $t'<0$ (hole doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi-surface of the hole doped cuprates. However, we find $t'<0$ strongly suppresses superconductivity. The $t'>0$ (electron doped) region shows the expected circular Fermi pocket of holes around the $(π,π)$ point and a broad low-doped region of coexisting antiferromagnetism and $d$-wave pairing with a strong triplet $p$ component at wave-vector $(π,π)$ induced by the antiferromagnetism and $d$-wave pairing. The pairing for the electron low-doped system with $t'>0$ is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker $d$-wave pairing and striped $p$-wave pairing appears. In a small doping region near $x=0.08$ for $t'\sim-0.2$, we find a new type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

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arXiv2020

Effects of momentum-dependent quasiparticle renormalization on the gap structure of iron-based superconductors

We discuss the influence of momentum-dependent correlations on the superconducting gap structure in iron-based superconductors. Within the weak coupling approach including self-energy effects at the one-loop spin-fluctuation level, we construct a dimensionless pairing strength functional which includes the effects of quasiparticle renormalization. The stationary solution of this equation determines the gap function at $T_c$. The resulting equations represent the simplest generalization of spin fluctuation pairing theory to include the effects of an anisotropic quasiparticle weight. We obtain good agreement with experimentally observed anisotropic gap structures in LiFeAs, indicating that the inclusion of quasiparticle renormalization effects in the existing weak-coupling theories can account for the observed anomalies in the gap structure of Fe-based superconductors.

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arXiv2020

The overdoped end of the cuprate phase diagram

Studying the disappearance of superconductivity at the end of the overdoped region of the cuprate phase diagram offers a different approach for investigating the interaction which is responsible for pairing in these materials. In the underdoped region this question is complicated by the presence of charge and stripe ordered phases as well as the pseudogap. In the overdoped region the situation appears simpler with only a normal phase, a superconducting phase and impurity scattering. Here, for the overdoped region, we report the results of a combined dynamic cluster approximation (DCA) and a weak Born impurity scattering calculation for a $t-t'-U$ Hubbard model. We find that a decrease in the $d$-wave pairing strength of the two-particle scattering vertex is closely coupled to changes in the momentum and frequency structure of the magnetic spin fluctuations as the system is overdoped. Treating the impurity scattering within a disordered BCS $d$-wave approximation, we see how the combined effects of the decreasing $d$-wave pairing strength and weak impurity scattering lead to the end of the $T_c$ dome.

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arXiv2019

Effective pairing interaction in a system with an incipient band

The nature and mechanism of superconductivity in the extremely electron-doped FeSe based superconductors continues to be a matter of debate. In these systems, the hole-like band has moved below the Fermi energy, and various spin-fluctuation theories involving pairing between states near the electron Fermi surface and states of this incipient band have been proposed. Here, using a dynamic cluster quantum Monte Carlo calculation for a bilayer Hubbard model we show that the pairing in these systems can be understood in terms of an effective retarded attractive interaction between electrons near the electron Fermi surface.

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arXiv2018

Pairfield Fluctuations of the 2D Hubbard Model

At temperatures above the superconducting transition temperature the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here we study the d-wave pairfield susceptibility of a 2D Hubbard model for dopings which have a pseudogap (PG) and for dopings which do not. One knows that in both cases there will be a region of Kosterlitz-Thouless fluctuations as the transition at $T_{KT}$ is approached. Above this region we find evidence for Emery-Kivelson phase fluctuations for dopings with a PG and Gaussian amplitude fluctuations for dopings without a PG.

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arXiv2018

Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study

The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, $E_F$, which are still above the SC transition. We find that the SC susceptibility at low $T$ agrees quantitatively with the ME theory up to a dimensionless electron-phonon coupling $λ_0 \approx 0.4$ but deviates dramatically for larger $λ_0$. We find that for large $λ_0$ and small phonon frequency $ω_0 \ll E_F$ CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.

cond-mat.str-el↗

arXiv2017

Microscopic pairing fingerprint of the iron-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$

Resolving the microscopic pairing mechanism and its experimental identification in unconventional superconductors is among the most vexing problems of contemporary condensed matter physics. We show that Raman spectroscopy provides an avenue for this quest by probing the structure of the pairing interaction at play in an unconventional superconductor. As we study the spectra of the prototypical Fe-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$ for $0.22\le x \le 0.70$ in all symmetry channels, Raman spectroscopy allows us to distill the leading $s$-wave state. In addition, the spectra collected in the $B_{1g}$ symmetry channel reveal the existence of two collective modes which are indicative of the presence of two competing, yet sub-dominant, pairing tendencies of $d_{x^2-y^2}$ symmetry type. A comprehensive functional Renormalization Group (fRG) and random-phase approximation (RPA) study on this compound confirms the presence of the two sub-leading channels, and consistently matches the experimental doping dependence of the related modes. The synopsis of experimental evidence and theoretical modelling supports a spin-fluctuation mediated superconducting pairing mechanism.

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arXiv2017

Decrease of d-wave pairing strength in spite of the persistence of magnetic excitations in the overdoped Hubbard model

Evidence for the presence of high energy magnetic excitations in overdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) has raised questions regarding the role of spin-fluctuations in the pairing mechanism. If they remain present in overdoped LSCO, why does $T_c$ decrease in this doping regime? Here, using results for the dynamic spin susceptibility ${\rm Im}χ(q,ω)$ obtained from a determinantal quantum Monte Carlo (DQMC) calculation for the Hubbard model we address this question. We find that while high energy magnetic excitations persist in the overdoped regime, they lack the momentum to scatter pairs between the anti-nodal regions. It is the decrease in the spectral weight at large momentum transfer, not observed by resonant inelastic X-ray scattering (RIXS), which leads to a reduction in the $d$-wave spin-fluctuation pairing strength.

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arXiv2017

Role of vertex corrections in the matrix formulation of the random phase approximation for the multiorbital Hubbard model

In the framework of a multiorbital Hubbard model description of superconductivity, a matrix formulation of the superconducting pairing interaction that has been widely used is designed to treat spin, charge and orbital fluctuations within a random phase approximation (RPA). In terms of Feynman diagrams, this takes into account particle-hole ladder and bubble contributions as expected. It turns out, however, that this matrix formulation also generates additional terms which have the diagrammatic structure of vertex corrections. Here we examine these terms and discuss the relationship between the matrix-RPA superconducting pairing interaction and the Feynman diagrams that it sums.

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arXiv2016

s$_\pm$ pairing near a Lifshitz transition

Observation of robust superconductivity in some of the iron based superconductors in the vicinity of a Lifshitz point where a spin density wave instability is suppressed as the {hole} band drops below the Fermi energy raise questions for spin-fluctuation theories. Here we discuss spin-fluctuation pairing for a bilayer Hubbard model, which goes through such a Lifshitz transition. We find s$_\pm$ pairing with a transition temperature that peaks beyond the Lifshitz point and a gap function that has essentially the same magnitude but opposite sign on the incipient hole band as it does on the electron band that has a Fermi surface.

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arXiv2013

Quasi-Particle Interference Probe of the Self-Energy

Quasi-particle interference (QPI) measurements have provided a powerful tool for determining the momentum dependence of the gap of unconventional superconductors. Here we examine the possibility of using such measurements to probe the frequency and momentum dependence of the electron self-energy. For illustration, we calculate the QPI response function for a cuprate-like Fermi surface with an electron self-energy from an RPA approximation. Then we try to reextract the self-energy from the dispersion of the peaks in the QPI response function using different approaches. We show that in principle it is possible to extract the self-energy from the QPI response for certain nested momentum directions. We discuss some of the limitations that one faces.

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arXiv2012

First-principles band structure and FLEX approach to the pressure effect on $T_c$ of the cuprate superconductors

High-temperature cuprate superconductors have been known to exhibit significant pressure effects. In order to fathom the origin of why and how Tc is affected by pressure, we have recently studied the pressure effects on Tc adoptig a model that contains two cupper d-orbitals derived from first-principles band calculations, where the dz2 orbital is considere on top of the usually considered dx2-y2 orbital. In that paper, we have identified two origins for the Tc enhancement under hydrostatic pressure: (i) while at ambient pressure the smaller the hybridization of other orbital components the higher the Tc, an application of pressure acts to reduce the multiorbital mxing on the Fermi surface, which we call the orbital distillation effects, and (ii) the increase of the band width with pressure also contributes to the enhancement. In the present paper, we further elabolrate the two points. As for point (i), while the reduction of the apical oxygen height under pressure tends to increase the dz2 mixture, hence to lower Tc, here we show that this effect is strongly reduced in bi-layer materials due to the pyramidal coordination of oxygen atoms. As for point (ii), we show that the enhancement of Tc due to the increase in the band width is caused by the effect that the many-body renormalization arising from the self-energy is reduced.

cond-mat.supr-con↗

arXiv2012

Multiorbital analysis of the effects of uniaxial and hydrostatic pressure on $T_c$ in the single-layered cuprate superconductors

The origin of uniaxial and hydrostatic pressure effects on $T_c$ in the single-layered cuprate superconductors is theoretically explored. A two-orbital model, derived from first principles and analyzed with the fluctuation exchange approximation gives axial-dependent pressure coefficients, $\partial T_c/\partial P_a>0$, $\partial T_c/\partial P_c<0$, with a hydrostatic response $\partial T_c/\partial P>0$ for both La214 and Hg1201 cuprates, in qualitative agreement with experiments. Physically, this is shown to come from a unified picture in which higher $T_c$ is achieved with an "orbital distillation", namely, the less the $d_{x^2-y^2}$ main band is hybridized with the $d_{z^2}$ and $4s$ orbitals higher the $T_c$. Some implications for obtaining higher $T_c$ materials are discussed.

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arXiv2004

The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction

The gap function phi(k,omega), determined from a Lanczos calculation for a doped 2-leg t-J ladder, is used to provide insight into the spatial and temporal structure of the pairing interaction. It implies that this interaction is a local near-neighbor coupling which is retarded. The onset frequency of the interaction is set by the energy of an S=1 magnon-hole-pair and it is spread out over a frequency region of order the bandwith.

cond-mat.str-el↗

arXiv2004

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a Density Matrix Renormalization Group (DMRG) study of the ground-state properties of spin-1/2 frustrated $J_1-J_3$ Heisenberg $n_l$-leg ladders (with $n_l$ up to 8). For strong frustration ($J_3/J_1\simeq 0.5$), both even- and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.

cond-mat.str-el↗

arXiv2001

Friedel Oscillations and Charge Density Waves in Chains and Ladders

The density matrix renormalization group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is groundstate charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyse these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscillations from true charge density waves. We also discuss a different approach to extracting the correlation exponent from the finite size spectrum which uses exclusively open boundary conditions and can therefore take advantage of data for much larger system sizes. A general discussion of the Friedel oscillation wave-vectors is given, and a convenient Fourier transform technique is used to determine it. DMRG results are analysed on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the existence of a long-ranged charge density wave state in the t-J ladder at a filling of n=0.75 and near J/t \approx 0.25.

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