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arXiv:2210.10521

Temperature dependence of quasiparticle interference in ddd-wave superconductors

Harun Al Rashid, Garima Goyal, Alireza Akbari, Dheeraj Kumar Singh

Published Oct 19, 2022• 0 citations
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Abstract

We investigate the temperature dependence of quasiparticle interference in the high $T_c$-cuprates using an Exact-Diagonalization + Monte-Carlo based scheme to simulate the $d$-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition $T_c$. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

DOI
10.48550/arxiv.2210.10521

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We investigate the temperature dependence of quasiparticle interference in the high TcT_cTc​-cuprates using an Exact-Diagonalization + Monte-Carlo based scheme to simulate the ddd-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition TcT_cTc​. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.
We investigate the temperature dependence of quasiparticle interference in the high T_c T c -cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the d d -wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition T_c T c . However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.
In this paper, we study the quasiparticle scattering interference phenomenon in the presence of a single impurity within the renormalized Hubbard model. By calculating the energy and momentum dependence of the Fourier-transformed local density of states in the full Brillouin zone, we can qualitatively describe the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors using a single point-like impurity. In particular, we show that with increasing energy, the position of the peak along the nodal ([0, 0] → [ π, π ]) direction moves steadily to a large momentum region, while the position of the peak along the antinodal ([0, 0] → [ π , 0]) direction moves toward the center of the Brillouin zone.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature Tc{T}_{c}Tc​ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have ddd-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.
The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping t′t't′ is also studied.
We present determinant quantum Monte Carlo simulations of the hole-doped single-band Hubbard-Holstein model on a square lattice, to investigate how quasiparticles emerge when doping a Mott insulator (MI) or a Peierls insulator (PI). The MI regime at large Hubbard interaction UUU and small relative e-ph coupling strength $\ensuremath{\lambda}$ is quickly suppressed upon doping, by drawing spectral weight from the upper Hubbard band and shifting the lower Hubbard band towards the Fermi level, leading to a metallic state with emergent quasiparticles at the Fermi level. On the other hand, the PI regime at large $\ensuremath{\lambda}$ and small UUU persists out to relatively high doping levels. We study the evolution of the ddd-wave superconducting susceptibility with doping, and find that it increases with lowering temperature in a regime of intermediate values of UUU and $\ensuremath{\lambda}$.
The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference ΔdpΔ_{dp}Δdp​ between ddd and ppp electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when ΔdpΔ_{dp}Δdp​ decreases and the pure ddd-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate xxx contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.