Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1804.09271 · Physical review. B./Physical review. B

Direct connection between Mott insulators and d -wave high-temperature superconductors revealed by continuous evolution of self-energy poles

志朗 酒井, Marcello Civelli, Masatoshi Imada

Published Nov 7, 2018• 22 citations
arXivHTMLPDF

Abstract

The high-temperature superconductivity in copper oxides emerges when carriers are doped into the parent Mott insulator. This well-established fact has, however, eluded a microscopic explanation. Here we show that the missing link is the self-energy pole in the energy-momentum space. Its continuous evolution with doping directly connects the Mott insulator and high-temperature superconductivity. We show this by numerically studying the extremely small doping region close to the Mott insulating phase in a standard model for cuprates, the two-dimensional Hubbard model. We first identify two relevant self-energy structures in the Mott insulator: the pole generating the Mott gap and a relatively broad peak generating the so-called waterfall structure, which is another consequence of strong correlations present in the Mott insulator. We next reveal that either the Mott-gap pole or the waterfall structure (the feature at the energy closer to the Fermi level) directly transforms itself into another self-energy pole at the same energy and momentum when the system is doped with carriers. The anomalous self-energy yielding the superconductivity is simultaneously born exactly at this energy-momentum point. Thus created self-energy pole, interpreted as arising from a hidden fermionic excitation, continuously evolves upon further doping and considerably enhances the superconductivity. Above the critical temperature, the same self-energy pole generates a pseudogap in the normal state. We thus elucidate a unified Mott-physics mechanism, where the self-energy structure inherent to the Mott insulator directly gives birth to both the high critical superconducting temperature and pseudogap.

DOI
10.1103/physrevb.98.195109

Related papers

Nonperturbative Calculations for Spectroscopic Properties of Cuprate High-Temperature Superconductors

志朗 酒井

We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments on high-temperature superconducting cuprates. The unbiased nonperturbative theories have revealed the existence of a self-energy singularity in slightly doped Mott insulators, which is responsible for both the pseudogap formation and high-temperature superconductivity. The self-energy pole traces back to the Mott gap at zero doping, underscoring that Mott physics lies at the heart of both the pseudogap and high-temperature superconductivity. This mechanism of the pseudogap relies neither on competing order nor preformed pair while that of the high superconducting transition temperature does not necessitate a bosonic glue to mediate Cooper pairing. Instead, both mechanisms are linked to the singular self-energy inherent to the Mott insulator. The presence of the self-energy pole accounts for various spectroscopic anomalies reported so far in experiments, deforming the spectral structure in a manner beyond a simple mass renormalization. The low-energy electron dynamics, as computed with the self-energy pole, suggest the existence of a hidden fermionic excitation coupling to quasiparticles.

Journal of the Physical Society of Japan•Jul 12, 2023•15 citations

Doped high- T c cuprate superconductors elucidated in the light of zeros and poles of the electronic Green’s function

志朗 酒井, Yukitoshi Motome, Masatoshi Imada

We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-${T}_{c}$ superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-${T}_{c}$ cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a $d$-wavelike structure only below the Fermi level while it retains non-$d$-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-$d$-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the $d$-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.

arXiv:1004.2569•Physical Review B•Oct 4, 2010•113 citations

Self-energy pole optimization of superconductivity in the bilayer Hubbard model

Taka-Shi Fujiwara, 志朗 酒井, Ryotaro Arita

We study the real-frequency structure of the self-energy in the bilayer Hubbard model, using the dynamical cluster approximation. At half filling, the Mott insulator-band insulator (MI-BI) crossover involves a rearrangement of self-energy poles between the bonding and antibonding bands; these poles cross as the interlayer hopping $t_{\perp}$ is varied. Upon doping, this pole structure produces a band-selective pseudogap and enhances $s^{\pm}$-wave superconductivity. The order parameter is maximized near the MI-BI boundary, where low-energy anomalous self-energy poles develop simultaneously in both bands and cooperatively enhance the pairing. We further show that these self-energy poles can be interpreted as emergent fermionic excitations, offering an enhanced-pairing mechanism in common with the single-layer Hubbard model. The controllability of these poles through $t_{\perp}$ makes the bilayer system an unconventional platform for optimizing strongly correlated superconductivity.

arXiv:2607.24549•Jul 27, 2026•0 citations

Doping-driven evolution of the superconducting state from a doped Mott insulator: Cluster dynamical mean-field theory

Marcello Civelli

In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard $d$-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.

arXiv:0808.3948•Physical Review B•May 15, 2009•54 citations

Hidden fermionic excitation in the superconductivity of the strongly attractive Hubbard model

志朗 酒井, Marcello Civelli, Yusuke Nomura +1 more

We study the attractive Hubbard model within the dynamical mean-field theory, to elucidate how the pseudogap and superconductivity at strong attractive interaction are related to those found in the repulsive Hubbard model, and thereby to bridge cold fermions and cuprate high-temperature superconductors from a microscopic point of view. We propose that a unified understanding is obtained by investigating single-particle excitation dynamics, in which emergent and hidden fermions coupled to quasiparticles consistently account for the numerical results in both attractive and repulsive cases. In the attractive case, the quasiparticle dynamics is observable by virtually breaking a tightly bound pair, where we find two qualitatively different regions crossing over each other within the strong-coupling superconductivity phase. Among them, the region close to the critical temperature shares characteristic dynamics with the repulsive interaction case, where the normal and anomalous parts of the self-energy show strong low-energy peaks while they are hidden in the quasiparticle spectral weight. These prominent self-energy peaks are understood by the coupling of the quasiparticle to the hidden fermionic excitation, emergent from a strong-coupling effect. The pseudogap above the critical temperature is also accounted for by the same hidden fermion.

arXiv:1507.06409•Physical Review B•Nov 4, 2015•18 citations

Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators

Lorenzo Fratino, P. Sémon, G. Sordi +1 more

High-temperature superconductivity emerges upon doping a state of matter that is insulating because of interactions. A widely studied model considers one orbital per ${\mathrm{CuO}}_{2}$ unit cell on a square lattice with a strong intraorbital repulsion that leads to a so-called Mott-Hubbard insulator. Here we solve a model that takes into account, within each unit cell, two oxygen orbitals where there is no electron-electron repulsion and a copper orbital with strong electron-electron repulsion. The insulating phase is a so-called charge-transfer insulator, not a Mott-Hubbard insulator. Using cluster dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver and 12 atoms per cluster, we report the normal and superconducting phase diagram of this model as a function of doping, interaction strength, and temperature. As expected, the three-orbital model is consistent with the experimental observation that doped holes are located predominantly on oxygens, a result that goes beyond the one-orbital model. Nevertheless, the phase boundary between pseudogap and correlated metal, the Widom line, and the origin of the pairing energy (kinetic vs potential) are similar to the one-orbital model, demonstrating that these are emergent phenomena characteristic of doped Mott insulators, independently of many microscopic details. Broader implications are discussed.

arXiv:1602.02280•Physical review. B./Physical review. B•Jun 24, 2016•31 citations
The high-temperature superconductivity in copper oxides emerges when carriers are doped into the parent Mott insulator. This well-established fact has, however, eluded a microscopic explanation. Here we show that the missing link is the self-energy pole in the energy-momentum space. Its continuous evolution with doping directly connects the Mott insulator and high-temperature superconductivity. We show this by numerically studying the extremely small doping region close to the Mott insulating phase in a standard model for cuprates, the two-dimensional Hubbard model. We first identify two relevant self-energy structures in the Mott insulator: the pole generating the Mott gap and a relatively broad peak generating the so-called waterfall structure, which is another consequence of strong correlations present in the Mott insulator. We next reveal that either the Mott-gap pole or the waterfall structure (the feature at the energy closer to the Fermi level) directly transforms itself into another self-energy pole at the same energy and momentum when the system is doped with carriers. The anomalous self-energy yielding the superconductivity is simultaneously born exactly at this energy-momentum point. Thus created self-energy pole, interpreted as arising from a hidden fermionic excitation, continuously evolves upon further doping and considerably enhances the superconductivity. Above the critical temperature, the same self-energy pole generates a pseudogap in the normal state. We thus elucidate a unified Mott-physics mechanism, where the self-energy structure inherent to the Mott insulator directly gives birth to both the high critical superconducting temperature and pseudogap.
We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments on high-temperature superconducting cuprates. The unbiased nonperturbative theories have revealed the existence of a self-energy singularity in slightly doped Mott insulators, which is responsible for both the pseudogap formation and high-temperature superconductivity. The self-energy pole traces back to the Mott gap at zero doping, underscoring that Mott physics lies at the heart of both the pseudogap and high-temperature superconductivity. This mechanism of the pseudogap relies neither on competing order nor preformed pair while that of the high superconducting transition temperature does not necessitate a bosonic glue to mediate Cooper pairing. Instead, both mechanisms are linked to the singular self-energy inherent to the Mott insulator. The presence of the self-energy pole accounts for various spectroscopic anomalies reported so far in experiments, deforming the spectral structure in a manner beyond a simple mass renormalization. The low-energy electron dynamics, as computed with the self-energy pole, suggest the existence of a hidden fermionic excitation coupling to quasiparticles.
We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-Tc{T}_{c}Tc​ superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-Tc{T}_{c}Tc​ cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a ddd-wavelike structure only below the Fermi level while it retains non-ddd-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-ddd-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the ddd-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.
We study the real-frequency structure of the self-energy in the bilayer Hubbard model, using the dynamical cluster approximation. At half filling, the Mott insulator-band insulator (MI-BI) crossover involves a rearrangement of self-energy poles between the bonding and antibonding bands; these poles cross as the interlayer hopping t⊥t_{\perp}t⊥​ is varied. Upon doping, this pole structure produces a band-selective pseudogap and enhances s±s^{\pm}s±-wave superconductivity. The order parameter is maximized near the MI-BI boundary, where low-energy anomalous self-energy poles develop simultaneously in both bands and cooperatively enhance the pairing. We further show that these self-energy poles can be interpreted as emergent fermionic excitations, offering an enhanced-pairing mechanism in common with the single-layer Hubbard model. The controllability of these poles through t⊥t_{\perp}t⊥​ makes the bilayer system an unconventional platform for optimizing strongly correlated superconductivity.
In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard ddd-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.
We study the attractive Hubbard model within the dynamical mean-field theory, to elucidate how the pseudogap and superconductivity at strong attractive interaction are related to those found in the repulsive Hubbard model, and thereby to bridge cold fermions and cuprate high-temperature superconductors from a microscopic point of view. We propose that a unified understanding is obtained by investigating single-particle excitation dynamics, in which emergent and hidden fermions coupled to quasiparticles consistently account for the numerical results in both attractive and repulsive cases. In the attractive case, the quasiparticle dynamics is observable by virtually breaking a tightly bound pair, where we find two qualitatively different regions crossing over each other within the strong-coupling superconductivity phase. Among them, the region close to the critical temperature shares characteristic dynamics with the repulsive interaction case, where the normal and anomalous parts of the self-energy show strong low-energy peaks while they are hidden in the quasiparticle spectral weight. These prominent self-energy peaks are understood by the coupling of the quasiparticle to the hidden fermionic excitation, emergent from a strong-coupling effect. The pseudogap above the critical temperature is also accounted for by the same hidden fermion.
High-temperature superconductivity emerges upon doping a state of matter that is insulating because of interactions. A widely studied model considers one orbital per CuO2{\mathrm{CuO}}_{2}CuO2​ unit cell on a square lattice with a strong intraorbital repulsion that leads to a so-called Mott-Hubbard insulator. Here we solve a model that takes into account, within each unit cell, two oxygen orbitals where there is no electron-electron repulsion and a copper orbital with strong electron-electron repulsion. The insulating phase is a so-called charge-transfer insulator, not a Mott-Hubbard insulator. Using cluster dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver and 12 atoms per cluster, we report the normal and superconducting phase diagram of this model as a function of doping, interaction strength, and temperature. As expected, the three-orbital model is consistent with the experimental observation that doped holes are located predominantly on oxygens, a result that goes beyond the one-orbital model. Nevertheless, the phase boundary between pseudogap and correlated metal, the Widom line, and the origin of the pairing energy (kinetic vs potential) are similar to the one-orbital model, demonstrating that these are emergent phenomena characteristic of doped Mott insulators, independently of many microscopic details. Broader implications are discussed.