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:0808.3948 · Physical Review B

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

Marcello Civelli

Published May 15, 2009• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.79.195113

Related papers

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

Valence bond dynamical mean-field theory of doped Mott insulators with nodal/antinodal differentiation

Michel Ferrero, Pablo S. Cornaglia, Lorenzo De Leo +3 more

We introduce a valence bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates. We derive a low-energy description of these effects using a generalization of the slave-boson method.

arXiv:0806.4383•Europhysics Letters (EPL)•Mar 1, 2009•67 citations

Emergence of quasiparticles in a doped Mott insulator

Yao Wang, Yu He, Krzysztof Wohlfeld +9 more

Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.

arXiv:1909.09288•Communications Physics•Nov 13, 2020•17 citations

Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model

Emanuel Gull, Michel Ferrero, Olivier Parcollet +2 more

Cluster dynamical mean-field calculations based on 2-, 4-, 8-, and 16-site clusters are used to analyze the doping-driven metal-insulator transition in the two-dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole-doped side than on the electron-doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-${T}_{c}$ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi-liquid renormalizations are larger and the electron self-energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap on some parts of the Fermi surface but gapless behavior in other parts. On the electron-doped side the partially gapped regime does not occur, and the momentum dependence of the electron self-energy is less pronounced. Implications for the high-${T}_{c}$ cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.

arXiv:1007.2592•Physical Review B•Oct 1, 2010•192 citations

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

S. S. Kancharla, Bumsoo Kyung, David Sénéchal +4 more

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and $d$-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The $d$-wave order parameter is found to scale like the superexchange coupling $J$ for on-site interaction $U$ comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs ${T}_{c}∕{T}_{c}^{\mathit{max}}$ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of $d$-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, $d$-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.

arXiv:cond-mat/0508205•Physical Review B•May 23, 2008•184 citations

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

SungKun Kim, Hunpyo Lee

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Journal of the Korean Physical Society•Jun 1, 2017•2 citations
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 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 introduce a valence bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates. We derive a low-energy description of these effects using a generalization of the slave-boson method.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
Cluster dynamical mean-field calculations based on 2-, 4-, 8-, and 16-site clusters are used to analyze the doping-driven metal-insulator transition in the two-dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole-doped side than on the electron-doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-Tc{T}_{c}Tc​ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi-liquid renormalizations are larger and the electron self-energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap on some parts of the Fermi surface but gapless behavior in other parts. On the electron-doped side the partially gapped regime does not occur, and the momentum dependence of the electron self-energy is less pronounced. Implications for the high-Tc{T}_{c}Tc​ cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.