The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model is investigated by the renormalization group technique. The ``Van Hove'' scenario of non-Fermi-liquid behavior for high- ${T}_{c}$ compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on $\mathrm{L}{\mathrm{a}}_{2}\mathrm{C}\mathrm{u}{\mathrm{O}}_{4}$ .The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model is investigated by the renormalization group technique. The ``Van Hove'' scenario of non-Fermi-liquid behavior for high-${T}_{c}$ compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on $\mathrm{L}{\mathrm{a}}_{2}\mathrm{C}\mathrm{u}{\mathrm{O}}_{4}$.

arXiv:cond-mat/0110516Physical Review LettersJul 24, 2002111 citations

Superconductivity near two-dimensional Van Hove singularities: A determinant quantum Monte Carlo study

Gustav Romare, Daniel J. Shaffer, Alex Levchenko +2 more

The superconducting transition temperature $T_c$ of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths $|U| \lesssim W/3$ , where $W$ is the electronic bandwidth, $T_c$ is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of $T_c$ . For $|U| \gtrsim W/3$ , the maximum $T_c$ shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal $T_c$ in the model is achieved at intermediate $U$ and at a density away from the Van Hove point.The superconducting transition temperature $T_c$ of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths $|U| \lesssim W/3$, where $W$ is the electronic bandwidth, $T_c$ is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of $T_c$. For $|U| \gtrsim W/3$, the maximum $T_c$ shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal $T_c$ in the model is achieved at intermediate $U$ and at a density away from the Van Hove point.

arXiv:2604.13161Physical review. B./Physical review. BOct 1, 20260 citations

Quantum critical behaviour in a high-Tc superconductor

D. van der Marel, H. J. A. Molegraaf, Jan Zaanen +7 more

arXiv:cond-mat/0309172NatureSep 1, 2003363 citations

High T/sub c/ superconductor as a strongly correlated state

Vladimir Z. Kresin

Aug 1, 19870 citations

{T}_{c}

compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on

\mathrm{L}{\mathrm{a}}_{2}\mathrm{C}\mathrm{u}{\mathrm{O}}_{4}

The superconducting transition temperature

T_c

of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths

|U| \lesssim W/3

, where

W

is the electronic bandwidth,

T_c

is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of

T_c

. For

|U| \gtrsim W/3

, the maximum

T_c

shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal

T_c

in the model is achieved at intermediate

U

and at a density away from the Van Hove point.