Effect of superconductivity on the shape of flat bands

Abstract

For the first time, basing both on experimental facts and our theoretical consideration, we show that Fermi systems with flat bands should be tuned with the superconducting state. Experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity $V_F$ as a function of the temperature $T_c$ of superconduction phase transition have revealed $V_F\propto T_c\propto 1/N_s(0)$, where $N_s(0)$ is the density of states at the Fermi level. We show that the high-$T_c$ compounds $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\mathrm{x}}$ exhibit the same behavior. Such observation is a challenge to theories of high-$T_c$ superconductivity, since $V_F$ is negatively correlated with $T_c$, for $T_c\propto 1/V_F\propto N_s(0)$. We show that the theoretical idea of forming flat bands in strongly correlated Fermi systems can explain this behavior and other experimental data collected on both $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\mathrm{x}}$ and twisted bilayer graphene. Our findings place stringent constraints on theories describing the nature of high-$T_c$ superconductivity and the deformation of flat band by the superconducting phase transition.

5 pages, 2 figures

References in corpus (5)

• Scaling Behavior of Heavy Fermion Metals
• Universal Behavior of Two-Dimensional 3He at Low Temperatures
• Asymmetric tunneling, Andreev reflection and dynamic conductance spectra in strongly correlated metals
• Universal $T/B$ scaling behavior of heavy fermion compounds
• Critical magnetic fields and electron-pairing in magic-angle twisted bilayer graphene

Cited by in corpus (2)

• Common behavior of the scaled condensation energy for both high-$T_c$ and conventional superconductors
• Scaling behavior of superconductors