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Pseudogap-induced change in the nature of the Lifshitz transition in the two-dimensional Hubbard model

Maria C. O. Aguiar, Helena Bragança, Indranil Paul, Marcello Civelli

Abstract

We study the behavior of the density of states and the $B_{1g}$ nematic susceptibility extracted from Raman response data across the doping-driven Lifshitz transition comparing the weak and strong interaction cases. Our results were obtained using cluster dynamical mean field theory for the two-dimensional Hubbard model. In the weakly correlated Fermi liquid regime, both quantities are approximately symmetric around the Lifshitz transition doping $p_{LT}$. In the strongly correlated regime, the low-doping pseudogap leads to an asymmetric, discontinuous evolution when the Fermi surface changes from hole-like to electron-like at $p_{LT}$. The Lifshitz transition thus changes character because it is tied to the pseudogap-Fermi-liquid transition. These results are consistent with available observations and should foster further experimental investigations.

Pseudogap-induced change in the nature of the Lifshitz transition in the two-dimensional Hubbard model

Abstract

We study the behavior of the density of states and the nematic susceptibility extracted from Raman response data across the doping-driven Lifshitz transition comparing the weak and strong interaction cases. Our results were obtained using cluster dynamical mean field theory for the two-dimensional Hubbard model. In the weakly correlated Fermi liquid regime, both quantities are approximately symmetric around the Lifshitz transition doping . In the strongly correlated regime, the low-doping pseudogap leads to an asymmetric, discontinuous evolution when the Fermi surface changes from hole-like to electron-like at . The Lifshitz transition thus changes character because it is tied to the pseudogap-Fermi-liquid transition. These results are consistent with available observations and should foster further experimental investigations.

Paper Structure

This paper contains 13 sections, 13 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Model and Methodology
  3. Nematic susceptibility
  4. Numerical Results
  5. Lifshitz transition nature for weak and strong interactions
  6. Density of states results
  7. Nematic susceptibility results
  8. Fermi surface and Green's functions zeroes evolution in the pseudogap phase
  9. Conclusions
  10. Periodization of cluster observables
  11. Raman $\gamma(\mathbf{k})$ factor
  12. Density of states as a function of frequency
  13. Renormalized energy

Figures (8)

  • Figure 1: Local DOS at the Fermi level as a function of the chemical potential $\mu$ for (a) $U=3.5$ and (b) $U=8.0$. The insets show the doping $p$ as a function of $\mu$ corresponding to data in the respective main panel. The dashed red line in panel (a) marks the Lifshitz transition. Note that the DOS for $U=8.0$ is always smaller and varies in a broader range than it is the case for $U=3.5$.
  • Figure 2: Spectral function $A(\mathbf{k}, iw \rightarrow 0$) for $U=3.5$ and values of the chemical potential/doping close to the Lifshitz transition. The system is in the FL phase in both cases; in panel (a) it has an e-FS, while in (b) it has a h-FS.
  • Figure 3: (a) Spectral function and (b) imaginary part of the self-energy both at $\mathbf{k} = (0,\pi)$ as a function of frequency for $U=8.0$ and values of $\mu$ ($p$) very close to the FL-pseudogap transition.
  • Figure 4: $B_{1g}$ nematic susceptibility extracted from Raman response data as a function of the chemical potential $\mu$ for (a) $U=3.5$ and (b) $U=8.0$. The dashed red line in panel (a) denotes the Lifshitz transition. See the insets of Fig. \ref{['DOSvsmu']} for the $n \times \mu$ plots corresponding to the results in this figure.
  • Figure 5: Evolution of the spectral function $A(\mathbf{k}, iw \rightarrow 0$) for $U=8.0$ and different values of the chemical potential/doping, as indicated in each panel. In panel (a), the system in the FL phase; in the others, it is in the pseudogap phase.
  • ...and 3 more figures