Emergence of charge-2$e$ bosonic carriers and pseudogaps in the dynamics of residual electrons

Abstract

Emergence of charge-2$e$ bosonic carriers as tightly bound electrons presents perhaps the simplest route to understand the non-Fermi liquid behaviors widely observed in functional materials. However, such scenario is typically discarded when unbound electrons are observed near the chemical potential. Here, using attractive Hubbard model as a representative example, we demonstrate the emergence of such ''bosonic'' bound pairs in the presence of residual low-energy electrons through determinant quantum Monte Carlo computation of their propagators. Furthermore, above the superfluid temperature the electronic spectral function is found to display a typical non-Fermi liquid behavior, namely a pseudogap near the chemical potential. This study provides the microscopic foundation for scenarios of boson-fermion mixed liquid as effective descriptions for some of the strongly correlated functional materials.

Figures (3)

• Figure 1: Coexisting charge-2$e$ carriers and electrons under intermediate interaction strength. In the high-temperature normal state ($k_\mathrm{B}T=t/0.54$) above the superfluid temperature, under a weak on-site attraction ($U=t$) unbound electrons dominate the local spectral functions $A_-^{(1)}(\mathbf{x},\mathbf{x};\omega)$ (solid line) and $A_+^{(1)}(\mathbf{x},\mathbf{x};\omega)$ (dashed line) (a), without charge-2$e$ carriers near the chemical potential (d). In contrast, with strong on-site binding ($U=14t$), bound 2$e$-carriers dominates the phase space (f), such that electronic spectral function is fully gapped by the large binding energy (c). Interestingly, under an intermediate attraction ($U=5t$), when the phase space is already dominated by charge-2$e$ carriers (e), small density of residual electron carriers still persist (b) to utilize the large electronic kinetic energy. Notice the emergence of a pseudogap in (b) due to electrons' scattering against the phase-incoherent charge-2$e$ carriers.
• Figure 2: Long-lived mobile charge-2$e$ carriers. Corresponding to results in Fig. \ref{['fig:dos']}, under a weak attraction ($U=t$), unbound electrons dominates the phase space (first row), with no well-defined charge-2$e$ carriers near the chemical potential (4th row). In contrast, with a strong binding ($U=14t$) all electrons are part of the bound 2$e$-carriers with a long live time (sharp peak in frequency, 6th row), such that the electronic spectral function is fully gapped by the large binding energy (3rd row). Under an intermediate attraction ($U=5t$), when the phase space is dominated by the long-lived mobile charge-2$e$ carriers with well-defined dispersion near the chemical potential(5th row), small density (weight) of residual electron carriers persist (2nd row) to utilize the large electronic kinetic energy. Notice the emergence of a pseudogap in the electronic spectral function (2nd row) due to electrons' scattering against the phase-incoherent charge-2$e$ carriers.
• Figure 3: Schematic illustration of normal-state pseudogap in the eletronic spectral function and its proportionality to the superconducting gap in the superfluid state. Under an intermediate attraction, when the phase is dominated by charge-2$e$ carriers, low density of residual electrons persist and acquire weight transfer from around the chemical potential to higher energy due to dressing by charge-2$e$ carriers. Above the superfluid transition temperature, the charge-2$e$ carriers are not fully coherent, so the dressing leads to a pseudogap. In contrast, at low temperature the charge-2$e$ carriers becomes phase coherent, so the dressing leads to a clean "superconducting gap". Since both features originate from scattering against the same charge-2$e$ carriers, they are naturally proportional to each other.