Pseudogap metal induced by long-range Coulomb interactions

In correlated electron systems the metallic character of a material can be strongly suppressed near an integer concentration of conduction electrons as Coulomb interactions forbid the double occupancy of local atomic orbitals. While the Mott-Hubbard physics arising from such on-site interactions has been largely studied, several unexplained phenomena observed in correlated materials challenge this description and call for the development of new ideas. Here we explore a general route for obtaining correlated behavior that is decidedly different from the spin-related Mott-Hubbard mechanism and instead relies on the presence of unscreened, long-range Coulomb interactions. We find a pseudogap metal phase characterized by a divergent quasiparticle mass and the opening of a Coulomb pseudogap in the electronic spectrum. The destruction of the Fermi-liquid state occurs because the electrons move in a nearly frozen, disordered charge background, as collective charge rearrangements are drastically slowed down by the frustrating nature of long-range potentials on discrete lattices. The present pseudogap metal realizes an early conjecture by Efros, that a soft Coulomb gap should appear for quantum lattice electrons with strong unscreened interactions due to self-generated randomness.

Figure 1

Phase diagram of the triangular lattice model with long-range interactions. The line and the full symbols indicate the metal-insulator transition to a stripe-ordered Wigner crystal, signaled by the vanishing of the Drude weight $D$ ($N_s=18$ sites, using 121 TBCs). The color map is the Drude weight (697 grid points, $N_s=12$ sites, 400 TBCs). The gray dashed line is the charge ordering transition as obtained from the random-phase approximation, which ignores correlations and does not capture the extreme fragility of the Wigner crystal. The black dashed and dotted lines are strong-coupling estimates for the Wigner crystal melting (see text).

Figure 2

Pseudogap metal. (a) Spectral function $A\left(\omega \right)$ at $\alpha =1$ and $N_s=18$ and averaged over 16 TBCs, illustrating the pseudogap phenomenon. All spectra are smoothened by a Gaussian broadening $\delta =0.7t$. (b) Distribution of classical local potentials $P\left(\varphi \right)$ (broadening $\delta =0.05V$), showing the opening of the Coulomb gap; the dashed line is $P\sim e^{-V/\xi \left|\varphi \right|}$ with $\xi =2$; the values of $V/t$ and the color code are the same as in (a). (c) Drude weight $D$ (averaged over 121 TBCs) normalized by the exact noninteracting value $D_0=0.247$, quasiparticle weight $Z$ (angular averaged over the Fermi surface), and density of states $A\left(\mu \right)$ at the Fermi energy, divided by the noninteracting value. The inset shows $P\left(0\right)$, tracking the plasma dip. The dashed line is $P\left(0\right)\sim |V-V_c{|}^2$.

Figure 3

Soft collective excitations in the pseudogap phase. (a) Spectral function $\mathcal{D}\left(\omega \right)$ of the charge fluctuations, averaged over the Brillouin zone (Gaussian broadening $\delta =0.2t$). The inset shows the same quantity evaluated at the stripe-ordering wave vector $q=M$; this critical mode is also visible as a shoulder in the main panel (circles). (b) Frequency of the boson peak, controlling the timescale of the charge fluctuations.