Relevance of long-range screening in Mott transition examined via a hydrogen lattice

TL;DR

This work probes whether long-range screening qualitatively changes the Mott metal–insulator transition by studying a hydrogen lattice with charge self-consistent DFT+DMFT to capture screening effects. The authors reveal a charge-transfer insulator where the correlated CT gap $\tilde{E}_{CT}$ closes smoothly as the lattice constant is reduced, indicating a continuous MIT rather than a first-order transition driven by long-range screening. They demonstrate that the transition is governed by the competition between kinetic energy and strong local interactions, with CT physics largely insensitive to screening, and discuss potential narrow excitonic regimes and experimental tests. The result challenges Mott's original view that long-range screening drives a discontinuous MIT and supports a broader view that CT-driven MITs in real materials can be continuous.

Abstract

The Mott transition, a metal-insulator transition due to strong electronic interaction, is observed in many materials without an accompanying change of system symmetry. An important open question in Mott's proposal is the role of long-range screening, whose drastic change across the quantum phase transition may self-consistently make the transition more abrupt, toward a first-order one. Here we investigate this effect in a model system of hydrogen atoms in a cubic lattice, using charge self-consistent dynamical mean-field theory that incorporates approximately the long-range interaction within the density functional treatment. We found that the system is well within the charge-transfer regime and that the charge-transfer gap intimately related to the Mott transition closes smoothly instead. This indicates that the long-range screening does not play an essential role in this prototypical example. This finding can be understood from the fact that the obtained insulating phase in this model system is driven by strong local interaction, and the transition is associated with the closing of charge-transfer gap. Contrary to Mott's length scale argument, such energetic competition between kinetic energy and local interaction is thus insensitive to long-range screening.

Figures (6)

• Figure 1: Mott's picture of the key scales of metal-insulator transition: (a) radius $a_B$ of the particle-hole bound state, and (b) range $\lambda$ of screened long-range Coulomb attraction $V(r)$ as a function of relative distance $r$. (c) When the bound state density $\rho_B$ is confined within the Coulomb attraction, $a_B < \lambda$, the system is insulating. (d) Otherwise the system becomes metallic. The finite $\lambda$ at the transition dictates a first-order phase transition in this picture.
• Figure 2: (a) One-body density of states (DOS) in unit of (eV$\cdot$ unit cell)$^{-1}$ for $a=3.0\text{\AA}$ via standard DFT treatment, indicating a metallic system with a charge-transfer gap $E_{CT}$ above the chemical potential set as the reference energy at zero. (b) The same via DFT+DMFT at $T=0.01~$eV, giving an insulating system with a correlation-renormalized charge-transfer gap $\tilde{E}_{CT}$ across the chemical potential. (c) Smooth reduction of charge-transfer gap $E_{CT}$ and $\tilde{E}_{CT}$ as the lattice constant $a$ decreases toward the quantum critical point at $a_c$, below which $\tilde{E}_{CT} < 0$ and the system turns metallic with a gradual increase of itinerant hole carrier density reflected by the smooth reduction of $1s$ occupation within a fixed atomic sphere (d). Both (c) and (d) indicate a continuous quantum phase transition different from Mott's proposal.
• Figure 3: (a)Determination of charge-transfer gap (insulating gap) $\tilde{E}_{CT}$ in DFT+DMFT calculation. Red dashed line is the linear extrapolation near the edge of the gap. (b) Charge-transfer gap $\tilde{E}_{CT}$ as a function of lattice spacing $a$ at temperature 0.1 (green triangle), 0.02 (blue triangle), 0.04 (red circle) and 0.01 (black square) eV.
• Figure 4: Phase diagram of real hydrogen lattice as a function of temperature and lattice constant. The color map shows the value of DOS at chemical potential. Two dashed lines are the boundary of the coexistent region. The dark blue line $T_{BR}(a)$ is the Brinkman-Rice line marking the thermal destruction of metallic quasiparticles Brinkman1970. The inserted figure is the coexistent region with two boundaries $a_{c1}(T)$ and $a_{c2}(T)$ denoted by red and dark blue dashed lines respectively.
• Figure 5: DOS corresponds to $a= 2.78\text{\AA}$, on the metallic side of the coexistence region. In contrast to the behavior found for a single-band Hubbard model at half filling, here the destruction of metallic quasiparticles leaves behind a pre-formed gap.