Electric-field-driven Mott metal-insulator transition in correlated thin films: An inhomogeneous dynamical mean-field theory approach

Simulations are carried out based on the dynamical mean-field theory (DMFT) in order to investigate the properties of correlated thin films for various values of the chemical potential, temperature, interaction strength, and applied transverse electric field. Application of a sufficiently strong field to a thin film at half filling leads to the appearance of conducting regions near the surfaces of the film, whereas in doped slabs the application of a field leads to a conductivity enhancement on one side of the film and a gradual transition to the insulating state on the opposite side. In addition to the inhomogeneous DMFT, a local density approximation (LDA) is considered in which the particle density $n$, quasiparticle residue $Z$, and spectral weight at the Fermi level $A(\omega =0)$ of each layer are approximated by a homogeneous bulk environment. A systematic comparison between the two approaches reveals that the less expensive LDA results are in good agreement with the DMFT approach, except close to the metal-to-insulator transition points and in the layers immediately at the film surfaces. LDA values for $n$ are overall more reliable than those for $Z$ and $A(\omega =0)$. The hysteretic behavior (memory effect) characteristic of the bulk doping driven Mott transition persists in the slab.

Figure 1

Bulk (3D) electron density as a function of chemical potential for different temperatures at $U/t=13.2$. This value of the interaction is large enough for a gap to open in the spectral function of the solid. A corresponding plateau appears in the $n\left(\mu \right)$ curve. The simulations for different $\mu$ values are carried out recursively. Dashed (full) lines correspond to down- (up-) sweep. The hysteresis indicates the coexistence of two solutions. Offsets added for clarity.

Figure 2

Charge density deviation from half filling across the slab for different values of the applied field. Symbols indicate the full DMFT calculation; lines correspond to the LDA (panel (a)). Double occupancy across the slab for the insulating and metallic solution at zero field (panel (b)). $U/t=12$ and $\beta t=30$ (both panels).

Figure 3

Electron density across the slab at different temperatures and different values of the electric field. The overall density for the slab corresponds to half filling. Only “metallic” seeds were used. Symbols correspond to the full DMFT calculation, lines correspond to the LDA. $U/t=13.2$.

Figure 4

Variation of the $Z$ factor, Eq. (5), across the slab for the same simulation parameters as in Fig. 3. Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 5

The variation of the spectral weight at the Fermi level across the slab corresponding to the density and $Z$-factor data shown in Figs. 3 and 4. Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 6

Panels (e) and (f): Maximum-entropy method reconstruction of the spectral functions $A_i\left(\omega \right)$ throughout the slab. Data is interpolated between layers for clarity. Panels (a) and (b): Comparison of MEM results for $A(\omega =0)$ (blue lines with crosses) with those obtained by Eq. (6) (green lines with circles). Panels (c) and (d): a comparison of Eq. (9) (blue lines with crosses) and the Monte Carlo results (green lines with circles) for the density $n$. Left panels: $U/t=13.2,\mu =U/2,\beta t=30,V=4.5$ and average density corresponding to half filling. Right panels: $U/t=16.2,\beta t=10,V=6$ and average density per site in the slab $n=1.04$.

Figure 7

The effect of screening on a metallic slab, panels (a) and (c), and an insulating slab, panels (b) and (d). The effect is much more pronounced for the metallic case. $\alpha$ is the screening parameter described in Sec. 2.

Figure 8

Variation of the electron density throughout a 24 layer slab for selected values of the electric field, Hubbard $U$, and temperature. The average density for the whole slab is fixed at 1.04 electrons per site. The insets show how the chemical potential of the slab changes as the field is increased. This adjustment is necessary to keep the average electron density in the slab fixed. Symbols indicate the full DMFT calculation; lines correspond to the LDA.

Figure 9

Variation of the spectral weight at the Fermi level across a 24 layer slab for the same values of the electric field, Hubbard $U$, and temperature as in Fig. 8. The average density for the whole slab is fixed at 1.04 electrons per site. Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 10

Variation of the $Z$ factor across a 24 layer slab for the same values of the electric field, Hubbard $U$, and temperature as in Figs. 8 and 9. The average density for the whole slab is fixed at 1.04 electrons per site. Symbols indicate the full DMFT calculation; lines correspond to the LDA.

Figure 11

Electron density, spectral weight at the Fermi level, and $Z$ factor across a doped 24 layer slab for the same values of the electric field as in Figs. 8–10, but lower $U$. The average density in the slab is fixed at 1.04 electrons per site. The inset shows the change of $\mu$ necessary to keep the average density constant for different values of $V$. Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 12

Comparison of the $Z$ factor estimated from a fit, Eq. (10) (lines), and from the simple form, Eq. (5) (lines with symbols), across the slab for the same simulation parameters as in Figs. 3, 4, 5 (half-filled case, $U/t=13.2)$. Semitransparency indicates regions with low spectral weight at the Fermi level (see the last section of the Appendix for details).

Figure 13

Variation of the absolute value of $\mathrm{Im}\mathrm{\Sigma }(\omega =0)$ (estimated from a fit to the imaginary part of the self-energy) across the slab for the same simulation parameters as in Figs. 3, 4, 5 and Fig. 12 (half-filled case, $U/t=13.2)$. Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 14

Comparison of the $Z$ factor estimated from a fit, Eq. (10) (lines), and from the simple form, Eq. (5) (lines with symbols), across the slab for the same simulation parameters as in Figs. 8–10 (doped case). Semitransparency indicates regions with low spectral weight at the Fermi level (see the last section of the Appendix for details).

Figure 15

Variation of the absolute value of $\mathrm{Im}\mathrm{\Sigma }(\omega =0)$ (estimated from a fit to the imaginary part of the self-energy) across the slab for the same simulation parameters as in Figs. 8 and 9 and Fig. 14 (doped case). Symbols correspond to the full DMFT calculation, lines correspond to the LDA.

Figure 16

A plot of the imaginary part of $G\left(i{\omega }_n\right)$ for different layers in the slab illustrating the criterion used to distinguish between “metallic” and “insulating” parts of the slab (see text).