Mott transition and antiferromagnetism of cold fermions in the decorated honeycomb lattice

We investigate two-component ultracold fermions loaded in a decorated honeycomb lattice described by the Hubbard model with repulsive interactions and nearest-neighbor hopping. The phase transitions are studied by combining the cellular dynamical mean-field theory with the continuous-time quantum Monte Carlo method. For weak interactions, the quadratic band crossing point is broken to a linear band crossing point and the system becomes a semimetal. With increasing interaction, the system undergoes a first-order phase transition to an antiferromagnetic Mott insulator at low temperatures. Below the critical temperature, due to the charge nematic fluctuation, a nematic metal forms between the semimetal and the antiferromagnetic Mott insulator. The effects of lattice anisotropy are also addressed. Furthermore, we discuss how to detect these phases in real experiments.

Figure 1

(a) Structure of the decorated honeycomb lattice. Filled circles denote the A sites; open circles, B sites. The unit cell contains six sites: $a_1$, $a_2$, $a_3$, $b_1$, $b_2$, and $b_3$. Inside the small rectangular area [dotted (blue) line] and large rectangular area [dotted (blue) line] are the 6- and 12-site clusters, respectively, used in our analysis. Arrows $\vec{m}$ and $\vec{n}$ are the real lattice vectors. (b) Reciprocal space vectors $\overrightarrow{k_1}$ and $\overrightarrow{k_2}$ and first Brillouin zone [shaded (yellow) hexagon] of the decorated honeycomb lattice. (c) Band structure of the tight-binding model along the path $M\text{−}\Gamma \text{−}K\text{−}M$ shown in (b). There are six bands: ${\epsilon }_1$, ${\epsilon }_2$, ${\epsilon }_3$, ${\epsilon }_4$, ${\epsilon }_5$, and ${\epsilon }_6$. And there are Dirac points at $K$ and $K^{\prime }$ (not shown) and the quadratic band crossing point at $\Gamma$. (d) Noninteracting density of states (DOS) of the system at half-filling $f=1/2$. There are four van Hove singularities and two $\delta$ peaks.

Figure 2

Phase diagram for isotropic hopping ($\lambda =1.0$) Hubbard model on a decorated honeycomb lattice as a function of $U$ and $T$. Solid and dashed lines are the results obtained using the 6-site cluster ($N_c=6$) and 12-site cluster ($N_c=12$), respectively. There are four phases in the phase diagram: (i) semimetal (SM); (ii) antiferromagnetic insulator (AFI); (iii) nematic metal (NM); and (iv) paramagnetic insulator. The critical interaction and critical temperature of the SM-NM crossover are shown as ($U_{c1},T_{c1}$). Critical points of the phase transition to AFI are shown as ($U_{c2},T_{c2})$.

Figure 3

Enhancement of on-site self-energies across the semimetal and nematic metal transition with increasing $U$. The imaginary parts of the on-site propagator $G_{11}\left(i{\omega }_n\right)$ and on-site self-energy ${\Sigma }_{11}\left(i{\omega }_n\right)$ (inset) are plotted for different values of $U$ when $T=0.05$.

Figure 4

(a1, a2) Momentum-resolved spectral weight $A(k,0)$ at the Fermi level in the first Brillouin zone when $T=0.05$. (a1) Semimetal phase when $U=1.0$. Inset: Zoom-in of the spectral weight $A(k,0)$ around the center of the Brillouin zone. (a2) Nematic metal phase when $U=4.0$. (b1–b3) DOS $\rho \left(\omega \right)$ at various interactions when $T=0.05$. (b1) The zero density in the Fermi level at $U=1.0$ shows that the system is a semimetal. (b2) A finite density in the Fermi level at $U=4.0$, which indicates that the system stays in the nematic metal phase. (b3) A charge gap is opened at $U=6.0$, which means that the system is an insulator.

Figure 5

Evolution of double occupancy $D_{\mathrm{occ}}$ as a function of $U$ for various $T$. Solid arrows show the critical points of SM-NM crossover. And the critical points of the NM-AFI phase transtion are shown by dashed arrows.

Figure 6

Evolution of the antiferromagnetic order parameter $m$ and the single-particle gap $\Delta E$ as a function of $U$ when $\lambda =1.0$ and $T=0.05$. Insets: (a) Evolution of $m$ and $\Delta E$ as a function of $U$ at $\lambda =1.0$ and $T=0.2$; (b, c) two equivalent antiferromagnetic spin configurations of the antiferromagnetic insulator in a decorated honeycomb lattice.

Figure 7

Phase diagram of the Hubbard model on a decorated honeycomb lattice as a function of $U$ and the lattice anisotropy $\lambda$ when $T=0.067$. Solid and dashed lines are the results obtained using the 6-site cluster ($N_c=6$) and 12-site cluster ($N_c=12$), respectively. Leftmost (blue) lines show the phase crossover line of the semimetal and nematic metal; circles indicate critical points. Rightmost (black) lines show the phase translation line of the nematic metal and antiferromagnetic insulator; squares indicate critical points.