Interaction- and filling-induced quantum anomalous Hall effect in ultracold neutral Bose-Fermi mixtures on a hexagonal lattice

Shang-Shun Zhang, Heng Fan, and Wu-Ming Liu

Phys. Rev. A 87, 023622 – Published 19 February 2013

Abstract

We investigate the quantum anomalous Hall effect in a mixture of ultracold neutral bosons and fermions held on a hexagonal optical lattice. In the strong atom-atom interaction limit, composite fermions composed of one fermion with bosons or bosonic holes in the mixture are formed. Such composite fermions have already been generated successfully in experiment [Nat. Phys. 7, 642 (2011)]. Here we predict that this kind of composite fermion may provide a realization of the quantum anomalous Hall effect by tuning the atom-atom interaction or the filling of the bosons in the mixture. We also discuss the corresponding experimental signatures of the quantum anomalous Hall effect in the Bose-Fermi mixture on hexagonal optical lattice.

Received 4 June 2012

DOI:https://doi.org/10.1103/PhysRevA.87.023622

Authors & Affiliations

Shang-Shun Zhang, Heng Fan, and Wu-Ming Liu

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

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Vol. 87, Iss. 2 — February 2013

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Images

Figure 1
Left panel: Schematic of hexagonal lattice geometry structure and mean-field channels for composite fermion. The lattice contains two triangle sublattices, labeled by $A$ (open circle) and $B$ (black ball). The vector ${\vec{a}}_{i}, i = 1, 2, 3$ are the nearest-neighbor displacements from site $B$ to site $A$ . And vector ${\vec{b}}_{i}, i = 1, 2, 3$ are second-neighbor displacements. $ρ_{A}$ and $ρ_{B}$ denote the particle density at site $A$ and $B$ , respectively. $χ e^{i ϕ_{A, B}}$ is the second-neighbor-site hopping driven by the second-neighbor interaction. Right panel: Schematic of composite fermion for three types: one fermion, one fermion with one boson, one fermion with two bosons.Reuse & Permissions
Figure 2
Phase diagram for ground state of Bose-Fermi mixture in the limit $J \to 0$ on the $\tilde{μ}$ - $α$ plane. The blocks with different colors represent the regions with different composite particles formed, which is determined by Eq. (4). For each block, the ground state of the system is characterized by the type of the composite particle with $s$ and the number of the occupation of bosons $n$ . The region marked by the red dashed line is the region we considered in this work.Reuse & Permissions
Figure 3
(a) Spectrum corresponding to semimetal state. The spectrum remains gapless at the Dirac points as marked by the the red dashed circle. (b) Spectrum corresponding to QAH state. The spectrum at the Dirac points opens a gap when the filling of the bosons exceeds the critical value (marked by the blue dashed circle). The dimensionless chemical potential for bosons $\tilde{μ}$ is taken as $4.8$ and the other parameters are the same as for Fig. 4.Reuse & Permissions
Figure 4
Mass terms at the two Dirac points as a function of filling of bosons $\tilde{μ}$ . The composite fermion at the Dirac points gains mass when the filling of bosons exceeds the critical value ${\tilde{μ}}_{c}$ of about $4.5$ . The parameters used here [in units of $E_{r}$ , where $E_{r} = ℏ^{2} k_{r}^{2} / (2 m)$ is the recoil energy in experiment [43] ] are $J_{F, 1} = J_{B, 1} = 0.4$ , $J_{F, 2} = 0$ , $J_{B, 2} = 0.7$ , $U = 15$ , and $α = 0.5$ .Reuse & Permissions
Figure 5
Mass terms at the two Dirac points as a function of interaction ratio $α$ . The composite fermion at the Dirac points gains a mass when $α$ exceeds the critical value $α_{c}$ about $0.48$ , and this curve stops at $α_{s}$ . The filling of bosons is chosen as $\tilde{μ} = 4.8$ and the other parameters used here are the same as for Fig. 4.Reuse & Permissions
Figure 6
Phase diagram with respect to interaction ratio $α$ and filling of bosons $\tilde{μ}$ . The phase of the mixture for $s = 0$ in the region $- 1 < α < 0$ is the same as for $0 < α < 1$ . The parameters used here are the same as for Fig. 4. In the blocks with orange color, the QAH state is formed, with the pase boundary parallel to the $\tilde{μ}$ axes. The red dashed line represents the case we considered in Fig. 4 with $α = 0.5$ . The green line is the schematic of the path for the $α$ axes in Fig. 5. The red point denotes the place where the system enters the region with $s = 1$ and the corresponding interaction ratio is denoted as $α_{s}$ .Reuse & Permissions

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