Kavli Affiliate: Gang Su
| First 5 Authors: Jin-Wei Dong, Yu-Han Lin, Ruiqing Fu, Gang Su, Ziqiang Wang
| Summary:
Loop current order has been suggested as a promising candidate for the
spontaneous time-reversal symmetry breaking $2a_0 times 2a_0$ charge density
wave (CDW) revealed in vanadium-based kagom’e metals avs ($A$ = K, Rb, Cs)
near van Hove filling $n_text{vH} = 5/12$. Weak-coupling analyses and mean
field calculations have demonstrated that nearest-neighbor Coulomb repulsion
$V_1$ and next-nearest-neighbor Coulomb repulsion $V_2$ drives, respectively,
real and imaginary bond-ordered CDW, with the latter corresponding to
time-reversal symmetry breaking loop current CDW. It is important to understand
the inter-layer correlation of these bond-ordered CDWs and its consequences in
the bulk kagom’e materials. To provide physical insights, we investigate in
this paper the $c$-axis stacking of them, loop current CDW in particular, on
the minimal bilayer kagom’e lattice. The bare susceptibilities for stacking of
real and imaginary bond orders are calculated for the free electrons on the
bilayer kagom’e lattice with inter-layer coupling $t_perp=0.2t$, which splits
the van Hove filling to $n_{+text{vH}}=4.64/12$ and $n_{-text{vH}}=5.44/12$.
While real and imaginary bond-ordered CDWs are still favored, respectively, by
$V_1$ and $V_2$, their inter-layer coupling is sensitive to band filling $n$.
They tend to stack symmetrically near $n_{pmtext{vH}}$ with identical bond
orders in the two layers and give rise to a $2a_0 times 2a_0 times 1c_0$ CDW.
On the other hand, they prefer to stack antisymmetrically around $n_text{vH}$
with opposite bond orders in the two layers and lead to a $2a_0 times 2a_0
times 2c_0$ CDW. The concrete bilayer $t$-$t_perp$-$V_1$-V$_2$ model is then
studied. We obtain the mean-field ground states and determine the inter-layer
coupling as a function of band filling at various interactions. The nontrivial
topological properties of loop current CDWs are studied …
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