Kavli Affiliate: Jing Wang
| First 5 Authors: Yi-Kun Fang, Yi-Kun Fang, , ,
| Summary:
We present a systematic investigation of all sixteen marginally relevant
fermion-fermion interactions in two-dimensional time-reversal symmetry-breaking
kagom’e semimetals hosting a quadratic band crossing point. Employing a
momentum-shell renormalization group approach that treats every interaction on
equal footing, we derive energy-dependent flow equations that capture the
hierarchical evolutions of interaction parameters. Our analysis begins by
tracking the energy-dependent flows of fermion-fermion interactions. The
interaction couplings go towards divergence at a critical energy scale,
signaling quantum critical behavior. Such behavior is characterized by a
certain fixed point (FP) whose characteristics depends intimately on structural
parameters $d_0,1,2,3$ that cluster the microscopic model into rotationally
symmetric and asymmetric cases. Then, we identify two stable FPs in the
rotationally symmetric and nine additional FPs in asymmetric case dubbed
FP$_1-10$. Their boundary conditions are approximately demarcated and
established by linear and plane fitting techniques in the structural parameter
space. Furthermore, we examine distinct interaction-driven instabilities nearby
these FPs by incorporating the relevant external source terms and computing
their susceptibilities. It indicates that the charge density wave and
superconductivity become dominant at FP$_2,4,5,6,8$ and FP$_1,9,10$, while
the $x$-current and bond density prevail at FP$_3$ and FP$_7$, respectively. In
addition to these leading states, several underlying subordinate instabilities
are presented as well. These results would be helpful to further study the
low-energy critical behavior in 2D kagom’e QBCP and related materials.
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