Abstract
We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-1/2 fermionic system on the kagomé lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the x-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.
Highlights
Interest has gradually shifted from linear-dispersion toward quadratic-dispersion fermi materials with up and down bands parabolically touching at certain quadratic band crossing point (QBCP) for both two [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] and three dimensions [18, 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72]
We can iors of 2D spin-1/2 QBCP electric systems sitting on the select the non-interacting parts of effective action (6) as kagome lattice in the presence of these marginal fermion- an original fixed point at which they are invariant during fermion interactions
We notice that fermionfermion interactions are strongly energy-dependent and driven to be divergent at some critical energy scale denoted by lc in the low-energy regime, which always is an unambiguous signature for the emergence of phase transitions [47, 48, 51, 81,82,83,84,85,86,87,88]
Summary
Past two decades have witnessed a phenomenally rapid development of semimetal materials [1,2,3,4,5,6,7,8,9,10,11,12] that feature well-known discrete Dirac points accompanied by gapless quasi-particle excitations and linear energy dispersions along two or three directions [1,2,3,4,5,6,7,8,9, 12,13,14,15,16,17,18,19,20,21]. The main reasons are ascribed to the finite density of states at the Fermi surface together with its unique gapless quasiparticles (QPs) from discrete QBCPs developed by the crossings of up and down parabolical bands, leading to the possibility of weak coupling interaction-driven instability [44, 48, 51, 52] These 2D QBCP materials are suggested to be realized on some collinear spin density wave state [73], Lieb lattice [74], checkerboard [43, 48] and kagome lattices [44, 55, 75] with distinct kinds of symmetries under point group consideration [44, 47, 48].
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