Higgs amplitude mode in massless Dirac fermion systems

Abstract

The Higgs amplitude mode in superconductors is the condensed matter analogy of Higgs bosons in particle physics. We investigate the time evolution of Higgs amplitude mode in massless Dirac systems, induced by a weak quench of an attractive interaction. We find that the Higgs amplitude mode in the half-filling honeycomb lattice has a logarithmic decaying behaviour, qualitatively different from the 1/ √ t decay in the normal superconductors. Our study is also extended to the doped cases in honeycomb lattice. As for the 3D Dirac semimetal at half filling, we obtain an undamped oscillation of the amplitude mode. Our finding is not only an important supplement to the previous theoretical studies on normal fermion systems, but also provide an experimental signature to characterize the superconductivity in 2D or 3D Dirac systems.

Optical response of Higgs mode in superconductors at clean limit

“…However, rather than straightening out the situation, these theoretical descriptions make the understanding of the existing and growing experimental findings muddled. Specifically, early theoretical studies of the nonlinear optical response in superconductors have used the Bloch [26][27][28][29][30][34][35][36][37][38][39][40] or Liouville [41][42][43][44][45] equation derived in Anderson pseudospin picture 46 , with the vector potential A alone. The second-order light-matter interaction H p = e 2 A 2 τ 3 /(2m) naturally emerges in these descriptions [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] as a pseudo field along z direction, with τ i being the Pauli matrices in Nambu space.…”

“…Specifically, early theoretical studies of the nonlinear optical response in superconductors have used the Bloch [26][27][28][29][30][34][35][36][37][38][39][40] or Liouville [41][42][43][44][45] equation derived in Anderson pseudospin picture 46 , with the vector potential A alone. The second-order light-matter interaction H p = e 2 A 2 τ 3 /(2m) naturally emerges in these descriptions [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] as a pseudo field along z direction, with τ i being the Pauli matrices in Nambu space. This interaction can pump the quasiparticle correlation (i.e., pseudospin precession) and then causes the fluctuation of the order parameter, which was directly considered as the Higgs mode to explain the experimental findings [26][27][28][29][30][34][35][36][37][38][39][41]…”

“…The second-order light-matter interaction H p = e 2 A 2 τ 3 /(2m) naturally emerges in these descriptions [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] as a pseudo field along z direction, with τ i being the Pauli matrices in Nambu space. This interaction can pump the quasiparticle correlation (i.e., pseudospin precession) and then causes the fluctuation of the order parameter, which was directly considered as the Higgs mode to explain the experimental findings [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] . Nevertheless, a latter symmetry analysis in Anderson pseudospin picture finds a vanishing (finite) correlation between amplitude (phase) mode and external pseudo field 47 .…”

“…This implies that the theoretically obtained order-parameter fluctuation in Bloch or Liouville equation is a phase fluctuation rather than the claimed amplitude one 48 . Moreover, with the isotropic pump effect alone, the Bloch or Liouville equation in the literature [26][27][28][29][30][34][35][36][37][38][39][41][42][43][44] fails to drive the optical current and hence derive the superfluid density, since no drive effect (i.e., linear light-matter interaction) is included.…”

Influence of montmorillonite on the properties of halogen–antimony flame retardant polypropylene composites

“…However, BEO flame retardant system can produce a lot of smoke in the combustion process, which it is a controversial problem of the somke for environmental pollution and harmful human body. Therefore, it is necessary to search for a kind of environmentally friendly materials to replace BEO on the basis of ensuring the flame retardant effect .…”