超导体中$\mathbb{Z}_2$对称性自发击穿引起的多重Higgs模的出现
Emergence of multiple Higgs modes due to spontaneous breakdown of a $\mathbb{Z}_2$ symmetry in a superconductor
摘要：
研究了Bardeen-Cooper-Schrieffer（BCS）超导体中的Higgs模。基于BCS哈密顿量的U（1）对称性对Higgs模不是必需的这一发现，我们研究了赝自旋表象中的类伊辛哈密顿量.我们表明，Higgs模式出现的最低激发态的类伊辛哈密顿量由于自发击穿的$\mathbb{Z}_2$对称性下的时间反转操作$\mathcal T$在赝自旋空间。我们进一步预测存在多个Higgs模式，量子化能量$2(n+1)Δ_0$（$0\le n\le N_{k_F}$），其中$Δ_0$是超导能隙，$n$是一个整数，和$N_{k_F}$是费米表面上的状态数。
英文摘要：
We study the Higgs mode in a Bardeen-Cooper-Schrieffer (BCS) superconductor. Motivated by the observation that U(1) symmetry of the BCS Hamiltonian is not essential for the Higgs mode, we study the Ising-like Hamiltonian in the pseudospin representation. We show that the Higgs mode emerges as the lowest excited state of the Ising-like Hamiltonian due to spontaneous breakdown of $\mathbb{Z}_2$ symmetry under the time-reversal operation $\mathcal T$ in the pseudospin space. We further predict the existence of multiple Higgs modes that have quantized energy $2(n+1)Δ_0$ ($0\le n\le N_{k_F}$), where $Δ_0$ is the superconducting gap, $n$ is an integer, and $N_{k_F}$ is the number of states on the Fermi surface.
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