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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 $2(n+1)Delta_0$ ($0le nle N_{k_F}$), where $Delta_0$ is the superconducting gap, $n$ is an integer, and $N_{k_F}$ is the number of states on the Fermi surface.
Superconductivity is a quantum phenomena arising, in its simplest form, from pairing of fermions with opposite spin into a state with zero net momentum. Whether superconductivity can occur in fermionic systems with unequal number of two species disti
We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addit
We investigate the non-equilibrium behavior of BCS superconductors subjected to slow ramps of their internal interaction strength. We identify three dynamical regimes as a function of ramp duration. For short ramp times, these systems become non-supe
An SDW antiferromagnetic (SDW-AF) low temperature phase transition is generally observe and the AF spin fluctuations are considered to play an important role for the superconductivity paring mechanism in FeAs superconductors. However, a similar magne
We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, $Delta_pm(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only $Delta_+(t)$ is nonzero. Howev