Chiral Higgs Mode in Nematic Superconductors

Abstract

Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, M x Bi 2 Se 3 (M=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from sub-dominant pairing channels to the EM response.Introduction. Spontaneous symmetry breaking is an important concept that spreads across the diverse fields of modern physics. The recent discovery of two-fold rotation symmetry in superconducting compounds, M x Bi 2 Se 3 (M = Cu, Sr, Nb), has stimulated an intense discussion of superconductivity with a new class of spontaneous symmetry breaking [1][2][3][4][5][6][7][8][9][10][11]. The rotation symmetry breaking in the basal plane is compatible with odd-parity time-reversal invariant pairing belonging to the two-dimensional irreducible representation (E u ) of the D 3d symmetry, which exhibits twofold symmetric gap anisotropy (Fig. 1). The anisotropy is represented by a nematic order parameter [12]. The odd-parity superconductor (SC) M x Bi 2 Se 3 has also attracted much attention as a prototype of DIII topological SCs that host helical Majorana fermions [13][14][15][16][17][18][19][20][21].

Direction and symmetry transition of the vector order parameter in topological superconductors CuxBi2Se3

“…The lack of change of the Knight shift below T c for all angles (Fig. 9) as contrary to what found in the nematic phase 16 is consistent with existing theory that the dvector for the chiral phase would be pointing to the c-axis 42 . Thus, our finding suggests that superconductors with strong spin-orbital interaction 14 is a land much more fertile than we thought.…”

“…One of the crucial parameters important for selecting between the two states is the Fermi surface shape. It has been theoretically shown by several groups that the chiral state can be stabilized when the Fermi surface becomes more two-dimensional [42][43][44] . Experimentally, photoemission and quantum oscillation measurements have suggested that the Fermi surface becomes more two-dimensional as carrier density increases 45,46 .…”

Nematic Superconductivity in Doped Bi2Se3 Topological Superconductors

“…However, there are several issues unresolved; in particular, apparent inconsistency in the nematic direction and its relation to the possibly existing in-plane symmetry-breaking field are most important subjects to be investigated next. Also, predicted novel phenomena originating from nematic superconductivity, such as the superconductivity-fluctuation-induced nematic order above T c [105], the chiral Higgs mode in the electromagnetic response [106], spin polarization of Majorana quasiparticles in a vortex core [107], and nematic Skyrmion texture near half-quantum vortices [108], would be worth seeking for.…”

Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors

“…The kernel of the matrix in Eq. ( 54) gives the eigenfrequencies of bosonic excitations, ω C Γ (q) (Γ = D, E), and the damping rates of each mode [100]. The right-hand side of Eq.…”