Quasiparticles and optical conductivity in the mixed state of Weyl superconductors with unconventional pairing

Abstract

Previous investigations have revealed that the Weyl superconductor (WeylSC), realized in a superconductor-topological insulator heterostructure, can exhibit the Landau levels (LLs) of Bogoliubov quasiparticles in the presence of a vortex lattice. Here, we investigate the low-energy quasiparticle (QP) excitations in the mixed state of heterostructure WeylSCs with unconventional pairing. We find that the spin-singlet $d$-wave pairing induces flat Dirac-LLs of Bogoliubov QPs, whereas the excitation spectra for the spin-triplet chiral $p$-wave pairing show noticeable dispersion, except for the chiral symmetry-protected, dispersionless, zeroth Landau level (ZLL). Distinct QP excitations in the vortex lattice of WeylSCs result in different optical responses, which are manifested as characteristic magneto-optical conductivity curves. We also show that, compared to the topologically protected, charge-neutral, localized Majorana zero mode (MZM), the chiral symmetry-protected ZLL is non-charge-neutral and delocalized. Both of these zero modes may be observed in the mixed state of a heterostructure topological superconductor.

Figures (7)

• Figure 1: The excitation spectrum of the intrinsic WeylSC along the momentum $k_z$ ($k_x=k_y=0$) in zero magnetic field (dashed gray lines) and in the vortex lattice (solid red lines), with the magnetic length $l_B=22$, $\Delta_0=1$ and $\mu=2$.
• Figure 2: Excitation spectra of WeylSC model (\ref{['Ham_TBWeyl']}) in zero magnetic field, with $k_z=\tfrac{\pi}{2}$ and $\Delta_0=0.5$. (a) $d_{x^2-y^2}$ pairing. (b) $p_x-ip_y$ pairing. The solid red and dashed gray lines denote $\mu=1$ and $\mu=0$, respectively.
• Figure 3: (a) Magnetic unit cell $l_B \times l_B$ containing two vortices (orange solid circle) with $l_B=6a_0$. (b) A momentum path (green lines) in the first Brillouin zone of the vortex lattice.
• Figure 4: Excitation spectra in the vortex lattice of heterostructure WeylSCs, with $l_B=22$, $k_z=\tfrac{\pi}{2}$ and $\Delta_0=0.5$. (a) $d_{x^2-y^2}$ pairing. (b) $p_x-ip_y$ pairing. The solid red and dashed gray lines indicate $\mu=0$ and $\mu=0.1$, respectively.
• Figure 5: The normalized intensity profile $|\Phi(x,y)|^2/|\Phi(x,y)|^2_{max}$ of zero-energy modes in a $22\times 22$ magnetic unit cell, with $\Delta_0=0.5$. Two vortices are located at ($5.5$, $5.5$) and ($16.5$, $16.5$), respectively. (a) The confined phase of the PB model. (b) The deconfined phase of the PB model, where the red arrow denotes the in-plane supercurrent in the $x$ direction, with $\mathit{K}=4\Delta_0$. (c) The $d_{x^2-y^2}$ pairing WeylSC. (d) The $p_x-ip_y$ pairing WeylSC.