Dirty Weyl semimetals: Stability, phase transition and quantum criticality

We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetal and the phase diagram of dirty double Weyl semimetal at finite energies.Comment: 5 pages and 5 figures (Supplementary: 6 pages and 5 figure): Published version, added discussion, new results and reference

Magnetic Field Response and Chiral Symmetry of Time Reversal Invariant Topological Superconductors

We study the magnetic field response of the Majorana Kramers pairs of a one-dimensional time-reversal invariant (TRI) superconductors (class DIII) with or without a coexisting chirality symmetry. For unbroken TR and chirality invariance the parameter regimes for nontrivial values of the (Z_2) DIII-invariant and the (Z) chiral invariant coincide. However, broken TR may or may not be accompanied by broken chirality, and if chiral symmetry is unbroken, the pair of Majorana fermions (MFs) at a given end survives the loss of TR symmetry in an entire plane perpendicular to the spin-orbit coupling field. Conversely, we show that broken chirality may or may not be accompanied by broken TR, and if TR is unbroken, the pair of MFs survives the loss of broken chirality. In addition to explaining the anomalous magnetic field response of all the DIII class TS systems proposed in the literature, we provide a realistic route to engineer a "true" TR-invariant TS, whose pair of MFs at each end is split by an applied Zeeman field in arbitrary direction. We also prove that, quite generally, the splitting of the MFs by TR-breaking fields in TRI superconductors is highly anisotropic in spin space, even in the absence of the topological chiral symmetry.Comment: 4+ pages, 3 figures, slightly re-written, citations adde

Robust Zero Energy Bound States Localized at Magnetic Impurities in Iron-based Superconductors

We investigate the effect of spin-orbit coupling on the in-gap bound states localized at magnetic impurities in multi-band superconductors with unconventional (sign-changed) and conventional (sign-unchanged) $s$-wave pairing symmetry, which may be relevant to iron-based superconductors. Without spin-orbit coupling, for spin-singlet superconductors it is known that such bound states cross zero energy at a critical value of the impurity scattering strength and acquire a finite spin-polarization. Moreover, the degenerate, spin-polarized, zero energy bound states are unstable to applied Zeeman fields as well as deviation of the impurity scattering strength away from criticality. Using a T-matrix formalism as well as analytical arguments, we show that, in the presence of spin-orbit coupling, the zero-energy bound states localized at magnetic impurities in unconventional, sign-changed, $s$-wave superconductors acquire surprising robustness to applied Zeeman fields and variation in the impurity scattering strength, an effect which is absent in the conventional, sign-unchanged, $s$-wave superconductors. Given that the iron-based multi-band superconductors may possess a substantial spin-orbit coupling as seen in recent experiments, our results may provide one possible explanation to the recent observation of surprisingly robust zero bias scanning tunneling microscope peaks localized at magnetic impurities in iron-based superconductors provided the order parameter symmetry is sign changing $s_{+-}$-wave.Comment: 8 pages, 5 figure