Theory of quasiparticle scattering interference on the surface of topological superconductors

Abstract

Topological superconductors, such as noncentrosymmetric superconductors with strong spin-orbit coupling, exhibit protected zero-energy surface states, which possess an intricate helical spin structure. We show that this nontrival spin character of the surface states can be tested experimentally from the absence of certain backscattering processes in Fourier-transform scanning tunneling measurements. A detailed theoretical analysis is given of the quasiparticle scattering interference on the surface of both nodal and fully gapped topological superconductors with different crystal point-group symmetries. We determine the universal features in the interference patterns resulting from magnetic and nonmagnetic scattering processes of the surface quasiparticles. It is shown that Fourier-transform scanning tunneling spectroscopy allows us to uniquely distinguish among different types of topological surface states, such as zero-energy flat bands, arc surface states, and helical Majorana modes, which in turn provides valuable information on the spin and orbital pairing symmetry of the bulk superconducting state.

Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe 2

“…Because no well-defined interface exists between TSSs and bulk states in stoichiometric PbTaSe 2 and both states contribute to the measured tunneling current, which is evident from our QPI images, experimentally, it is not straightforward to separate the contribution between bulk and TSS superconductivity in a tunneling spectrum, and realistic theoretical models are required for comparison. Further experiments, such as band-selective superconducting gap mapping using QPI ( 53 ) or impurity-dependent spin-polarized QPI imaging ( 54 ), are more suitable for understanding the superconductivity on TSSs and bulk states in PbTaSe 2 .…”

Topological surface states in nodal superconductors

“…Although such experiments could give unambiguous demonstration of the edge states, these proposals assume a fully-gapped pairing state, so it is unclear if they would apply to a nodal system. The surface states of a topological superconductor could be more directly demonstrated using quasiparticle interference spectroscopy [65,130], which has already been successfully used to evidence topological insulator surface states [131]. This can probe the spin character of the surface states, as scattering between states with opposite spin polarization (i.e.…”

Helical spin texture of surface states in topological superconductors

“…For example, the opposite sign of the spin polarization of the surface states on opposite sides of the surface Brillouin zone forbids spin-independent scattering between them [40]. This characteristic property, which results in a partial protection of the surface states against localization from nonmagnetic impurities [47], can be observed experimentally using quasiparticle-interference patterns measured by scanning tunneling microscopy [41]. Another possibility is to probe the surface-state polarization by bringing the NCS into contact with a ferromagnet.…”

“…It was found that, depending on the crystal point group and the superconducting pairing symmetry, NCSs can exhibit either dispersing Majorana surface states, zero-energy surface flat bands, or arc surface states, as well as edge modes which are not topologically protected. Recalling the situation in topological insulators, these surface states generally exhibit an intricate helical spin texture [37][38][39][40][41].…”

“…The nontrivial spin texture of NCS surface states is predicted to have important consequences for the surface physics [14,20,[37][38][39][40][41][42]. For example, the helical character of the spin texture forbids spin-independent scattering between states on opposite sides of the surface Brillouin zone [40], which leaves signatures in Fouriertransformed scanning tunneling spectroscopy [41]. The spin polarization of the edge states also determines their coupling to magnetic exchange fields [14,20,39,40,42].…”