Odd-parity surface magnetism in a Kondo insulator

Abstract

We formulate a theory of spin-polarized tunneling between a nanowire tip of a topological Kondo insulator SmB$_6$ and the bi-collinear antiferromagnet Fe$_{1+x}$Te in which the tunneling conductance which measures magnetic contrast changes sign when the bias is reversed. First we show that no time-reversal-symmetric tip, however strong its spin-momentum locking is, can produce experimentally observed magnetic contrast, which implies that time reversal must be broken at the tip surface. Within a mean-field treatment of the surface theory of SmB$_6$ we find that the interaction between conduction $d$- and $f$-electrons drives a surface phase transition near $T_c\approx10$ K in which the time-reversal-odd component of the Kondo hybridization amplitude condenses in the same symmetry channel as an out-of-plane surface magnetization, gapping out the Dirac surface states. Below the transition the spin-resolved spectral function of each gapped surface Dirac cone is odd in energy about its node. For a charge-neutral apex the Fermi level lies between the surface $\overline{\Gamma}$ and $\overline{X}$ Dirac nodes, so the spin-polarized conductance, which is determined by this function at the bias energy, reverses its sign close to zero bias. This sign change is thus a spectroscopic signature of time-reversal symmetry breaking on the surface of SmB$_6$.