$\mathcal{Z}_2$ classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator

Abstract

Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a [Formula: see text]-classification formula for these states. By calculating the [Formula: see text] index, the antiferromagnetic insulating states are classified into AFTI or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems.

Magnetic and topological transitions in three-dimensional topological Kondo insulator

“…The topological transitions between TI s are generated by closing and reopening of the insulating gap at certain HSP, leading to an inversion of parity and consequently the shifting of Z 2 index. 10 In above, we have set t ′ f /t f = t ′ d /t d , under which the Dirac points in TI s all cross the Fermi energy, leading to the vanishment of Fermi surface. For TKI candidate SmB 6 , medium- sized surface Fermi rings aroundΓ andX were detected through ARPES, verifying it in a STIΓX phase.…”

“…15,21 Based on the PM phase diagrams of TI s , we now study the AF transitions in TKI. In our previous work, the original K-R method of symmetric PAM 19,20 has been generalized to treat AF phases in non-symmetric case, 10 which can be applied to TKI. The resulting mean-field Hamiltonian is rather complicated in that in addition to n f , η and µ, two AF order parameters m f and h should be determined, besides, two renormalization factors Z 1 and Z 2 arise.…”

Valence transition in topological Kondo insulator

“…k and ǫ f k are determined by their corresponding EHAs 46 . S k = (sin k · a 1 , sin k · a 2 , sin k · a 3 ), 12 where a 1 , a 2 , a 3 are the element vectors of cubic lattice.…”

“…where f (i) k = 1/(1 + e E (i) k /T ) is the Fermi distribution of quasi-particles, and equals the step function θ(−E (i) k ) at zero temperature. The set of equations determining the parameters n f , m f , h, η, µ can be obtained through the zero point of the derivation of free energy (Eq.9) with respect to them, by using the formulas of matrix elements (H k ) nm in Eq.5 46 .…”

“…On the other hand, for SmB 6 and TKI candidate golden SmS, near the pressure-driven magnetic boundary, the valence of Sm ion shows an active increase 30,31,45 , similarly, at low temperatures, the pressure-induced magnetic transition in YbInCu 4 holds simultaneously a FOVT 38 , therefore, the relation of FOVT or valence crossover in TKI (and also in other heavy-fermion systems) to the magnetic transition should be clarified in an unified framework. Particularly, in TKI, variation of model parameters can produce various topological phases and distinct transition processes among them, and can driven magnetic transition as well 46,47 , so interest questions arise, as how the FOVT or valence crossover appears in TKI? what is the relation between FOVT, topological transitions and magnetic transition?…”