Magnetic and topological transitions in three-dimensional topological Kondo insulator

Abstract

By using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulating phases (TIs) in three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to third neighbor, we identify four strong topological insulating (STI) phases and two weak topological insulating (WTI) phases, then the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH, f -electron energy level and hybridization constant. We also find an insulator-metal transition from a STI phase which has surface Fermi rings and spin textures in qualitative agreement to TKI candidate SmB6. In weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams, and depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into AF topological insulator (AFTI) and non-topological AF insulator (nAFI), according to their Z2 indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTI, showing distinguishable surface dispersions around their Dirac points.

Valence transition in topological Kondo insulator

“…This mechanism of FOVT in PAM is very similar to that of Falicov-Kimball model, since in both models the U fc term plays a crucial role in generating the FOVT [46][47][48][49]. Previous works have shown that the variation of f or V can lead to a sign reversal of the parity at certain TRIM through closing and reopening of bulk insulating gap, resulting in successive topological transitions [5,7,24]. Consequently, both STI and WTI can be further classified according to their bandinversion points (or the locations of Dirac points) [7,23,24].…”

“…In Fig. 2b, the phase diagram around the QCP is shown in enlarged pattern, in which the FOVT successively converges with the topological boundaries at two points, one at U f c =4.38 and ǫ f =−2.93, the other at U f c =4.82 and ǫ f =−3.19, separating the FOVT into three segments: (1) when 4.31< U f c <4.38, FOVT occurs near conventional STIΓ X -WTI X transition ( the subscripts denote the Dirac points on the surface Brillouin zone 47 ); (2) when 4.38< U f c <4.82, FOVT occurs simultaneously with first-order STIΓ X -WTI X transition; (3) when U f c >4.82, a first-order STIΓ X -STI M transition takes place at FOVT. Below the QCP, namely when U f c <4.31, U f c is insufficient to produce FOVT, but rather a valence crossover between Kondo region and MV.…”

“…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?…”

“…In these TKIs, the strong spin-orbit coupling in the hybridization between d and f electrons guarantees time-reversal symmetry (TRS) and generates a band inversion between d and f states at certain time-reversal-invariant momenta (TRIM), which are the eight high-symmetry points in three-dimensional (3D) Brillouin zone (BZ), leading to the Z 2 classification of the Kondo insulating states into strong topological insulator (STI), weak topological insulator (WTI) and normal Kondo insulator (nKI) [3,4,6,21,22]. Moreover, both STI and WTI can be further classified according to their band-inversion points (consequently the locations of Dirac points) [7,23,24]. Via the spin-and angle-resolved photoemission spectroscopy (SARPES), the metallic surface states with Dirac points at Γ and X points have been observed in SmB 6 , confirming its strong topological characteristic [13,25].…”

Two ultra-stable novel allotropes of tellurium few-layers*

“…Layers of group IV elements, known as silicene, [10][11][12] germanene, [13] stanene, [14,15] and layers of a group III element, i.e., borophenes, [16][17][18] as well as group V fewlayers, i.e., 2D P, [19][20][21][22][23] As, [24] Sb, [25] and Bi, [26] were subsequently predicted and synthesized or isolated. These mono-and few-layers of groups III, IV, and V elements were experimentally shown or were theoretically predicted to have tunable bandgap, [7,12,23,24] high carrier mobility, [19][20][21]25] strong light absorption and response in infrared and visible lights ranges, [27,28] exceptional mechanical and frictional properties, [5,17,22] catalysis activities, [29] topological electronic states, [8,10,14,26,[30][31][32][33][34][35] superconductivity, [36,37] and among the others. [38] However, the few-layer forms of group VI elements are still ambiguous and are yet to be unveiled.…”