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Crossover of Magnetoresistance from Fourfold to Twofold Symmetry in SmB6 Single Crystal, a topological Kondo insulator

Topological Kondo insulators have been attracting great attention from the condensed-matter physics community due to their fascinating topological and strongly correlated properties. Here, we report angle-dependent c-axis magnetoresistance (MR) oscillations in a Kondo insulator, SmB6 single crystal, in a magnetic field of up to 13 T rotated in the ab-plane. Four-fold symmetric MR oscillations are first observed above 8 K, which result from the four-fold (C4) degeneracy of the bulk Fermi surface of SmB6. With decreasing temperature down to 2.3 K, the C4 symmetry of the MR oscillations gradually weakens and C2 symmetry appears. This demonstrates a crossover from three-dimensional bulk states to two-dimensional surface states and implies the possible emergence of topological nematic states. Our experimental observations shed new light on the metallic surface states and nematic states in the Kondo insulator SmB6.


Introduction
Strongly correlated electron systems have been attracting great attention from the condensedmatter physics community due to their many exotic electronic and magnetic properties, such as high critical temperature (high-T c ) superconductivity, colossal magnetoresistance (MR), and electronic nematic states [1][2][3]. Samarium hexaboride (SmB 6 ) is well known as a strongly correlated electron system, in which the 4f-electrons hybridize with the conduction 5d-electrons and form a narrow Kondo energy gap, E g ≈ 15 meV [4][5][6][7]. The magnetic, optical, and thermal transport properties of this narrow-gap semiconductor have been extensively investigated in the last half-century [8][9][10][11][12]. The most puzzling issue is the lack of divergence in the resistivity at low temperatures, which has always been attributed to in-gap states [13][14][15][16]. Recently, there have been theoretical and experimental demonstrations that such in-gap states might be topological surface states [17][18][19][20][21][22][23][24].
Possible topological surface states were observed at the X and Г points of the surface Brillouin zone Magnetotransport is a helpful way to understand and explore the electronic states in strongly correlated systems and topological insulators [30][31][32].

Experimental Measurements
Single crystals of SmB 6 were grown by the conventional aluminum (Al) flux method. The sample was etched with acid to remove the leftover Al on the surface. Figure 1(a) displays the CsCltype crystal structure of SmB 6 . It can be seen that the Sm ions are located at the corner sites of the unit cell, while the B 6 octahedron is located at the body center of the cubic lattice. Figure 1

Results and Discussion
Firstly, we attempt to use an empirical formula to ( In this formula, the contribution of each of the four   [25,26]. On the basis of ARPES experiments, the four electron pockets enclose the X point in the first Brillouin zone [25][26][27][28]. Only one isotropic electron pocket is located at the Г point.
According to the results of qualitative analysis, the c-axis resistivity can be set using [37,43,44]. The C 2 symmetry of the angle-dependent MR was observed in the temperature range where a resistance plateaus appears. In such a range, it is widely believed that the Kondo insulator SmB 6 has an insulating bulk with a Kondo gap and 2D metallic surface states [21][22][23][24]. Therefore, the transition of MR from C 4 to C 2 symmetry indicates a crossover from 3D metallic bulk states to 2D metallic surface states with an insulating bulk.
Very recently, we noticed that a theoretical model has been established to explain our experimental observations [53]. This theoretical model demonstrates that the C 2 symmetry of the angledependent MR in SmB 6 may originate from the nematic surface states on the FS [53].
An electronic nematic state is a translationally invariant metallic phase with a spontaneously generated spatial anisotropy [3,54]. Such a state has been observed in strongly correlated systems including URu 2 Si 2 , Sr 3 Ru 2 O 7 , and superconductors [3,[54][55][56][57]. In the topological Kondo insulator SmB 6 , strong interactions may drive this system into rotational-symmetry-breaking nematic states [53]. In addition, the anisotropy in the FS of SmB 6 may also promote the formation of nematic states at low temperatures. The nematic phase breaks the

Conclusion
In summary, we first experimentally observed angle-dependent c-axis MR oscillations in SmB 6 single crystal, which is a topological Kondo insulator, in a magnetic field rotated in the ab-