Quantum Oscillation in Narrow-Gap Topological Insulators

Zhang, Long; Song, Xueyang; Wang, Fa

doi:10.1103/physrevlett.116.046404

Cited by 103 publications

(136 citation statements)

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“…2 demonstrates again the validity of the Fermi liquid theory in SmB 6 . The mysterious sudden enhancement of quantum oscillation amplitude in SmB 6 reported by Tan et al [13] has attracted much attention as a rare 3D example of the deviation from the LK formula, which has been suggested as a reflection of unconventional quantum oscillation [19][20][21]32,33]. In our dHvA studies down to 40 mK, however, such behavior is not repeated, even though we apply up to 45 T magnetic field, stronger than that used in Ref.…”

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confidence: 41%

“…Furthermore, the deviation of LK behavior in FZ-grown samples was taken as evidence for the exotic nature of oscillations [13]; we note that a similar double-step feature was observed in topological nodal semimetal ZrSiS [41], in which the Fermi surface nesting leads to two LK behavior with two different effective masses. This is a more realistic origin than the various unconventional quantum oscillation models [19][20][21]23,24,32,33]. Overall, the topological surface state explanation is still the most natural one for all of our observations of the magnetic quantum oscillations in flux-grown SmB 6 .…”

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confidence: 96%

“…To make it more confusing, no quantum oscillations have ever been observed in transport measurements [12,14,15]. Several theories have been proposed to reconcile the puzzling experimental results [16][17][18] as well as to explain the enriched exotic low-temperature behaviors in SmB 6 [19][20][21][22][23][24]. The key problem to the * Corresponding author.…”

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Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

et al. 2017

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The Kondo insulator samarium hexaboride (SmB 6 ) has been intensely studied in recent years as a potential candidate of a strongly correlated topological insulator. One of the most exciting phenomena observed in SmB 6 is the clear quantum oscillations appearing in magnetic torque at a low temperature despite the insulating behavior in resistance. These quantum oscillations show multiple frequencies and varied effective masses. The origin of quantum oscillation is, however, still under debate with evidence of both twodimensional Fermi surfaces and three-dimensional Fermi surfaces. Here, we carry out angle-resolved torque magnetometry measurements in a magnetic field up to 45 Tand a temperature range down to 40 mK. With the magnetic field rotated in the (010) plane, the quantum oscillation frequency of the strongest oscillation branch shows a fourfold rotational symmetry. However, in the angular dependence of the amplitude of the same branch, this fourfold symmetry is broken and, instead, a twofold symmetry shows up, which is consistent with the prediction of a two-dimensional Lifshitz-Kosevich model. No deviation of LifshitzKosevich behavior is observed down to 40 mK. Our results suggest the existence of multiple light-mass surface states in SmB 6 , with their mobility significantly depending on the surface disorder level. DOI: 10.1103/PhysRevX.7.031054 Subject Areas: Condensed Matter Physics, Strongly Correlated Materials, Topological InsulatorsIn Kondo insulators, the physics is controlled by the strong many-body interactions [1]. The hybridization between the localized f elections and conduction d electrons causes the formation of Kondo singlets, which leads to a quench of local-magnetic-moment characteristics. Also, a narrow hybridization gap is developed at low temperature, resulting in a crossover from metallic to insulating behavior. In recent years, topological nontriviality is suggested to be hosted by Kondo insulators [2,3]. The opposite parity in the f band (odd) and d band (even) protects a band inversion similar to that in normal Z 2 topological insulators. In particular, the very large spin-orbit coupling in the renormalized f electrons can give a system ground state with "nontrivial" topological order, i.e., a different topological invariant from that in vacuum. As a result, a gapless two-dimensional (2D) Dirac electron state, known as the topological surface state, has to exist at certain high-symmetry points in the surface Brillouin zone. Such predictions point out the Kondo insulators as promising candidates of interaction-driven topological insulators, subsequently make this family a focus of attention in condensed-matter physics.The cubic structured SmB 6 , the very first confirmed member of Kondo insulators [4], has been elaborately studied as the most feasible example of the electron-correlated threedimensional (3D) strong topological insulator [5][6][7]. A large amount of experimental observations on this material have been published [8], with some giving hints of the topological surface ...

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Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

et al. 2017

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“…Since the flux through the unit cell in α-(BEDT-TTF) 2 I 3 is larger than that in graphene, it is expected to find the dHvA-like oscillation at lower magnetic field. Very recently, the dHvA-like oscillation in the system with no Fermi surface has been observed in SmB 6 65 and studied theoretically in many models [66][67][68][69] .…”

Section: Eq (D11) the Site Numbermentioning

confidence: 99%

Three-quarter Dirac points, Landau levels, and magnetization in α−(BEDT−TTF)2I3

Kishigi

Hasegawa

2017

Phys. Rev. B

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The energies as a function of the magnetic field (H) and the pressure are studied theoretically in the tight-binding model for the two-dimensional organic conductor, α-(BEDT-TTF)2I3, in which massless Dirac fermions are realized. The effects of the uniaxial pressure (P ) are studied by using the pressure-dependent hopping parameters. The system is semi-metallic with the same area of an electron pocket and a hole pocket at P < 3.0 kbar, where the energies (ε 0 D ) at the Dirac points locate below the Fermi energy (ε 0 F ) when H = 0. We find that at P = 2.3 kbar the Dirac cones are critically tilted. In that case a new type of band crossing occurs at "three-quarter"-Dirac points, i.e., the dispersion is quadratic in one direction and linear in the other three directions. We obtain new magnetic-field-dependences of the Landau levels (εn); εn − ε 0 D ∝ (nH)4/5 at P = 2.3 kbar ("three-quarter"-Dirac points) and |εn − ε 0 F | ∝ (nH) 2 at P = 3.0 kbar (the critical pressure for the semi-metallic state). We also study the magnetization as a function of the inverse magnetic field. We obtain two types of quantum oscillations. One is the usual de Haas van Alphen (dHvA) oscillation, and the other is the unusual dHvA-like oscillation which is seen even in the system without the Fermi surface.

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“…Two scenarios involving three-dimensional bulk interpretation were proposed recently [42,43]. However, both scenarios suggest the existence of quantum oscillations even for band insulators of certain types: either a simple band insulator of itinerant electrons hybridized with a localized flat band can exhibit quantum oscillations if the cyclotron energy is comparable to the electronic gap [42]; alternatively, an insulator with inverted bands can show quantum oscillations in its bulk low-energy DOS due to the periodic gap narrowing in magnetic fields [43].…”

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Bulk Fermi Surface of Charge-Neutral Excitations inSmB6or Not: A Heat-Transport Study

Cui

Dong

et al. 2016

Phys. Rev. Lett.

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Recently there have been increasingly hot debates on whether a bulk Fermi surface of chargeneutral excitations exists in the topological Kondo insulator SmB6. To unambiguously resolve this issue, we performed the low-temperature thermal conductivity measurements of a high-quality SmB6 single crystal down to 0.1 K and up to 14.5 T. Our experiments show that the residual linear term of thermal conductivity at zero field is zero, within the experimental accuracy. Furthermore, the thermal conductivity is insensitive to magnetic field up to 14.5 T. These results exclude the existence of fermionic charge-neutral excitations in bulk SmB6, such as scalar Majorana fermions or spinons, thus put a strong constraint on the explanation of the quantum oscillations observed in SmB6.Topological insulator is a novel quantum state of matter, and has been suggested theoretically and observed experimentally [1][2][3][4][5]. Like the edge channel found in the quantum Hall system, the strong spin-orbit coupling in a three dimensional topological insulator leads to a nontrivial and robust conducting surface state. This metallic state is protected by the time-reversal symmetry. Studies on topological insulators have later stimulated the search for many other topological materials, such as topological crystalline insulators, Weyl and Dirac semimetals, and topological Kondo insulator [6][7][8][9]. Especially, interaction effect could play an important role in topological Kondo insulators and render exotic physics in them.As one of the most historical heavy-fermion (HF) materials, SmB 6 has been studied for more than 50 years [10,11] and was recently shown to be a topological Kondo insulator [12]. For decades, the low-temperature conductivity in SmB 6 remains puzzling: its resistivity shows insulating behavior down to a few Kelvins but saturates down to the lowest temperature upon further reducing the temperature. This puzzle was successfully resolved by recent transport experiments, which show that the material is a bulk insulator but with a metallic surface [13,14], consistent with the theoretical prediction that SmB 6 is a topological Kondo insulator [9,[15][16][17]. At high temperatures, transport properties are dominated by thermal excitations in the insulating bulk, and thus insulating behaviors are observed. At low temperatures, however, bulk excitations vanishes because of the energy gap, and surface signals become dominant. The existence of the metallic surface states is now well established and observed in a number of experiments [18][19][20][21][22][23][24][25][26][27][28][29][30][31].Although electric transport measurements so far show that the bulk of SmB 6 has no gapless charge carriers (namely a finite charge-gap), there exist other experiments suggesting possible gapless excitations in the bulk. Especially, the recent quantum oscillation measurement claims multiple Fermi seas in the bulk of an insulating SmB 6 sample [20], in direct contradiction with transport measurements. As the electrical transport only measures the ch...

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Quantum Oscillation in Narrow-Gap Topological Insulators

Cited by 103 publications

References 24 publications

Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

Three-quarter Dirac points, Landau levels, and magnetization in α−(BEDT−TTF)2I3

Bulk Fermi Surface of Charge-Neutral Excitations inSmB6or Not: A Heat-Transport Study

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