- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

Z. Xiang1, B. Lawson1, T. Asaba1, C. Tinsman1, Lu Chen1, C. Shang2, X. H. Chen2, and Lu Li1,*

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 2Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Key Laboratory of Strongly-coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, China

  • *Corresponding author. luli@umich.edu
PDF

Phys. Rev. X 7, 031054 – Published 25 September, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031054

Abstract

The Kondo insulator samarium hexaboride (SmB6) 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 SmB6 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 two-dimensional Fermi surfaces and three-dimensional Fermi surfaces. Here, we carry out angle-resolved torque magnetometry measurements in a magnetic field up to 45 T and 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 Lifshitz-Kosevich behavior is observed down to 40 mK. Our results suggest the existence of multiple light-mass surface states in SmB6, with their mobility significantly depending on the surface disorder level.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Strong interactions among electrons have led to novel phenomena such as high-temperature superconductivity, while topological materials constitute a new type of substance that protects exotic electronic states. Kondo insulators—a type of insulator based on rare-earth elements—bridge these two exciting frontiers. They are the only experimentally demonstrated materials in which strong electronic interactions coexist with topological protections; the interior is a perfect insulator and yet the surface is conductive. This is not only fundamentally new, but it also opens doors for electronics that use the conductive surfaces for circuits. Researchers have debated the origin of magnetic oscillations, known as the de Hass-van Alphen (dHvA) effect, observed in Kondo insulators, a curious behavior since it is a key feature of metals. We provide crucial evidence—an angular dependence of quantum oscillation amplitude—that suggests these oscillations originate in the surface of samarium hexaboride (SmB6), a typical Kondo insulator.

We measured the dHvA signals using torque magnetometry in single crystals of SmB6 at many different tilt angles between magnetic fields and crystal axes. Besides the 2D-like angular dependence of dHvA oscillation frequencies, the angle-dependent amplitude breaks the fourfold rotational symmetry of the cubic crystal structure. The angular and temperature dependence of dHvA amplitudes are both consistent with the behavior of a 2D Fermi-liquid system down to 40 mK in a strong magnetic field of 45 T.

Our results show that quantum oscillations in a Kondo insulator come from the surface, which is consistent with the interpretation of topologically protected surface states and should shed light on future work pursuing topological protection in strongly correlated systems.

Article Text

References (71)

  1. P. S. Riseborough, Heavy Fermion Semiconductors, Adv. Phys. 49, 257 (2000).
  2. M. Dzero, K. Sun, V. Galitski, and P. Coleman, Topological Kondo Insulators, Phys. Rev. Lett. 104, 106408 (2010).
  3. M. Dzero, K. Sun, P. Coleman, and V. Galitski, Theory of Topological Kondo Insulators, Phys. Rev. B 85, 045130 (2012).
  4. A. Menth, E. Buehler, and T. Geballe, Magnetic and Semiconducting Properties of SmB6, Phys. Rev. Lett. 22, 295 (1969).
  5. T. Takimoto, SmB6: A Promising Candidate for a Topological Insulator, J. Phys. Soc. Jpn. 80, 123710 (2011).
  6. V. Alexandrov, M. Dzero, and P. Coleman, Cubic Topological Kondo Insulators, Phys. Rev. Lett. 111, 226403 (2013).
  7. F. Lu, J. Z. Zhao, H. Weng, Z. Fang, and X. Dai, Correlated Topological Insulators with Mixed Valence, Phys. Rev. Lett. 110, 096401 (2013).
  8. M. Dzero, J. Xia, V. Galitski, and P. Coleman, Topological Kondo Insulators, Annu. Rev. Condens. Matter Phys. 7, 249 (2016).
  9. D.-J. Kim, J. Xia, and Z. Fisk, Topological Surface State in the Kondo Insulator Samarium Hexaboride, Nat. Mater. 13, 466 (2014).
  10. S. Thomas, D. J. Kim, S. B. Chung, T. Grant, Z. Fisk, and J. Xia, Weak Antilocalization and Linear Magnetoresistance in the Surface State of SmB6, Phys. Rev. B 94, 205114 (2016).
  11. N. Xu et al., Direct Observation of the Spin Texture in SmB6 as Evidence of the Topological Kondo Insulator, Nat. Commun. 5, 4566 (2014).
  12. G. Li, Z. Xiang, F. Yu, T. Asaba, B. Lawson, P. Cai, C. Tinsman, A. Berkley, S. Wolgast, Y. S. Eo, Dae-Jeong Kim, C. Kurdak, J. W. Allen, K. Sun, X. H. Chen, Y. Y. Wang, Z. Fisk, and L. Li, Two-Dimensional Fermi Surfaces in Kondo Insulator SmB6, Science 346, 1208 (2014).
  13. B. Tan, Y.-T. Hsu, B. Zeng, M. C. Hatnean, N. Harrison, Z. Zhu, M. Hartstein, M. Kiourlappou, A. Srivastava, M. D. Johannes, T. P. Murphy, J.-H. Park, L. Balicas, G. G. Lonzarich, G. Balakrishnan, and S. E. Sebastian, Unconventional Fermi Surface in an Insulating State, Science 349, 287 (2015).
  14. S. Wolgast, Y. S. Eo, T. Oztürk, G. Li, Z. Xiang, C. Tinsman, T. Asaba, B. Lawson, F. Yu, J. W. Allen, K. Sun, L. Li, Ç. Kurdak, D.-J. Kim, and Z. Fisk, Magnetotransport Measurements of the Surface States of Samarium Hexaboride Using Corbino Structures, Phys. Rev. B 92, 115110 (2015).
  15. F. Chen, C. Shang, Z. Jin, D. Zhao, Y. P. Wu, Z. J. Xiang, Z. C. Xia, A. F. Wang, X. G. Luo, T. Wu, and X. H. Chen, Magnetoresistance Evidence of a Surface State and a Field-Dependent Insulating State in the Kondo Insulator SmB6, Phys. Rev. B 91, 205133 (2015).
  16. V. Alexandrov, P. Coleman, and O. Erten, Kondo Breakdown in Topological Kondo Insulators, Phys. Rev. Lett. 114, 177202 (2015).
  17. O. Erten, P. Ghaemi, and P. Coleman, Kondo Breakdown and Quantum Oscillations in SmB6, Phys. Rev. Lett. 116, 046403 (2016).
  18. R. Peters, T. Yoshida, H. Sakakibara, and N. Kawakami, Coexistence of Light and Heavy Surface States in a Topological Multiband Kondo Insulator, Phys. Rev. B 93, 235159 (2016).
  19. J. Knolle and N. R. Cooper, Quantum Oscillations without a Fermi Surface and the Anomalous de Haas–van Alphen Effect, Phys. Rev. Lett. 115, 146401 (2015).
  20. L. Zhang, X.-Y. Song, and F. Wang, Quantum Oscillation in Narrow-Gap Topological Insulators, Phys. Rev. Lett. 116, 046404 (2016).
  21. H. K. Pal, F. Piéchon, J.-N. Fuchs, M. Goerbig, and G. Montambaux, Chemical Potential Asymmetry and Quantum Oscillations in Insulators, Phys. Rev. B 94, 125140 (2016).
  22. J. Pixley, R. Yu, S. Paschen, and Q. Si, Global Phase Diagram and Momentum Distribution of Single-Particle Excitations in Kondo Insulators, arXiv:1509.02907.
  23. G. Baskaran, Majorana Fermi Sea in Insulating SmB6: A Proposal and a Theory of Quantum Oscillations in Kondo Insulators, arXiv:1507.03477.
  24. O. Erten, P.-Y. Chang, P. Coleman, and A. M. Tsvelik, Skyrme Insulators: Insulators at the Brink of Superconductivity, Phys. Rev. Lett. 119, 057603 (2017).
  25. P. C. Canfield and Z. Fisk, Growth of Single Crystals from Metallic Fluxes, Philos. Mag. B 65, 1117 (1992).
  26. D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, England, 2009).
  27. A. A. Taskin and Y. Ando, Quantum Oscillations in a Topological Insulator Bi1−xSbx, Phys. Rev. B 80, 085303 (2009).
  28. Y. Ando, Topological Insulator Materials, J. Phys. Soc. Jpn. 82, 102001 (2013).
  29. W. K. Park, L. Sun, A. Noddings, D.-J. Kim, Z. Fisk, and L. H. Greene, Topological Surface States Interacting with Bulk Excitations in the Kondo Insulator SmB6 Revealed via Planar Tunneling Spectroscopy, Proc. Natl. Acad. Sci. U.S.A. 113, 6599 (2016).
  30. M. Dzero, M. G. Vavilov, K. Kechedzhi, and V. M. Galitski, Nonuniversal Weak Antilocalization Effect in Cubic Topological Kondo Insulators, Phys. Rev. B 92, 165415 (2015).
  31. P. Syers, D. Kim, M. S. Fuhrer, and J. Paglione, Tuning Bulk and Surface Conduction in the Proposed Topological Kondo Insulator SmB6, Phys. Rev. Lett. 114, 096601 (2015).
  32. J. Knolle and N. R. Cooper, Excitons in Topological Kondo Insulators: Theory of Thermodynamic and Transport Anomalies in SmB6, Phys. Rev. Lett. 118, 096604 (2017).
  33. H. K. Pal, Quantum Oscillations from Inside the Fermi Sea, Phys. Rev. B 95, 085111 (2017).
  34. J. Singleton, Studies of Quasi-Two-Dimensional Organic Conductors Based on BEDT-TTF Using High Magnetic Fields, Rep. Prog. Phys. 63, 1111 (2000).
  35. W. A. Phelan, S. M. Koohpayeh, P. Cottingham, J. W. Freeland, J. C. Leiner, C. L. Broholm, and T. M. McQueen, Correlation between Bulk Thermodynamic Measurements and the Low-Temperature-Resistance Plateau in SmB6, Phys. Rev. X 4, 031012 (2014).
  36. M. E. Valentine, S. Koohpayeh, W. A. Phelan, T. M. McQueen, P. F. S. Rosa, Z. Fisk, and N. Drichko, Breakdown of the Kondo Insulating State in SmB6 by Introducing Sm Vacancies, Phys. Rev. B 94, 075102 (2016).
  37. W. Phelan, S. Koohpayeh, P. Cottingham, J. Tutmaher, J. Leiner, M. Lumsden, C. Lavelle, X. Wang, C. Hoffmann, M. Siegler, N. Haldolaarachchige, D. P. Young, and T. M. McQueen, On the Chemistry and Physical Properties of Flux and Floating Zone Grown SmB6 Single Crystals, Sci. Rep. 6, 20860 (2016).
  38. Y. Nakajima, P. Syers, X. Wang, R. Wang, and J. Paglione, One-Dimensional Edge State Transport in a Topological Kondo Insulator, Nat. Phys. 12, 213 (2016).
  39. P. K. Biswas, M. Legner, G. Balakrishnan, M. C. Hatnean, M. R. Lees, D. M. Paul, E. Pomjakushina, T. Prokscha, A. Suter, T. Neupert, and Z. Salman, Suppression of Magnetic Excitations Near the Surface of the Topological Kondo Insulator SmB6, Phys. Rev. B 95, 020410(R) (2017).
  40. X.-Y. Feng, H. Zhong, J. Dai, and Q. Si, Dirac-Kondo Semimetals and Topological Kondo Insulators in the Dilute Carrier Limit, arXiv:1605.02380.
  41. S. Pezzini, M. R. van Delft, L. Schoop, B. Lotsch, A. Carrington, M. I. Katsnelson, N. E. Hussey, and S. Wiedmann, Unconventional Mass Enhancement around the Dirac Nodal Loop in ZrSiS, arXiv:1701.09119.
  42. T. Terashima, C. Terakura, Y. Umeda, N. Kimura, H. Aoki, and S. Kunii, Ferromagnetism vs Paramagnetism and False Quantum Oscillations in Lanthanum-Doped CaB6, J. Phys. Soc. Jpn. 69, 2423 (2000).
  43. C. Larson and W. Gordon, Low-Field de Haas–van Alphen Study of the Fermi Surface of Aluminum, Phys. Rev. 156, 703 (1967).
  44. N. Ashcroft, The Fermi Surface of Aluminium, Philos. Mag. 8, 2055 (1963).
  45. K. Yamaji, On the Angle Dependence of the Magnetoresistance in Quasi-Two-Dimensional Organic Superconductors, J. Phys. Soc. Jpn. 58, 1520 (1989).
  46. A. I. Coldea, J. D. Fletcher, A. Carrington, J. G. Analytis, A. F. Bangura, J.-H. Chu, A. S. Erickson, I. R. Fisher, N. E. Hussey, and R. D. McDonald, Fermi Surface of Superconducting LaFePO Determined from Quantum Oscillations, Phys. Rev. Lett. 101, 216402 (2008).
  47. N. Harrison, R. Bogaerts, P. H. P. Reinders, J. Singleton, S. J. Blundell, and F. Herlach, Numerical Model of Quantum Oscillations in Quasi-Two-Dimensional Organic Metals in High Magnetic Fields, Phys. Rev. B 54, 9977 (1996).
  48. N. Harrison, A. House, I. Deckers, J. Caulfield, J. Singleton, F. Herlach, W. Hayes, M. Kurmoo, and P. Day, de Haas–van Alphen Study of the Charge-Transfer Salt α−(BEDT−TTF)2KHg(SCN)4 Pulsed Magnetic Fields of Up to 54 T, Phys. Rev. B 52, 5584 (1995).
  49. B. Ramshaw, B. Vignolle, J. Day, R. Liang, W. Hardy, C. Proust, and D. Bonn, Angle Dependence of Quantum Oscillations in YBa2Cu3O6.59 Shows Free-Spin Behaviour of Quasiparticles, Nat. Phys. 7, 234 (2011).
  50. K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, and A. Firsov, Two-Dimensional Gas of Massless Dirac Fermions in Graphene, Nature (London) 438, 197 (2005).
  51. A. A. Taskin, K. Segawa, and Y. Ando, Oscillatory Angular Dependence of the Magnetoresistance in a Topological Insulator Bi1−xSbx, Phys. Rev. B 82, 121302 (2010).
  52. Y.-S. Fu, T. Hanaguri, K. Igarashi, M. Kawamura, M. Bahramy, and T. Sasagawa, Observation of Zeeman Effect in Topological Surface State with Distinct Material Dependence, Nat. Commun. 7, 10829 (2016).
  53. C. J. Lin, X. Y. He, J. Liao, X. X. Wang, V. Sacksteder IV, W. M. Yang, T. Guan, Q. M. Zhang, L. Gu, G. Y. Zhang, C. G. Zeng, X. Dai, K. H. Wu, and Y. Q. Li, Parallel Field Magnetoresistance in Topological Insulator Thin Films, Phys. Rev. B 88, 041307 (2013).
  54. I. Garate and M. Franz, Magnetoelectric Response of the Time-Reversal Invariant Helical Metal, Phys. Rev. B 81, 172408 (2010).
  55. A. A. Zyuzin, M. D. Hook, and A. A. Burkov, Parallel Magnetic Field Driven Quantum Phase Transition in a Thin Topological Insulator Film, Phys. Rev. B 83, 245428 (2011).
  56. A. Sulaev, M. Zeng, S.-Q. Shen, S. K. Cho, W. G. Zhu, Y. P. Feng, S. V. Eremeev, Y. Kawazoe, L. Shen, and L. Wang, Electrically Tunable In-Plane Anisotropic Magnetoresistance in Topological Insulator BiSbTeSe2 Nanodevices, Nano Lett. 15, 2061 (2015).
  57. L.-X. Wang, Y. Yan, L. Zhang, Z.-M. Liao, H.-C. Wu, and D.-P. Yu, Zeeman Effect on Surface Electron Transport in Topological Insulator Bi2Se3 Nanoribbons, Nanoscale 7, 16687 (2015).
  58. L. Wu, W.-K. Tse, M. Brahlek, C. M. Morris, R. V. Aguilar, N. Koirala, S. Oh, and N. P. Armitage, High-Resolution Faraday Rotation and Electron-Phonon Coupling in Surface States of the Bulk-Insulating Topological Insulator Cu0.02Bi2Se3, Phys. Rev. Lett. 115, 217602 (2015).
  59. T. Liang, Q. Gibson, M. N. Ali, M. Liu, R. Cava, and N. Ong, Ultrahigh Mobility and Giant Magnetoresistance in the Dirac Semimetal Cd3As2, Nat. Mater. 14, 280 (2015).
  60. T. Champel and V. Mineev, de Haas–van Alphen Effect in Two- and Quasi-Two-Dimensional Metals and Superconductors, Philos. Mag. B 81, 55 (2001).
  61. V. Laukhin, A. Audouard, H. Rakoto, J. Broto, F. Goze, G. Coffe, L. Brossard, J. Redoules, M. Kartsovnik, N. Kushch, L. I. Buravov, A. G. Khomenko, E. B. Yagubskii, S. Askenazy, and P. Pari, Transport Properties and Giant Shubnikov–de Haas Oscillations in the First Organic Conductor with Metal Complex Anion Containing Selenocyanate Ligand, (ET)2TlHg(SeCN)4, Physica (Amsterdam) 211B, 282 (1995).
  62. S. E. Sebastian, N. Harrison, M. Altarawneh, R. Liang, D. Bonn, W. Hardy, and G. Lonzarich, Chemical Potential Oscillations from Nodal Fermi Surface Pocket in the Underdoped High-Temperature Superconductor YBa2Cu3O6+x, Nat. Commun. 2, 471 (2011).
  63. S. G. Sharapov, V. P. Gusynin, and H. Beck, Magnetic Oscillations in Planar Systems with the Dirac-like Spectrum of Quasiparticle Excitations, Phys. Rev. B 69, 075104 (2004).
  64. J. G. Analytis, R. D. McDonald, S. C. Riggs, J.-H. Chu, G. Boebinger, and I. R. Fisher, Two-Dimensional Surface State in the Quantum Limit of a Topological Insulator, Nat. Phys. 6, 960 (2010).
  65. J. Xiong, Y. Luo, Y. H. Khoo, S. Jia, R. J. Cava, and N. P. Ong, High-Field Shubnikov–de Haas Oscillations in the Topological Insulator Bi2Te2Se, Phys. Rev. B 86, 045314 (2012).
  66. C. Putzke, L. Malone, S. Badoux, B. Vignolle, D. Vignolles, W. Tabis, P. Walmsley, M. Bird, N. E. Hussey, C. Proust, and Antony Carrington, Inverse Correlation between Quasiparticle Mass and Tc in a Cuprate High-Tc Superconductor, Sci. Adv. 2, e1501657 (2016).
  67. A. A. Taskin and Y. Ando, Berry Phase of Nonideal Dirac Fermions in Topological Insulators, Phys. Rev. B 84, 035301 (2011).
  68. Y. Luo, H. Chen, J. Dai, Z.-A. Xu, and J. D. Thompson, Heavy Surface State in a Possible Topological Kondo Insulator: Magnetothermoelectric Transport on the (011) Plane of SmB6, Phys. Rev. B 91, 075130 (2015).
  69. W. Ruan, C. Ye, M. Guo, F. Chen, X. Chen, G.-M. Zhang, and Y. Wang, Emergence of a Coherent In-Gap State in the SmB6 Kondo Insulator Revealed by Scanning Tunneling Spectroscopy, Phys. Rev. Lett. 112, 136401 (2014).
  70. S. Rößler, T.-H. Jang, D.-J. Kim, L. Tjeng, Z. Fisk, F. Steglich, and S. Wirth, Hybridization Gap and Fano Resonance in SmB6, Proc. Natl. Acad. Sci. U.S.A. 111, 4798 (2014).
  71. L. Jiao, S. Rößler, D. Kim, L. Tjeng, Z. Fisk, F. Steglich, and S. Wirth, Additional Energy Scale in SmB6 at Low-Temperature, Nat. Commun. 7, 13762 (2016).

Outline

Information

Phys. Rev. X 7, 031054– Published 25 September, 2017
  • Received 12 May 2017
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation