Emergent mystery in the Kondo insulator samarium hexaboride

A Publisher Correction to this article was published on 14 August 2020

This article has been updated


Samarium hexaboride (SmB6) is an example of a Kondo insulator, in which strong electron correlations cause a band gap to open. SmB6 hosts both a bulk insulating state and a conductive surface state. Within a Fermi-liquid framework, the strongly correlated ground-state electronic structure can be mapped to a simple state resembling a topological insulator. Although uncertainties remain, many experiments provide compelling evidence that the conductive surface states have a topological origin. However, the bulk behaviour is less well understood and some experiments indicate bulk in-gap states. This has inspired the development of many theories that predict the emergence of new bulk quantum phases beyond Landau’s Fermi-liquid model. We review the current progress on understanding both the surface and the bulk states, especially the experimental evidence for each. A mystery centres on the existence of the bulk in-gap states and why they appear in some experiments but not others. Adding to the mystery is why quantum oscillations in SmB6 appear only in magnetization but not in resistivity. We conclude by elaborating on three questions: why SmB6 is worth studying, what can be done to move forwards and what other correlated insulators could give additional insight.

Key points

  • The Kondo insulator samarium hexaboride (SmB6) is a perfect insulator owing to strong electronic correlations. It is the first experimentally confirmed example of a strongly correlated topological material.

  • The topological band structure and the consequent metallic surface states are determined and protected by the crystal point symmetry in SmB6. The universal topological predictions are confirmed by spin-resolved and angle-resolved photoemission spectroscopy, although some unresolved issues remain.

  • Surface electrical transport is established in SmB6. Spin-dependent experiments both confirm basic topological predictions and indicate the potential for spin-based electronic applications.

  • There is a mystery as to whether Landau-level quantum oscillations in SmB6 have a bulk or surface-state origin, and why they appear only in magnetization.

  • The mystery calls for a new growth method for SmB6, a broad search for other strongly correlated topological materials and further detailed theoretical pictures for the possible ground states of mixed-valent materials.

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Fig. 1: Schematic bulk band structure and topological surface states of SmB6.
Fig. 2: Transport characterization of SmB6.
Fig. 3: ARPES data on (100) and (111) surfaces, supporting the theory of a topological surface state.
Fig. 4: Alternative understanding of SmB6 (100) surface states, based on ARPES spectra of cleaved float-zone samples.
Fig. 5: Quantum oscillations in magnetization of SmB6 indicating a 2D Fermi surface.
Fig. 6: Bulk quantum-oscillation pattern in SmB6 crystals.
Fig. 7: Bulk magnetic excitations of SmB6.

Change history

  • 14 August 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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L.L. thanks the NSF (award no. DMR-1707620 for high-field electrical transport) and the DOE (award no. DE-SC0020184 for high-field magnetometry), and K.S. thanks the NSF (award no. NSF-EFMA-1741618 for theory) for supporting this work. All authors thank P.F.S. Rosa and Z. Fisk for illuminating discussions and P. Coleman for sharing his valuable suggestions on the demagnetization effect in isotropic paramagnets. All authors, especially J.W.A., thank J.D. Denlinger for generously sharing his extensive knowledge of SmB6 ARPES studies.

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Correspondence to Lu Li.

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Supplementary information


1 × 2 reconstruction

The freedom from complete bulk coordination can allow surface atoms to spontaneously ‘reconstruct’ to take atomic positions altered from the perfect surface termination of the bulk. In a ‘1 × 2’ or ‘2 × 1’ reconstruction, the alteration doubles the length of one of the two translation vectors of the surface unit cell, which halves the surface Brillouin zone in one direction. For the cubic crystal SmB6, this halving has the effect of rendering the \(\bar{\Gamma }\) and the \(\bar{{\rm{X}}}\) points of the un-reconstructed surface Brillouin zone to be equivalent.

Weak antilocalization

A quantum correction to conductance arising from quantum-interference effects in materials with strong spin–orbit interaction.

Edelstein effect

Accumulation of transverse spin due to the flow of an electric current in a thin film or a two-dimensional material with a strong spin–orbit interaction.

Corbino structures

A transport geometry with concentric circular contacts used to measure the electrical conductivity of a material.

Shubnikov–de Haas oscillations

Oscillations observed in transport measurements performed on conductors as a function of magnetic field. The oscillations arise from the formation of Landau levels separated from each other by the cyclotron energy.


Fermi-surface pockets refer to the location of conducting surface electrons or holes in reciprocal space. For the (001) surface, a cubic material with a lattice constant a, the Γ-pocket refers to the surface electrons located around the Γ point, (0,0), and the X-pockets refers to the electrons located around X points, (0,π/a) and (π/a,0).


Stoichiometry refers to the ratio of different atoms forming a crystal. For a stoichiometric material, the ratio is described by a fraction of natural numbers (i.e. 1:6 in the case of SmB6). Off-stoichiometry is a measure of disorder, where the ratio of constituent atoms deviates from the expected fraction of natural numbers.

Lifshitz–Kosevich model

Also known as the Lifshitz–Kosevich formula, a theoretical formula describing the magnetic-field dependence of oscillatory physical properties as a result of the Landau-level quantizations in metals. A consequence of Landau’s Fermi-liquid theory, the Lifshitz–Kosevich model explains particularly well the temperature dependence of the oscillatory magnitude of quantum oscillations.

Auxiliary-boson treatment

Also known as the auxiliary-boson method. Implies the use of any of several theoretical techniques for the study of strongly correlated quantum systems, where quantum dynamics and the effects of strong interactions among quantum particles are characterized through introducing additional (auxiliary) degrees of freedom.

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Li, L., Sun, K., Kurdak, C. et al. Emergent mystery in the Kondo insulator samarium hexaboride. Nat Rev Phys 2, 463–479 (2020). https://doi.org/10.1038/s42254-020-0210-8

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