Electronic state of every solid is basically classified into two
categories according to its electrical responses: insulator or
metal. A textbook of modern solid state physics explains that shape
of a Fermi surface plays a key role in most physical properties in
metals. One of the well-established experimental methods to detect
a Fermi surface is measurement of quantum oscillations that is a
periodic response of physical quantities with respect to external
magnetic fields. As insulators do not host Fermi surface, it is
believed that they do not exhibit any quantum oscillations. This
book presents a comprehensive review of recent observations of
quantum oscillations in the Kondo insulators, SmB6 and YbB12, and
discusses how the observations are demonstrated by a newly proposed
mechanism where emergent charge-neutral fermions exhibit quantum
oscillations instead of bare electrons. It also focuses on
topological properties of Kondo insulators, and demonstrates that
YbB12 hosts a surface metallic conduction owing to its non-trivial
band structure. Further it presents the experiments of specific
heat and thermal conductivity in YbB12 down to ultra-low
temperature to discuss the possible low-energy excitations from a
Fermi surface of neutral fermions. The demonstrated gapless and
itinerant fermionic excitations, that is the significant
contribution from charge neutral fermions, violates Wiedemann-Franz
law. The discoveries point out a highly unconventional phase of
quantum state-electrically insulating but thermally
metallic-realized in the bulk of topological Kondo insulators.
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