Topological
states
of
quantum
matter
represent
a
rapidly
developing
area
of
research,
where
a
fascinating
variety
of
exotic
phenomena
occur,
ranging
from
unusual
transport
properties
to
fractionalized
excitations
that
may
emerge
at
system’s
defects.
Of
particular
recent
interest
has
been
the
topic
of
strongly-interacting
topological
phases,
where
electronic
correlations
and
topology
both
play
an
important
role.
In
this
talk,
I
will
review
recent
theoretical
and
experimental
work
on
a
relatively
new
class
of
such
interacting
topological
material
system
–
topological
Kondo
insulators,
which
appear
as
a
result
of
interplay
between
strong
correlations
and
spin-orbit
interactions.
I
will
start
by
explaining
in
simple
terms
the
basics
of
topological
quantum
matter,
including
the
by
now
standard
theory
of
topological
band
insulators.
Then,
I
will
use
these
concepts
to
show
that
the
conduction
electrons
and
localized
magnetic
moments
in
certain
heavy
fermion
compounds
hybridize
to
give
rise
to
a
topological
insulating
behavior.
I
will
explain
key
experimental
results,
which
have
confirmed
our
predictions
in
the
Samarium
hexaboride
heavy
fermion
compound,
where
the
long-standing
puzzle
of
the
residual
low-temperature
conductivity
has
been
shown
to
originate
from
topological
surface
states.
I
will
also
mention
several
recent
theory-experiment
collaborative
projects
that
led
to
the
development
of
a
“topological
device”
and
new
methods
to
extend
topological
behavior
in
Kondo
insulators
from
a
few
Kelvin
to
room
temperature.
In
conclusion,
I
will
discuss
a
series
of
recent
puzzling
experiments,
which
unexpectedly
observed
quantum
oscillations,
typical
to
a
metal,
coming
from
an
inert,
insulating
bulk
of
Kondo
insulators,
which
may
represent
a
smoking
gun
of
a
new
fractionalized
state
of
matter.