Ground state properties of intermediate valence
Strongly correlated narrow-gap semiconductors, denoted also as Kondo insulators, have attracted much attention in the last few years. The formation of the
small transport and spin gap close to the Fermi level EF
in these compounds is believed to
originate from the hybridization of the narrow and localized f-states with the broad s, p or d-type conduction band. The
intermediate valence compound SmB6 was the first of these
materials to be discovered and it is one of the most often studied of this
class. Experiments have shown that the hybridization gap, which is responsible
for the decrease of electrical conductivity below 70K, has a width of Eg» 10-20meV. The further decrease of conductivity below 15K can be associated with a direct activation energy Ed »3-5 meV, which corresponds to transitions of electrons between the bottom of the conduction band and the in-gap states at EF. These states also seem to be responsible for the residual conductivity of this material below 3-5 K, and its properties appear to depend on the content of impurities and imperfections in the sample. Activation energy calculations
have shown that the residual conductivity is of non-activated (metallic)
nature. However, there are still open questions about the gap structure
and the properties of in-gap states. The purpose of the present study was
to investigate SmB6 by point-contact (PC) spectroscopy and specific heat
measurements and thus to contribute to the understanding of its ground
The differential conductance dI/dU of SmB6-SmB6 junctions
has been investigated between 0.1 and 4.2 K as function of lateral contact
size. The zero-bias PC conductance varied between 0.01mS
and 1mS. Two different regimes of charge transport have been distinguished.
Large junctions were in the diffusive regime, in which the conductance
is dominated by the bulk conductivity. Small junctions were in the tunnelling
regime and electrons can tunnel through the contact either by single hopping
event s liken the bulk material or as evanescent waves when the zero-bias
conductance is smaller than about 10mS. The
position of the spectral anomalies, which are related to the different
activation energies and band gaps of mB6 did not depend on the
contact size. To estimate the average density of states of our tunnel junctions
we normalized the spectra taken at 0.1K with respect to the voltage-dependent
background, averaged the normalized spectra, and fitted the average spectrum
by functional dependencies of the density of states, assuming a constant
transmission probability. A good fit is obtained by assuming a constant
background of » % 45 and two energy-dependent
parts of the density of states as shown in Fig. 2. The one part, g1(E), has a gap of » 21meV (full width at half maximum), while the other part, g2(E), has a gap of »4.5meV. These gaps may be attributed to Eg and to Ed, respectively. These results agree with those of planar SmB6-Pb tunnel junctions, and the values of Eg and Ed fit well those derived from other experiments. The large background conductance
originates in this case from states at lattice distortions and surface
of the PC area.
Figure 2: Average dI/dU(U) tunnel spectrum (solid circles) and a
fit (white line through the data points) calculated using the density of states (dotted line). g(E) is the sum of g1(E) and g2(E) plus a constant background.
In order to obtain additional information about the
properties of the background (in-gap) states at EF, the
heat capacity was measured. Fig. 3 shows the specific heat of samples a
and b as C(T)/T in the 0.1-3K range. Since sample b
with a higher content of impurities has a larger C than sample a,
impurities clearly influence the density of states at EF.
Additional contributions to C of sample b, which is between 1 and
3K by a factor 3-4 larger than C of sample a, may come from
contributions at higher T and from surface states as this sample
was polished. Another remarkable feature is the increase of C(T)/T
towards lower temperatures, which resembles the enhancement of the specific
heat in heavy fermion systems. As this enhancement is more pronounced for
the sample with less impurities (a) it can not be associated with
the presence of impurity states.
Figure 3: Specific heat of SmB6 in C/T-T2 plot.
It is unlikely to explain the enhancement
of C/T by a magnetic contribution or by a formation of a magnetic state
since no corresponding signal for such processes was observed in the
magnetic susceptibility down to 10mK. We can also exclude a very low temperature
Schottky anomaly because of additional activation energy was detected below
2 K. Thus the electronic part, which is connected with the metallic (in-gap)
states at EF, is probably responsible for the observed behavior
of the heat capacity of SmB6. Moreover, the increase of C(T)/T
below about 2K very likely demonstrates the formation of an intrinsic coherent state within these in-gap states.
K. Flachbart, S. Gabáni, V. Pavlík, M. Reiffers, P. Samuely
K. Gloos (Tech. Univ. Darmstadt), M. Orendáč (P.J.Š.Univ. Košice),
E. Konovalova, Y. Paderno (IPM UAS Kiev).