Evidence for charge Kondo effect in superconducting Tl-doped PbTe Page: 3 of 5
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3
5
4
3
E
0 2
1
0
-10
1 2 3 4 5
H (T)
FIG. 3: Representative magnetoresistance, Ap - p(H) -
p(H - 0), for x - 0.4% at 1.8 K. Upper inset shows tem-
perature dependence of the resistivity in fields of 0 and 5 T.
The data for 5 T have been shifted down by po(5 T) -po(0 T)
= 4.8 p(? cm. Lower inset shows temperature dependence of
susceptibility for different Ti concentrations.
an average value of 106 m/s for holes in the anisotropic
L pockets and 105 m/s for holes in the heavier E pock-
ets. Based on these estimates, the mean free path l is
relatively large at 130 A. With the large resulting val-
ues of kFl, at approximately 7 for x 0.4%, it is very
unlikely that the low-temperature upturn in resistivity is
due to localization effects. Furthermore, the observed T2
temperature dependence of the resistivity is not readily
identified with such a scenario.
To further probe the origin of the normal-state resis-
tivity anomaly, the transverse magnetoresistance of the
samples was measured, taking care to avoid spurious
Hall contributions. Representative data for x 0.4%
are shown in Fig. 3. In all cases, the magnetoresistance
is positive, following a B2 dependence for temperatures
above T, or fields above Hc2. Furthermore, the overall
temperature dependence of the resistivity shows the same
Kondo-like upturn even in an applied field (upper inset
to Fig. 3) and is presumably shifted to a higher value due
to a standard Kohler's rule type magnetoresistance. This
behavior is consistent with the absence of both electron-
electron effects and weak localization, which, even in the
presence of strong spin-orbit scattering, would cause a
B1/2 field dependence at high fields. Furthermore, this
behavior precludes a magnetic Kondo effect as the origin
of the resistivity anomaly, for which a field of 5 T would
cause a substantial negative magnetoresistance.
To verify the absence of magnetic impurities, suscepti-
bility measurements for several samples of each Tl con-
centration were made for arbitrary crystal orientations
in an applied field of 1000 Oe using a commercial Quan-
tum Design SQuID magnetometer. Representative data
are shown in the lower inset to Fig. 3 as a function of- p( T - 4.Aluom
-a -
0 10 200 300
- ( K)
- I I0I
-x * -.3
- -.... "
' -3.0 "Y-- ... .,',. -
0 10T (K200 "300temperature. The susceptibility is diamagnetic for all
Tl concentrations due to the small density of states and
becomes less diamagnetic with increasing hole concen-
tration. The weak temperature dependence arises from
a temperature dependence of both the band gap and ef-
fective mass of PbTe [24]. Significantly, the lack of a
Curie-like paramagnetic term from the T1 dopants is con-
sistent with the absence of magnetic impurities down to
< 5 ppm, limited by the resolution of the measurement.
Hence, the low-temperature upturn in the resistivity of
Tl-doped PbTe follows a temperature dependence char-
acteristic of the Kondo effect in the absence of magnetic
impurities.
Thallium substitutes on the Pb site in PbTe. Calcula-
tions by Weiser [12] indicate that Tll+ has a lower energy
than T13+ in the lattice. Tl impurities therefore initially
act as acceptors, adding one hole per T1 to the valence
band, as observed in Hall measurements [17]. However,
the calculated energy difference between 1+ and 3+ im-
purity states, which can be modeled by SE 2(o -p)+U
[4] (where Eo is the energy to remove an electron from the
6s orbital and U < 0), is very small [12]. Indeed, for a
finite concentration of Tl impurities, the chemical po-
tential of holes in the system can reach the special value
p* co+U/2 for which the two valence states become ex-
actly degenerate (6E 0). A value of p larger than this
would correspond to all of the impurities being 3+. How-
ever, additional Tl impurities beyond this critical value
cannot increase p beyond p* because conversion of all of
the impurities to T13+ would add electrons to the valence
band, which would act to reduce rather than increase p.
Therefore, for Tl concentrations beyond a characteris-
tic critical value, the chemical potential remains pinned
at the special value p*, and any additional Tl impurities
act in a self-compensating manner such that both valence
states are present in equilibrium. This behavior has been
confirmed by Hall measurements, which show that for Tl
concentrations beyond approximately 0.5% the Hall co-
efficient saturates to a constant value corresponding to
approximately 1020 holes per cm3 [4, 25]. Significantly,
the Tl concentration at which this happens is remarkably
close to the concentration at which we observe the onset
of superconductivity (Fig. 1). Furthermore, within such
a scenario, it is natural to consider a charge Kondo ef-
fect, in which the conduction electrons interact with the
two degenerate valence states of the Tl impurities, and
pseudo-spin flip processes proceed via virtual excitations
to the skipped valence state. In the absence of orbital de-
generacy, the Kondo screening would proceed via a single
channel, so the observation of a resistivity anomaly fol-
lowing a T2 dependence at low temperatures is strong
evidence for such a state.
If we associate the observed resistivity upturn of Tl-
doped PbTe with a Kondo-like mechanism, then we can
estimate the characteristic Kondo temperature by fit-
ting the data in the insets to Fig. 2c and 2d to pimp ~
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Fisher, I. Evidence for charge Kondo effect in superconducting Tl-doped PbTe, article, January 11, 2010; United States. (https://digital.library.unt.edu/ark:/67531/metadc935240/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.