Pis’ma v ZhETF, vol. 109, iss. 11, pp. 751 - 752
© 2019
June 10
Non-linear Hall effect in three-dimensional Weyl and Dirac semimetals
O.O.Shvetsov, V.D.Esin, A.V.Timonina, N.N.Kolesnikov, E.V.Deviatov1)
Institute of Solid State Physics of the Russian Academy of Sciences, 142432 Chernogolovka, Russia
Submitted 16 April 2019
Resubmitted 16 April 2019
Accepted 18
April 2019
DOI: 10.1134/S0370274X19110067
Non-linear Hall effect has been predicted in a wide
age V2ωxy for the second harmonics of the ac excitation
class of time-reversal invariant materials [1], like topo-
current I. The measured V2ωxy is below 0.1 µV, it slightly
logical crystalline insulators, two-dimensional transi-
(about 10 %) depends on temperature in 1.4-4.2 K in-
tion metal dichalcogenides, and three-dimensional Weyl
terval. The curve is obviously non-linear, V2ωxy ∼ I2.
and Dirac semimetals [2]. Recently, the time-reversal-
This behavior well corresponds [3, 4] to the expected
invariant non-linear Hall (NLH) effect has been reported
for NLH effect. However, this interpretation can not be
for two-dimensional layered dichalcogenides [3, 4]. It
accepted without additional arguments. For example, if
stimulates a search for the Berry curvature dipole in-
the potential contacts are not symmetric in respect to
duced NLH effect in three-dimensional crystals, where
the current line, we also obtain non-linear, V2ωxy ∼ I2
Dirac and Weyl semimetals are excellent candidates.
curve. In this case the signal level is one order of mag-
In the experiments [3, 4] on two-dimensional WTe2,
nitude higher, about 1 µV, which better corresponds to
the the second-harmonic Hall voltage depends quadrat-
typical thermopower values.
ically on the longitudinal current. On the other hand,
To experimentally determine the origin of the ef-
topological materials are characterized by strong ther-
fect in every of these two cases, we apply an external
moelectric effects, which also appear as a second-
magnetic field. In the case of the symmetric configura-
harmonic quadratic signal. For this reason, it is impor-
tion, ΔV2ωxy(B) = V2ωxy(B) - V2ωxy(B = 0) is nearly odd
tant to experimentally distinguish between the Berry
function, i.e. V2ωxy(B) depends on the magnetic field di-
curvature dipole induced NLH effect and a thermoelec-
rection: V2ωxy(B) is diminishing for the positive fields,
tric response while searching for the NLH effect in non-
while it is increasing for the negative ones. In contrast,
magnetic materials.
V2ωxy(B) increases for both field directions for the non-
Cd3As2 crystals were grown by crystallization of
symmetric connection scheme. In this case, V2ωxy(B) even
molten drops in the convective counterflow of argon held
quantitatively resembles Cd3As2 magnetoresistence [5].
at 5 MPa pressure. The energy-dispersive X-ray spec-
The observed behavior can be reproduced not only
troscopy (EDX) and X-ray powder diffractograms al-
for different samples in different cooling cycles, but also
ways confirmed pure Cd3As2 with I41cd noncentrosym-
can be demonstrated for another three-dimensional ma-
metric group. WTe2 compound was synthesized from
terial, like WTe2 Weyl semimetal. As a result, we obtain
elements by reaction of metal with tellurium vapor in
non-linear second-harmonic xy signal V2ωxy ∼ I2, which
the sealed silica ampule. The X-ray diffraction confirms
demonstrates different magnetic field behavior, even- or
Pmn21 orthorhombic single crystal WTe2.
odd-type, for nonsymmetric or strictly symmetric con-
Figure 1 shows a top-view image of a sample. We en-
figurations of voltage probes, respectively.
sure, that the measured voltage is antisymmetric with
respect to the voltage probe swap and it is independent
The odd V2ωxy(B) dependence is a good argument for
of the ground probe position. We check, that the lock-in
NLH origin of the non-zero second-harmonic Hall volt-
signal is also independent of the modulation frequency
age: if the ac excitation current generates sample mag-
(about 110 Hz). The measurements are performed in
netization, the latter should be sensitive to the direction
a standard 1.4-4.2 K cryostat equipped with supercon-
of external magnetic field. More precisely, it is possible
ducting solenoid.
to demonstrate from the kinetic equation (in the spirit
In the case of the symmetric configuration, like de-
of [1]), that second - order response is absent in classical
picted in Figure 1a, we obtain clearly non-zero Hall volt-
Hall effect, while it is an odd function of magnetic field
for the spectrum with Berry curvature (Weyl semimet-
1)e-mail: dev@issp.ac.ru
als).
Письма в ЖЭТФ том 109 вып. 11 - 12
2019
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