Quantum linear magnetoresistance in NbTe2

Article abstract of DOI:10.1016/j.ssc.2018.02.019

NbTe₂ is a quasi-2D layered semimetal with charge density wave ground state showing a distorted-1T structure at room temperature. Here we report the anisotropic magneto-transport properties of NbTe₂. An anomalous linear magnetoresistance up to 30% at 3 K in 9 T was observed, which can be well explained by a quantum linear magnetoresistance model. Our results reveal that a large quasi-2D Fermi surface and small Fermi pockets with linearly dispersive bands coexist in NbTe₂. The comparison with the isostructural TaTe₂ provides more information about the band structure evolution with charge density wave transitions in NbTe₂ and TaTe₂.

Full text of DOI:10.1016/j.ssc.2018.02.019

Solid State Communications 275 (2018) 16–20
Contents lists available at ScienceDirect
Solid State Communications
journal homepage: www.elsevier.com/locate/ssc
Communication
Quantum linear magnetoresistance in NbTe2
,
,
,
,c,d,*
Hongxiang Chen a b, Zhilin Li a, Xiao Fan a b, Liwei Guo a **, Xiaolong Chen a
a Research & Development Center for Functional Crystals, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,
Beijing 100190, China
b University of Chinese Academy of Sciences, Beijing 100049, China
c School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China
d Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
A R T I C L E I N F O
Communicated by D.D. Sarma
A B S T R A C T
NbTe2 is a quasi-2D layered semimetal with charge density wave ground state showing a distorted-1T structure at
room temperature. Here we report the anisotropic magneto-transport properties of NbTe2. An anomalous linear
magnetoresistance up to 30% at 3 K in 9 T was observed, which can be well explained by a quantum linear
magnetoresistance model. Our results reveal that a large quasi-2D Fermi surface and small Fermi pockets with
linearly dispersive bands coexist in NbTe2. The comparison with the isostructural TaTe2 provides more infor-
mation about the band structure evolution with charge density wave transitions in NbTe2 and TaTe2.
Keywords:
A. NbTe2
B. Linear magnetoreisistance
C. Charge density wave
D. Anisotropy
1. Introduction
surface morphology studied by transmission electron microscope (TEM)
[12,13], scanning tunneling microscope (STM) [14], and low energy
Transition metal dichalcogenides (TMDCs), MX2 (M ¼ transition
metal, X ¼ S, Se, or Te), are a series of layered compounds with weak
interlayer interactions governed by van der Waals forces. Depending on
constituent elements M and X, these dichalcogenides can vary from
semiconducting to metallic and even superconducting in transport
property [1]. The diversity in properties and their sensitivity to thickness
[2,3] have drawn much attention recently. Since Te atom is less negative
than S and Se atoms in electronegativity, so more charge is expected to
transfer [4] from p bands of Te to the d bands of metal M, leading to an
electron diffraction (LEED) [14,15]. Besides, an intriguing metastable
phase under heat pulses [16] or electron beam irradiations of a certain
dose [15] has been detected. Similar to NbSe2 [17] and doped or inter-
calated IrTe2, NbTe2 shows a coexistence of charge density wave (CDW)
and superconductivity [18,19]. The superconductivity was found below
0.74 K in NbTe2. Interestingly, it was found the low critical field Hc1 is
extremely small, less than 0.5 Oe. Unlike TaTe2, NbTe2 does not show a
further clustering at low temperatures as appeared in LT-TaTe2. Instead,
it exists a structure transition from distorted-1T(1T0) phase to 1T phase
when temperature is above 550 K (as shown in Fig. 1(a)) [20]. Hence,
NbTe2 is a better platform to study the structural and electronic prop-
erties of 1T0 phase.
ε
oxidation state M(4ꢀ )þ in MTe2. The charge-transfer results in structural
distortions and then unusual properties ensue. Recently, considerable
attention has been paid on the intrinsic properties of MTe2 and many
fascinating phenomena like new Fermions [5], extreme large magneto-
resistance(MR) [6], linear MR [7], and superconductivity [8,9] were
found in WTe2, TaTe2, doped or intercalated IrTe2 and etc.
We have previously studied the magneto-transport and magnetic
properties of the low temperature phase of TaTe2 (LT-TaTe2) [7]. Shortly
after our report, the superconductivity with Tc~4 K under high pressures
in TaTe2 was found [10]. TaTe2 and NbTe2 are isostructural and both
show double-zigzag chain-like metal atom modulations at room tem-
perature [11]. The double-zigzag chain-like structure was observed in the
The energy band structure and Fermi surface of 1T0-NbTe2 have been
studied by first-principle calculations and angle-resolved photoelectron
emission spectroscopy (ARPES) [14]. The detected Fermi surface is
diffusive and an experimental study on the magneto-transport properties
in NbTe2 is still lacking. Here, we present a systematical study on the
anisotropic magneto-transport properties of 1T0-NbTe2. A detailed com-
parison in anisotropic magneto-transport properties between NbTe2 and
TaTe2 is given to clarify the origin of the quantum linear MR in both
materials. Our results on magneto-transport properties of NbTe2 are
* Corresponding author. Research & Development Center for Functional Crystals, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,
Chinese Academy of Sciences, Beijing 100190, China.
** Corresponding author.
E-mail addresses: lwguo@iphy.ac.cn (L. Guo), chenx29@iphy.ac.cn (X. Chen).
https://doi.org/10.1016/j.ssc.2018.02.019
Received 19 September 2017; Received in revised form 23 February 2018; Accepted 28 February 2018
Available online 7 March 2018
0038-1098/© 2018 Elsevier Ltd. All rights reserved.

H. Chen et al.
Solid State Communications 275 (2018) 16–20
physical property measurement system (PPMS) with highest magnetic
field of 9 T. A standard four probes technique is applied to measure the
in-plane resistivity and the MR defined as ðρxxðB;TÞ ꢀ ρxxð0;TÞÞ=ρxxð0;TÞ.
Field and temperature dependent Hall resistance Rxy(B, T) measurements
were carried out using a six-probes method. Angle-dependent MRs
(ADMR) were measured using a rotation option of PPMS.
3. Results and discussion
3.1. XRD and EDX analysis of NbTe2
The single crystal samples were checked by XRD (Fig. 1(b)). The
strong diffraction peaks can be indexed as (00l), consistent with the
ICDD-PDF 21-0605. Fig. 1(a) presents the crystal structure of 1T0-NbTe2
(Space group C2/m (No. 12), Z ¼ 6, a ¼ 19.39 Å, b ¼ 3.642 Å,
c ¼ 9.375 Å, β ¼ 134.58ꢁ) [11]. The single crystals are brittle and can be
easily cleaved along (001) plane. The layered characteristics can be
found in the SEM image showing thin platelets. The cleaved plane is flat
and clean without any iodine trace left as supported by EDX data of
Fig. 1(c). The EDX indicated the composition of Nb:Te ¼ 35:65, in well
agreement with the ratio of chemical stoichiometry of NbTe2. According
to the experimental data of XRD and the EDX analysis, we confirmed the
crystals are NbTe2.
3.2. Magneto-transport properties of 1T0-NbTe2
We measured the temperature-dependent resistivity of several sam-
ples from different batches and found the residual resistance ratio
(RRR ¼ ρxxð300 KÞ=ρxxð3 KÞ) values are in the range of 10–20. We chose
the sample with RRR~20 to study its magneto-transport properties in
detail. The resistivity of NbTe2 is 115.5 μΩ cm at 300 K, and 5.8 μΩ cm at
3 K. The in-plane resistivity ρxx (0, T) (Fig. 2(a)) shows a typical metallic
behaviour. A small thermal hysteresis is observed near room temperature
between the cooling and warming cycles with a rate of 5 K/min. Hall
resistances at different temperatures are shown in Fig. 2(b). All the Hall
resistances show a positive linear dependence on magnetic field B, which
indicates that almost no carrier concentration changed with increasing
field and the dominant charge carriers in NbTe2 are holes, similar to that
in TaTe2. The Hall coefficient, RH
increasing temperature, which is opposite to LT-TaTe2. The net carrier
¼
d
ρxyðBÞ=dB, increases with
Fig. 1. (a) Schematical crystal structures of 1T-NbTe2 and 1T0-NbTe2. The solid
lines indicate the unit cells. (b) X-ray diffraction pattern of a TaTe2 single crystal
measured at room temperature. Inset: an optical image of typical single crystals
from different batches. (c) The energy spectrum data of a cleaved sample sur-
face. Inset: SEM morphology of a cleaved NbTe2 sample surface. The square
indicates the analyzed zone of EDX analysis on a sample surface.
concentration is given by ðnh ꢀ neÞ ¼ 1=ðeRHÞ and the carrier mobility is
given by
μ
¼ RH=ρxx. The carrier concentration ðnh ꢀ neÞ and mobility
both decrease with increasing temperature as shown in Fig. 2(c). The net
carrier concentration ðnh ꢀ neÞ is about 1.7 ꢂ 1021 cmꢀ3 and the mobility
is about 607 cm2/(V s) at 3 K.
The transverse MRs versus magnetic field at low temperatures are
presented in Fig. 3(a). A relatively large MR reached 30% was observed
under a 9 T field at 3 K and did not show any signs of saturation in
measured field range. A crossover of MRs from a semi-classical weak-
field B2 dependence to a nearly linear B dependence was observed when
the magnetic field is beyond a critical field B*. In order to determine the
critical field B*, the differential MR versus field, dMR/dB, is plotted as
shown in Fig. 3(b) dMR/dB is linearly proportional to B with a large
positive slope in low fields, but reached a much reduced slope when field
is higher than B* (B*~1.85 T at 3 K), which is determined by an inter-
section of two linear fitting lines (as shown by the guide lines in
Fig. 3(b)). The critical field shifts to a higher field with increasing tem-
perature, as shown in Fig. 3(c). The dependence of the critical field B* on
temperature is shown with blue square in Fig. 3(d), which can be well
helpful to reveal the electronic structure evolution with CDW transitions
in NbTe2 and TaTe2.
2. Material and methods
Single crystals of NbTe2 were grown by an improved chemical vapor
transport (CVT) method [21,22]. Niobium foil (99.99%), Te powder
(99.99%), and little amount of iodine (99%) were loaded into an evacuated
silica tube in cross section diameter of 1 cm and long 15 cm. The tube was
heated in a two-zone furnace at 550 ꢁC for 1 day, and then rise the tem-
perature to 850 ꢁC at the hot end and 750 ꢁC at the cool end. Maintaining
this temperature gradient for one week and then cooled naturally, crystals
with metal luster were obtained (See the inset of Fig. 1(b)) at the cool end.
The crystals are usually thin platelets oriented along [001] or long ribbons,
and over half centimeters in at least one dimension. The composition of the
prepared NbTe2 sample was checked by energy-dispersive x-ray analysis
(EDX). X-ray diffraction (XRD) pattern was collected using a PANalytical
X'Pert PRO diffractometer with Cu radiation.
2
fitted with the red solid curve satisfying B* ¼ ð1=2eℏvF2ÞðEF þ kBTÞ with
vF ꢃ 5.7(3) ꢂ 104 m/s and EF ꢃ 8.2(3) meV. The critical field dependence
on temperature suggested the existence of electronic band with linear
dispersion [23] in 1T0-NbTe2 and will be discussed in the following.
From the Hall resistance measurements, the carrier concentration of
NbTe2 can be deduced to be in the order of 1020~1021 cmꢀ3, which is
The resistivity measurements were performed on a Quantum Design
17

H. Chen et al.
Solid State Communications 275 (2018) 16–20
much higher than the quantum limit to observe a quantum linear MR
[24], but similar to the case in LT-TaTe2 [7]. Therefore, here we discuss
the linear MR of NbTe2 with the model of quantum linear MR in layered
semimetals proposed by Abrikosov [25]. The high carrier concentration
in quasi-2D materials indicates the existence of relatively large normal
Fermi surface in 1T0-NbTe2. According to the quantum model of Abri-
kosov [25], the linear MR in 1T0-NbTe2 suggests that apart from the large
Fermi surface exists in 1T0-NbTe2, there should exist some small Fermi
pockets with almost linear band dispersions in NbTe2. As well known, an
applied magnetic field will induce the Landau level (LL) splitting. In the
quantum limit at a specific temperature and a field, LL spacing becomes
larger than both the Fermi energy EF and the thermal fluctuations kBT.
Consequently, only the lowest Landau level is occupied for the small
Fermi pockets and a quantum linear MR ensues [24].
For energy band with linear dispersion [26], the splitting between the
lowest and the first Landau level can be described by Δ1 ¼ jEꢄ1 ꢀ E0j ¼
pffiffiffiffiffiffiffiffiffiffiffi
ꢄvF 2ℏeB, where vF is the Fermi velocity. When the quantum limit is
approached in a linear energy band, the critical field B* should satisfy the
equation B* ¼ ð1=2eℏv2F ÞðEF þ kBTÞ [23]. As shown in Fig. 3(c), the
2
critical field deduced from our 1T0-NbTe2 sample could be well fitted by
the equation B* ¼ ð1=2eℏv2F ÞðEF þ kBTÞ [23]. The fitting results (See
2
Fig. 3(d)) yield the Fermi level EF ꢃ 8.2(3) meV, and the Fermi velocity
vF ꢃ 5.7(3) ꢂ 104 m/s. They are about two times larger and 65.2% higher
than the values in LT-TaTe2, respectively. Furthermore, it is deduced that
the Δ1 ¼ EF þ kBT at the critical field B*, satisfying the regime of
quantum limit. These results strongly support that the linear MR
behaviour originates from the Dirac states formed by the Fermi surface
reconstruction in 1T0-NbTe2.
The MR of NbTe2 under low temperature and high magnetic field is
contributed by both normal carriers and carriers with linear band
dispersion. The observed MR is mainly contributed by normal carriers
when B < B*, so dMR/dB is linearly proportional to B with a large posi-
tive slope. When B > B*, the quantum linear MR contributed by carriers
with linear band dispersion will be dominated, whose effect will resulted
in a saturation of dMR/dB at high fields. However, in the case, the MR
contributed from normal carriers is still remained, whose effect will lead
to a weak dependence on field B. Consequently, as a total effect, dMR/dB
will not be saturate to a constant, but show a much weak dependence on
field B as shown in Fig. 3(B).
As suggested by the magneto-transport behaviors of NbTe2, the Fermi
surface of NbTe2 are composed by the relatively large Fermi pockets and
small Fermi pockets with linear band dispersion. While, we observed
almost a single band behaviour in the Hall resistance measurement as
shown in Fig. 2(B). We consider this is due to the carriers transport in
NbTe2 are dominated by holes contributed from the large Fermi surfaces,
and the mobility of carriers contributed from different bands may be very
close. Meanwhile, according to the quantum linear MR model [25], the
carrier density in small Fermi pocket with linear band dispersions is
about 1018 cmꢀ3. It is three orders of magnitude lower than that in the
normal states, ~1021 cmꢀ3, and hence can be neglected in Hall resistance
contribution compared with that of the normal carriers. Besides, in our
work, the highest measured magnetic field is 9 T, and we think the
multi-band feature may be observed under higher fields.
3.3. ADMR of 1T0-NbTe2
The ADMR at azimuth angle φ ¼ 90ꢁ are shown in Fig. 4(a) and (b).
When φ ¼ 90ꢁ, the magnetic field is perpendicular to the flowing current
along the b axis. The detailed geometry of ADMR measurements, polar
angle θ and azimuth angle φ are defined in the inset of Fig. 4(a), where a
field dependent MR at several angles of θ ¼ 0ꢁ, 30ꢁ, 60ꢁ, and 90ꢁ are
measured. It is noted a linear MR is observed at each polar angle at high
fields. Furthermore, the ADMR at 5 K in 9 T is shown in Fig. 4(b). It is
seen that the ADMR has maximums (MR ¼ 30%) when θ ¼ 0ꢁ and 180ꢁ.
The MR decreases to minimums (MR ¼ 17%) at θ ¼ 90ꢁ and 270ꢁ, which
decreases by about 43% compared to the maximum. The ADMR could be
well fitted by a function of jcosθj as shown in Fig. 4(b), which indicates a
quasi-2D Fermi surface [27] exists in 1T0-NbTe2. But the slight deviation
implies existence of three dimensional electronic transport in 1T0-NbTe2
as reported in the similar material [28].
Fig. 2. (a) Temperature dependent resistivity of 1T0-NbTe2. Inset: the configu-
ration of six-probes method. (b) The field dependent Hall resistance (Rxy) at
different temperatures. (c) Temperature dependence of carrier concentration
and mobility.
4. Discussion
Linear MR under high field seems widely exist in layered CDW and
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H. Chen et al.
Solid State Communications 275 (2018) 16–20
Fig. 4. Anisotropic MRs (a) Polar angle θ (φ ¼ 90ꢁ) dependent MR at 5 K in 9 T.
The fitting curve fitted by the function of jcosθj is shown by the red curve. (b)
Field dependent MR at four θ angles (θ¼0ꢁ, 30ꢁ, 60ꢁ, and 90ꢁ). Inset: the ge-
ometry of angle dependent MR measurements.
550 K. As we all know, the CDW transition is accompanied by compli-
cated band-folding [36], and may induced a band with linear dispersion.
Linear MRs are observed in both of 1T0-NbTe2 and LT-TaTe2, and can be
well explained by the quantum linear MR model. So we suggest that the
linear MR in 1T0-NbTe2 and LT-TaTe2 should be resulted from the Fermi
pockets with linearly dispersive bands in the 1T0 phase. In our previous
LT-TaTe2 results, MR shows complicated anisotropy with a two-fold
symmetry at low temperatures and high fields which revealed the
anisotropy of the small Fermi pockets in Dirac states, while here a simple
two-fold symmetric anisotropy was found in 1T0-NbTe2 indicating there
exists relatively simple small Fermi pockets with linearly dispersive
bands.
5. Conclusions
Fig. 3. (a) Magnetic field dependent MR at different temperatures. (b) Depen-
dence of differential MR on magnetic field at different temperatures. A critical
field B* is defined as the intersection between the two fitting lines for dMR/dB
against B in low field semi-classical regime and high field quantum regime. (c)
Dependence of critical field B* on temperature, data are marked by blue squares.
In conclusion, anisotropic magneto-transport properties of 1T0-NbTe2
were studied systematically based on high quality single crystals of
NbTe2 with RRR ¼ 20. Carrier concentration and mobility of NbTe2 both
decreases with increasing temperature. The high carrier concentration
around 1021 cmꢀ3 indicates the existence of relatively large normal Fermi
surface. The observed anisotropic linear MR at low temperatures under
high fields suggests existing a quasi-2D characteristic in Fermi surface of
1T0-NbTe2. The linear MR and the well fitted critical field B* versus
temperature strongly support the inference of existing small Fermi
pockets with linearly dispersive bands in 1T0-NbTe2. The simple two-fold
symmetry MR in 1T0-NbTe2 indicates the small Fermi pockets in 1T0-
NbTe2 possessing relative high symmetry compared with that in LT-
spin density wave (SDW) compounds, such as iron pnictides [23,29],
2H-NbSe2, 2H-TaSe2 [30], LT-TaTe2 and so on. The MRs in these mate-
rials are relatively large but smaller than that in some Dirac or Weyl
semimetals [31–34] and compensated semimetals [6,35]. The linear MR
in 1T0-NbTe2 is quite similar to that of LT-TaTe2. At room temperature,
NbTe2 and TaTe2 both are 1T0 structure, while TaTe2 shows a further
clustering along b axis below 170 K, which is absent in NbTe2. While
1T0-NbTe2 transforms into the 1T phase when temperature is higher than
19

H. Chen et al.
Solid State Communications 275 (2018) 16–20
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