Raman shift (cm-1) 200 400 600 - CNRweb.nano.cnr.it/heun/wp-content/uploads/2019/06/Poster... ·...
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Non-Classical Longitudinal Magneto-Resistance in Anisotropic Black Phosphorus F. Telesio, 1 N. Hemsworth, 2 W. Dickerson, 2 M. Petrescu, 3 V. Tayari, 2 Oulin Yu, 3 D. Graf, 4 M. Serrano-Ruiz, 5 M. Caporali, 5 M. Peruzzini, 5 M. Carrega, 1 T. Szkopek, 2 S. Heun, 1 and G. Gervais 3 1 NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy 2 Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec, H3A 2A7, Canada 3 Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada 4 National High Magnetic Field Laboratory, Tallahassee, FL 32310, United States 5 Istituto Chimica dei Composti OrganoMetallici-CNR, I-50019 Sesto Fiorentino, Italy Abstract Resistivity measurements of a few-layer black phosphorus (bP) crystal in parallel magnetic fields up to 45 T are reported as a function of the angle between the in-plane field and the source-drain (S-D) axis of the device. The crystallographic directions of the bP crystal were determined by Raman spectroscopy, with the zigzag axis found within 5° of the S-D axis, and the armchair axis in the orthogonal planar direction. A transverse magneto-resistance (TMR) as well as a classically forbidden longitudinal magneto-resistance (LMR) are observed. Both are found to be strongly anisotropic and non-monotonic with increasing in-plane field. Surprisingly, the relative magnitude (in %) of the positive LMR is larger than the TMR above ~32 T. Considering the known anisotropy of bP whose zigzag and armchair effective masses differ by a factor of approximately seven, our experiment strongly suggests this LMR to be a consequence of the anisotropic Fermi surface of bP. The authors thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 670173) for funding the project PHOSFUN by an ERC Advanced Grant. bP FET Device (16±1) nm thick bP flake Two top gates TG1 and TG2 fabricated with a combination of PO x and Al 2 O 3 (cf. W. Dickerson et al., APL 112, (2018) 173101) n = 2.2 x 10 12 cm -2 and μ = 83 cm 2 /(Vs) at 1.5 K, 11.4 T microscope objective Sample Polarizer (half wavelength retarder) Side view Laser beam Laser polarization mirror Detector Rayleigh rejection filters Crystal orientation: polarized Raman -180 -90 0 5 10 15 20 A 2 g Raman Intensity (a. u.) (°) 20 μm φ polarization S D TG 1 TG 2 In - plane Magnetotransport Hybrid 45 T magnet Tallahassee, USA The sample is mounted on a rotator and it rotates in the plane of magnetic field. A longitudinal magnetoresistance has been measured in 1994 in bulk bP but never been understood [T. Strutz et al, Physica B 194 (1994) 1185]. The conventional model based on Lorentz force cannot produce longitudinal magnetoresistance LMR, since Ԧ ∥ Ԧ = ( +Ԧ × ) 300mK, V TG2 =-1V 0 10 20 30 40 50 -0.04 0.00 0.04 0.08 0.12 (R(B)-R(0))/R(0) Magnetic field (T) ⊥ , = −90° TMR ∥ , = 0° LMR Low Field Regime 300mK, V TG2 =-1V 0 10 20 30 40 50 -0.04 0.00 0.04 0.08 0.12 (R(B)-R(0))/R(0) Magnetic field (T) ∥ , = 0° ⊥ , = −90° TMR LMR bP has an elliptical in-plane Fermi surface Elastic mean free path: , = 3.2 Ioffe-Regel criterion: = , , = 1.9 Close to strong localization Consistent with previous literature on disordered/localized bP [1] [1] N. Iwasaki et al, Chemistry Lett. 14 (1985) 119; T.-H. Lee et al, Phys. Stat. Sol. RRL 10 (2016) 819, S. J. Choi et al, Nano Letters 16 (2016) 3969, G. Long et al Nanotechnology 29 (2018) 035204 ; N. Hemsworth et al, PRB 94 (2016) 245404. High Field Regime 0 10 20 30 40 50 -0.04 0.00 0.04 0.08 0.12 (R(B)-R(0))/R(0) Magnetic field (T) 300mK, V TG2 =-1V ⊥ , = −90° TMR ∥ , = 0° LMR [2] Pal and Maslov, PRB 81 (2010) 214438 [3] Goswami, Pixley and Das Sarma, PRB 92 (2015) 075205 [4] Son and Spivak, PRB 88 (2013) 104412 LMR can arise in case of Fermi surface anisotropy [2] Its sign can be negative or positive (and it can change) for different scattering mechanisms, from short range to long range scattering [3] This picture still holds in a semiclassical regime [4] Conclusions In-plane magnetoresistance of a bP FET The observed behavior is strongly anisotropic Fermi surface anisotropy, with the field rotating in the plane where anisotropy is pronounced, plays a crucial role in explaining this phenomenon F. Telesio et al., arXiv:1808.00858 200 400 600 0 1 2 3 4 5 Intensity (a. u.) Raman shift (cm -1 ) A 2 g A 1 g B 2g Si -0.03 0.00 0.03 0.06 0.09 0.12 (R(B)-R(0))/R(0) 168 174 180 186 192 Resistance (k ) -180 -135 -90 -45 0 45 -0.03 0.00 0.03 (R(B)-R(0))/R(0) (°) 172 176 Resistance (k ) 45 T 40 T 37.5 T 35 T 32.5 T 30 T 26 T 20 T 15 T 9.9 T 22 T 0 T 20 μm φ B S D TG1 TG2 -1 0 1 200 300 400 500 600 R (k) V TG2 (V)
Transcript of Raman shift (cm-1) 200 400 600 - CNRweb.nano.cnr.it/heun/wp-content/uploads/2019/06/Poster... ·...
Non-Classical Longitudinal Magneto-Resistance in Anisotropic Black Phosphorus
F. Telesio,1 N. Hemsworth,2 W. Dickerson,2 M. Petrescu,3 V. Tayari,2 Oulin Yu,3 D. Graf,4 M. Serrano-Ruiz,5 M. Caporali,5 M. Peruzzini,5
M. Carrega,1 T. Szkopek,2 S. Heun,1 and G. Gervais3
1 NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy2 Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec, H3A 2A7, Canada
3 Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada4 National High Magnetic Field Laboratory, Tallahassee, FL 32310, United States
5 Istituto Chimica dei Composti OrganoMetallici-CNR, I-50019 Sesto Fiorentino, Italy
AbstractResistivity measurements of a few-layer black phosphorus (bP) crystal in parallel magnetic fields up to 45 T are reported as a function of the angle between the in-plane field and thesource-drain (S-D) axis of the device. The crystallographic directions of the bP crystal were determined by Raman spectroscopy, with the zigzag axis found within 5° of the S-D axis, and thearmchair axis in the orthogonal planar direction. A transverse magneto-resistance (TMR) as well as a classically forbidden longitudinal magneto-resistance (LMR) are observed. Both arefound to be strongly anisotropic and non-monotonic with increasing in-plane field. Surprisingly, the relative magnitude (in %) of the positive LMR is larger than the TMR above ~32 T.Considering the known anisotropy of bP whose zigzag and armchair effective masses differ by a factor of approximately seven, our experiment strongly suggests this LMR to be aconsequence of the anisotropic Fermi surface of bP.The authors thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 670173) for funding the projectPHOSFUN by an ERC Advanced Grant.
bP FET Device (16±1) nm thick bP flake
Two top gates TG1 and TG2 fabricated
with a combination of POx and Al2O3
(cf. W. Dickerson et al., APL 112,
(2018) 173101)
n = 2.2 x 1012 cm-2 and µ = 83 cm2/(Vs)
at 1.5 K, 11.4 T
microscope
objective
Sample
Polarizer
(half wavelength retarder)
Side view
Laser beam
Laser polarization
mirror
Detector
Rayleigh rejection filters
Crystal orientation:polarized Raman
-180 -90 0
5
10
15
20
A2 g
R
am
an
In
ten
sit
y (
a.
u.)
(°)
20 μm
φ polarization
S
D
TG1
TG2
In-plane Magnetotransport
Hybrid 45 T magnet Tallahassee, USA
The sample is mounted on a rotator and it rotates in the plane of magnetic field.
A longitudinal magnetoresistance has been measured in 1994 in bulk bP but never been understood [T. Strutz et al, Physica B 194 (1994) 1185].
The conventional model based on Lorentz force cannot produce longitudinal magnetoresistance
LMR, since Ԧ𝑣 ∥ 𝐵
Ԧ𝐹 = 𝑞(𝐸 + Ԧ𝑣 × 𝐵)
300mK, VTG2=-1V
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
𝐵 ⊥ 𝐼, 𝜑 = −90°
TMR
𝐵 ∥ 𝐼, 𝜑 = 0°
LMR
Low Field Regime
300mK, VTG2=-1V
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
𝐵 ∥ 𝐼, 𝜑 = 0°
𝐵 ⊥ 𝐼, 𝜑 = −90°
TMR
LMR
bP has an elliptical in-planeFermi surface
Elastic mean free path:
𝑙𝑒,𝑧𝑧 = 3.2 𝑛𝑚
Ioffe-Regel criterion:
𝛼 = 𝑙𝑒,𝑧𝑧𝑘𝐹,𝑧𝑧 = 1.9
Close to strong localization
Consistent with previous literature on disordered/localized bP [1]
[1] N. Iwasaki et al, Chemistry Lett. 14 (1985) 119; T.-H. Lee et al, Phys. Stat. Sol. RRL 10 (2016) 819, S. J. Choi et al, Nano Letters 16 (2016) 3969, G. Long et al Nanotechnology 29 (2018) 035204 ; N. Hemsworthet al, PRB 94 (2016) 245404.
High Field Regime
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
300mK, VTG2=-1V
𝐵 ⊥ 𝐼, 𝜑 = −90°
TMR
𝐵 ∥ 𝐼, 𝜑 = 0°
LMR
[2] Pal and Maslov, PRB 81 (2010) 214438[3] Goswami, Pixley and Das Sarma,
PRB 92 (2015) 075205[4] Son and Spivak, PRB 88 (2013) 104412
LMR can arise in case of Fermi surface anisotropy [2]
Its sign can be negative or positive (and it can change) for different scattering mechanisms, from short range to long range scattering [3]
This picture still holds in a semiclassical regime [4]
Conclusions
In-plane magnetoresistance of a bP FET
The observed behavior is stronglyanisotropic
Fermi surface anisotropy, with the fieldrotating in the plane where anisotropy ispronounced, plays a crucial role inexplaining this phenomenon
F. Telesio et al., arXiv:1808.00858
200 400 600
0
1
2
3
4
5
Inte
nsity (
a. u.)
Raman shift (cm-1)
A2
gA
1
gB
2gSi
-0.03
0.00
0.03
0.06
0.09
0.12
(R(B
)-R
(0))
/R(0
)
168
174
180
186
192
Re
sis
tan
ce
(k
)
-180 -135 -90 -45 0 45
-0.03
0.00
0.03
(R(B
)-R
(0))
/R(0
)
(°)
172
176
Re
sis
tan
ce
(k
)
45 T
40 T
37.5 T
35 T32.5 T30 T26 T
20 T15 T9.9 T
22 T
0 T
20 μm
φ B
S
D
TG1
TG2
-1 0 1
200
300
400
500
600
R (
k
)
VTG2 (V)
