#
Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal T_{d}-WTe_{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussions

#### 3.1. Atomic Force Microscopy and Raman Spectroscopy

#### 3.2. Out-of-Plane Magnetotransport

#### 3.3. In-Plane Magnetotransport

#### 3.4. Static Optical Reflectivity

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MR | Magnetoresistance |

WSM | Weyl semimetals |

WQP | Weyl quasiparticles |

ABJ | Adler–Bell–Jakiw |

TMDC | Transition metal dichalcogenide |

AFM | Atomic force microscopy |

PDMS | Polydimethylsiloxane |

LIA | Lock-in amplifier |

ZFC | Zero field cooled |

FC | Field cooled |

MIT | Metal-to-insulator transition |

NLMR | Negative longitudinal magnetoresistance |

LLL | Lowest Landau level |

EBL | Electron beam lithography |

IR | Infra-red |

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**Figure 1.**(

**a**): Schematic illustration of the crystal structure of ${T}_{\mathrm{d}}$-WTe${}_{2}$ showing the directions of the a−, $b-$, and $c-$axes. (

**b**,

**c**): Optical image of the WTe${}_{2}$ samples S1 and S2, respectively.

**Figure 2.**(

**a**): AFM image of an exfoliated WTe${}_{2}$ flake dry transferred onto the SiO${}_{2}$/${p}^{++}$-Si substrate. (

**b**): Surface morphology recorded for a $\left(\right)open="("\; close=")">3.5\times 3.5$ AFM scan area of the transferred WTe${}_{2}$ flake. (

**c**): Optical microscopic image of 45 nm thick WTe${}_{2}$ flake used to measure Raman spectroscopy. The dot indicates the position of the laser spot during the Raman measurements. (

**d**): Raman spectra collected from the specimen in (

**c**) as-prepared and after seven days of exposure to air ambient.

**Figure 3.**Schematic illustration of the relative orientations of E, ${\mathsf{\mu}}_{0}H$, l and w relevant for the measurements of (

**a**): ${\mathrm{MR}}_{\perp}$ and (

**b**): ${\mathrm{MR}}_{\Vert}$.

**Figure 4.**(

**a**,

**b**): ${R}_{\mathrm{xx}}$ as a function of T at ${\mathsf{\mu}}_{0}{H}_{\perp}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$, ${\mathsf{\mu}}_{0}{H}_{\perp}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ and ${\mathsf{\mu}}_{0}{H}_{\perp}=7\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ for S1 and S2, respectively. (

**c**,

**d**): ${\mathrm{MR}}_{\perp}$ as a function of ${\mathsf{\mu}}_{0}{H}_{\perp}$ measured in the range $5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}\le T\le 150\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for S1 and S2, respectively. (

**e**,

**f**): ${\mathrm{MR}}_{\perp}$ as a function of ${\mathsf{\mu}}_{0}H$ at $\theta ={0}^{\circ}$ and $\theta ={90}^{\circ}$ at $T=5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for S1 and S2, respectively.

**Figure 5.**(

**a**,

**b**): FC transverse $\mathrm{MR}$ as a function of T recorded for ${\mathsf{\mu}}_{0}{H}_{\perp}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ and $7\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ for samples S1 and S2, respectively. (

**c**,

**d**): Estimated normalized ${\mathrm{MR}}_{\perp}$ defined as the ratio of ${\mathrm{MR}}_{\perp}\left(T\right)$ to ${\mathrm{MR}}_{\perp}\left(5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}\right)$ recorded by applying ${\mathsf{\mu}}_{0}{H}_{\perp}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ and ${\mathsf{\mu}}_{0}{H}_{\perp}=7\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ for S1 and S2, respectively. (

**e**,

**f**): calculated Kohler’s plots of S1 and S2 in the range $5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}\le T\le 100\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$.

**Figure 7.**(

**a**,

**b**): ${R}_{\mathrm{xx}}$ as a function of T with ${\mathsf{\mu}}_{0}{H}_{\perp}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ for S1 and S2, respectively. (

**c**,

**d**): ${\mathrm{MR}}_{\Vert}$ recorded as a function of ${\mathsf{\mu}}_{0}{H}_{\Vert}$ in the range $5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}\le T\le 100\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for S1 and S2, respectively. (

**e**,

**f**): ${\mathrm{MR}}_{\Vert}$ as a function of the azimuthal angle $\psi $ at $T=5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for S1 and S2, respectively.

**Figure 8.**(

**a**): Optical image of the sample S3. (

**b**): Negative ${\mathrm{MR}}_{\Vert}$ as a function of ${\mathsf{\mu}}_{0}{H}_{\Vert}$ — a fingerprint of the chiral anomaly measured for the configuration $\left(\right)$ for samples S1, S2 and S3. (

**c**): ${\mathrm{MR}}_{\Vert}$ measured at $T=5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for samples S1 and S3 in the configurations $\left(\right)$ and $\left(\right)$.

**Figure 9.**(

**a**): Reference spectra of the supercontinuum pulses recorded for two crossed polarizations. The peak at ∼675 nm is associated with the seed pulse used for supercontinuum generation. (

**b**): Optical microscopy image of the ∼45 nm ${T}_{\mathrm{d}}$-WTe${}_{2}$ sample. The directions of the linear polarization used in the experiments (‖ and ⊥ to the flake long axis) are also indicated in the image.

**Figure 10.**Reflectivity spectra for different T and ${\mathsf{\mu}}_{0}{H}_{\perp}$ as a function of the polarization for (

**a**): $T=300\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, ${\mathsf{\mu}}_{0}{H}_{\perp}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$; (

**b**): $T=300\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, ${\mathsf{\mu}}_{0}{H}_{\perp}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$; (

**c**): $T=50\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, ${\mathsf{\mu}}_{0}{H}_{\perp}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$ and (

**d**): $T=5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, ${\mathsf{\mu}}_{0}{H}_{\perp}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{T}$.

**Table 1.**Estimated values of ${\mathrm{MR}}_{\perp}$, ${\mathrm{MR}}_{\Vert}$ and ${\mathsf{\mu}}_{\mathrm{av}}$ at $T=5\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ and the critical temperature for observation of chiral anomaly in samples S1 and S2.

${\mathbf{MR}}_{\perp}$(%); $\mathit{T}=5\phantom{\rule{0.166667em}{0ex}}\mathbf{K}$; $\mathit{\theta}={90}^{\circ}$ | ${\mathbf{MR}}_{\Vert}$(%); $\mathit{T}=5\phantom{\rule{0.166667em}{0ex}}\mathbf{K}$; $\mathit{\psi}={90}^{\circ}$ | ${\mathbf{MR}}_{\Vert}$(%); $\mathit{T}=5\phantom{\rule{0.166667em}{0ex}}\mathbf{K}$; $\mathit{\psi}={0}^{\circ}$ | ${\mathsf{\mu}}_{\mathbf{av}}$$\left(\right)open="("\; close=")">{\mathbf{cm}}^{2}/\mathbf{V}.\mathit{s}$; $\mathit{T}=5\phantom{\rule{0.166667em}{0ex}}\mathbf{K}$ | Critical T (K) | |
---|---|---|---|---|---|

S1 | 1200 | 36 | −18 | 5000 | 120 |

S2 | 800 | 27 | −5 | 4100 | 80 |

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**MDPI and ACS Style**

Adhikari, R.; Adhikari, S.; Faina, B.; Terschanski, M.; Bork, S.; Leimhofer, C.; Cinchetti, M.; Bonanni, A.
Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal *T*_{d}-WTe_{2}. *Nanomaterials* **2021**, *11*, 2755.
https://doi.org/10.3390/nano11102755

**AMA Style**

Adhikari R, Adhikari S, Faina B, Terschanski M, Bork S, Leimhofer C, Cinchetti M, Bonanni A.
Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal *T*_{d}-WTe_{2}. *Nanomaterials*. 2021; 11(10):2755.
https://doi.org/10.3390/nano11102755

**Chicago/Turabian Style**

Adhikari, Rajdeep, Soma Adhikari, Bogdan Faina, Marc Terschanski, Sophie Bork, Claudia Leimhofer, Mirko Cinchetti, and Alberta Bonanni.
2021. "Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal *T*_{d}-WTe_{2}" *Nanomaterials* 11, no. 10: 2755.
https://doi.org/10.3390/nano11102755