We present magnetotransport, Seebeck effect, and magnetic torque measurements conducted on the Dirac semimetal PtBi2 single crystals with a temperature range of 1.8–300 K and magnetic field strength up to 14 T. A substantial, nonsaturating magnetoresistance (MR) that reaches 5.15  × 105% at 1.8 K and 9 T obeys a single-parameter scaling, suggesting an effective unified scattering rate across a broad temperature range from 1.8 to 250 K. Importantly, distinct quantum oscillations in the Seebeck coefficient identify multiple extremal orbits with frequencies F = 62.5–1476 T, which are mutually verified by the torque de Haas–van Alphen (dHvA) oscillations and result in small cyclotron masses m*  ≈ 0.072–0.16me via Lifshitz–Kosevich analysis. The angular evolution of the dominant frequencies supports three-dimensional multiband pockets/four groups of pockets, and an additional weak branch at F0  ≈ 62.5 T is robust against data-processing variations. Our results establish comprehensive quantum oscillations as a sensitive probe of multiband fermiology and scattering scaling in Dirac semimetals, with implications for understanding the mechanism of extreme MR behavior.

1.
R.
Niu
and
W. K.
Zhu
, “
Materials and possible mechanisms of extremely large magnetoresistance: A review
,”
J. Phys.: Condens. Matter
34
,
113001
(
2022
).
2.
B.
Fauqué
,
B.
Vignolle
,
C.
Proust
,
J.
Issi
, and
K.
Behnia
, “
Electronic instability in bismuth far beyond the quantum limit
,”
New J. Phys.
11
,
113012
(
2009
).
3.
B.
Fauqué
,
X.
Yang
,
W.
Tabis
,
M.
Shen
,
Z.
Zhu
,
C.
Proust
,
Y.
Fuseya
, and
K.
Behnia
, “
Magnetoresistance of semimetals: The case of antimony
,”
Phys. Rev. Mater.
2
,
114201
(
2018
).
4.
L.
Zhao
,
Q.
Xu
,
X.
Wang
,
J.
He
,
J.
Li
,
H.
Yang
,
Y.
Long
,
D.
Chen
,
H.
Liang
,
C.
Li
,
M.
Xue
,
J.
Li
,
Z.
Ren
,
L.
Lu
,
H.
Weng
,
Z.
Fang
,
X.
Dai
, and
G.
Chen
, “
Magnetotransport properties in a compensated semimetal gray arsenic
,”
Phys. Rev. B
95
,
115119
(
2017
).
5.
Y. Y.
Wang
,
Q. H.
Yu
,
P. J.
Guo
,
K.
Liu
, and
T. L.
Xia
, “
Resistivity plateau and extremely large magnetoresistance in NbAs2 and TaAs2
,”
Phys. Rev. B
94
,
041103
(
2016
).
6.
L.
Guo
,
Y.
Liu
,
G.
Gao
,
Y.
Huang
,
H.
Gao
,
L.
Chen
,
W.
Zhao
,
W.
Ren
,
S.
Li
,
X.
Li
,
S.
Dong
, and
R.
Zheng
, “
Extreme magnetoresistance and SdH oscillation in compensated semimetals of NbSb2 single crystals
,”
J. Appl. Phys.
123
,
155103
(
2018
).
7.
M. N.
Ali
,
J.
Xiong
,
S.
Flynn
,
J.
Tao
,
Q. D.
Gibson
,
L. M.
Schoop
,
T.
Liang
,
N.
Haldolaarachchige
,
M.
Hirschberger
,
N. P.
Ong
, and
R. J.
Cava
, “
Large, non-saturating magnetoresistance in WTe2
,”
Nature
514
,
205
(
2014
).
8.
X.
Huang
,
L.
Zhao
,
Y.
Long
,
P.
Wang
,
D.
Chen
,
Z.
Yang
,
H.
Liang
,
M.
Xue
,
H.
Weng
,
Z.
Fang
et al, “
Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs
,”
Phys. Rev. X
5
,
031023
(
2015
).
9.
C.
Shekhar
,
A. K.
Nayak
,
Y.
Sun
,
M.
Schmidt
,
M.
Nicklas
,
I.
Leermakers
,
U.
Zeitler
,
Y.
Skourski
,
J.
Wosnitza
,
Z.
Liu
et al, “
Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP
,”
Nat. Phys.
11
,
645
(
2015
).
10.
L. P.
He
,
X. C.
Hong
,
J. K.
Dong
,
J.
Pan
,
Z.
Zhang
,
J.
Zhang
, and
S. Y.
Li
, “
Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2
,”
Phys. Rev. Lett.
113
,
246402
(
2014
).
11.
T.
Liang
,
Q.
Gibson
,
M. N.
Ali
,
M.
Liu
,
R. J.
Cava
, and
N. P.
Ong
, “
Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2
,”
Nat. Mater.
14
,
280
(
2015
).
12.
N.
Jo
,
Y.
Wu
,
L.
Wang
,
P. P.
Orth
,
S. S.
Downing
,
S.
Manni
,
D.
Mou
,
D. D.
Johnson
,
A.
Kaminski
et al, “
Extremely large magnetoresistance and Kohler's rule in PdSn4: A complete study of thermodynamic, transport, and band-structure properties
,”
Phys. Rev. B
96
,
165145
(
2017
).
13.
Y. Y.
Lv
,
B. B.
Zhang
,
X.
Li
,
S. H.
Yao
,
Y. B.
Chen
,
J.
Zhou
,
S. T.
Zhang
,
M. H.
Lu
, and
Y. F.
Chen
,
Appl. Phys. Lett.
108
,
244101
(
2016
).
14.
D.
Miertschin
,
T.
Nguyen
,
S. R.
Bhandari
,
K.
Shtefiienko
,
C.
Phillips
,
B. A.
Magar
,
R.
Sankar
,
D. E.
Graf
, and
K.
Shrestha
, “
Anisotropic quantum transport in ZrSiS probed by high-field torque magnetometry
,”
Phys. Rev. B
110
,
085140
(
2024
).
15.
H.
Takatsu
,
J. J.
Ishikawa
,
S.
Yonezawa
,
H.
Yoshino
,
T.
Shishidou
,
T.
Oguchi
,
K.
Murata
, and
Y.
Maeno
,
Phys. Rev. Lett.
111
,
056601
(
2013
).
16.
N.
Kumar
,
Y.
Sun
,
N.
Xu
,
K.
Manna
,
M.
Yao
,
V.
Süss
,
I.
Leermakers
,
O.
Young
,
T.
Förster
,
M.
Schmidt
et al, “
Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2
,”
Nat. Commun.
8
,
1642
(
2017
).
17.
B.
Fauqué
,
Basic Physics of Functionalized Graphite
, edited by
P. D.
Esquinazi
(
Springer
,
2016
), Chap.
4
.
18.
M.
Kohler
, “
Zur magnetischen widerstandsänderung reiner metalle
,”
Ann. Phys.
424
(
1–2
),
211
–
218
(
1938
).
19.
N.
Luo
and
G. H.
Miley
, “
Kohler's rule and relaxation rates in high-Tc superconductors
,”
Physica C
371
,
259
(
2002
).
20.
C. L.
Zhang
,
Z.
Yuan
,
Q. D.
Jiang
,
B.
Tong
,
C.
Zhang
,
X. C.
Xie
, and
S.
Jia
, “
Electron scattering in tantalum monoarsenide
,”
Phys. Rev. B
95
,
085202
(
2017
).
21.
S.
Pate
,
B.
Chen
,
B.
Shen
,
K.
Li
,
X.
Zhou
,
D. Y.
Chung
,
R.
Divan
,
M. G.
Kanatzidis
,
U.
Welp
et al, “
Extended Kohler's rule of magnetoresistance in TaCo2Te2
,”
Phys. Rev. B
109
,
035129
(
2024
).
22.
A.
Feng
,
D.
Graf
,
A.
Stein
,
Y.
Liu
,
W.
Yin
, and
C.
Petrovic
, “
Magnetotransport properties of MoP2
,”
Phys. Rev. B
96
,
195107
(
2017
).
23.
Q. L.
Pei
,
W. J.
Meng
,
X.
Luo
,
H. Y.
Lv
,
F. C.
Chen
,
W. J.
Lu
,
Y. Y.
Han
,
P.
Tong
,
W. H.
Song
,
Y. B.
Hou
et al, “
Origin of the turn-on phenomenon in Td-MoTe2
,”
Phys. Rev. B
96
,
075132
(
2017
).
24.
J.
Xu
,
F.
Han
,
T.
Wang
,
L. R.
Thoutam
,
S. E.
Pate
,
M.
Li
,
X.
Zhang
,
Y. L.
Wang
,
R.
Fotovat
et al, “
Extended Kohler's rule of magnetoresistance
,”
Phys. Rev. X
11
,
041029
(
2021
).
25.
I. A.
Leahy
,
Y. P.
Lin
,
P. E.
Siegfried
,
A. C.
Treglia
,
J. C. W.
Song
,
R. M.
Nandkishore
, and
M.
Lee
, “
Nonsaturating large magnetoresistance in semimetals
,”
Proc. Natl. Acad. Sci. U. S. A.
115
,
10570
(
2018
).
26.
O.
Pavlosiuk
,
P.
Swatek
,
D.
Kaczorowski
, and
P.
Wiśniewski
, “
Magnetoresistance in LuBi and YBi semimetals due to nearly perfect carrier compensation
,”
Phys. Rev. B
97
(
23
),
235132
(
2018
).
27.
F.
Han
,
J.
Xu
,
A. S.
Botana
,
Z. L.
Xiao
,
Y. L.
Wang
,
W. G.
Yang
,
D. Y.
Chung
,
M. G.
Kanatzidis
,
M. R.
Norman
et al, “
Separation of electron and hole dynamics in the semimetal LaSb
,”
Phys. Rev. B
96
,
125112
(
2017
).
28.
W.
Gao
,
N.
Hao
,
F. W.
Zheng
,
W.
Ning
,
M.
Wu
,
X.
Zhu
,
G.
Zheng
,
J.
Zhang
,
J.
Lu
et al, “
Extremely large magnetoresistance in a topological semimetal candidate pyrite PtBi2
,”
Phys. Rev. Lett.
118
,
256601
(
2017
).
29.
L.
Zhao
,
L.
Xu
,
H.
Zuo
,
X.
Wu
,
G.
Gao
, and
Z.
Zhu
, “
Fermi surface and carrier compensation of pyrite-type PtBi2 revealed by quantum oscillations
,”
Phys. Rev. B
98
,
085137
(
2018
).
30.
W.
Gao
,
X.
Zhu
,
J.
Hu
,
S.
Li
,
F.
Zheng
,
H.
Zhang
,
M.
Wu
,
G.
Zheng
,
N.
Hao
,
P.
Zhang
,
W.
Ning
, and
M.
Tian
, “
De Haas van Alphen study on three-dimensional topological semimetal pyrite PtBi2
,”
Sci. Bull.
64
,
1496
–
1501
(
2019
).
31.
Z.
Zhu
,
X.
Lin
,
J.
Liu
,
B.
Fauqu'e
,
Q.
Tao
,
C.
Yang
,
Y.
Shi
, and
K.
Behnia
, “
Quantum oscillations, thermoelectric coefficients, and the Fermi surface of semimetallic WTe2
,”
Phys. Rev. Lett.
114
,
176601
(
2015
).
32.
X.
Xu
,
Z.
Kang
,
T.
Chang
,
H.
Lin
,
G.
Bian
,
Z.
Yuan
,
Z.
Qu
,
J.
Zhang
, and
S.
Jia
, “
Quantum oscillations in the noncentrosymmetric superconductor and topological nodal-line semimetal PbTaSe2
,”
Phys. Rev. B
99
,
104516
(
2019
).
33.
T.
Ideue
,
L.
Ye
,
J. G.
Checkelsky
,
H.
Murakawa
,
Y.
Kaneko
, and
Y.
Tokura
, “
Thermoelectric probe for Fermi surface topology in the three-dimensional Rashba semiconductor BiTeI
,”
Phys. Rev. B
92
,
115144
(
2015
).
34.
R.
Kealhofer
,
S.
Jang
,
S. M.
Griffin
,
C.
John
,
K. A.
Benavides
,
S.
Doyle
,
T.
Helm
,
P. J. W.
Moll
,
J. B.
Neaton
et al, “
Observation of a two-dimensional Fermi surface and Dirac dispersion in YbMnSb2
,”
Phys. Rev. B
97
,
045109
(
2018
).
35.
D.
Chen
,
B.
He
,
M.
Yao
,
Y.
Pan
,
H.
Lin
,
W.
Schnelle
,
Y.
Sun
,
J.
Gooth
,
L.
Taillefer
et al, “
Anomalous thermoelectric effects and quantum oscillations in the kagome metal CsV3Sb5
,”
Phys. Rev. B
105
,
L201109
(
2022
).
36.
Q.
Dong
,
J.
Wang
,
L.
Zhang
,
J.
Bai
,
Q.
Liu
,
J.
Cheng
,
P.
Liu
,
C.
Li
,
J.
Xiang
et al, “
Large power factor, anomalous Nernst effect, and temperature-dependent thermoelectric quantum oscillations in the magnetic Weyl semimetal NdAlSi
,”
Phys. Rev. B
108
,
205143
(
2023
).
37.
X.
Xu
,
J.
Yin
,
W.
Ma
,
H.
Tien
,
X.
Qiang
,
P. V.
Sreenivasa Reddy
,
H.
Zhou
,
J.
Shen
,
H.
Lu
,
T.
Chang
,
Z.
Qu
, and
S.
Jia
, “
Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6
,”
Nat. Commun.
13
,
1197
(
2022
).
38.
W.
Ouyang
,
A. C.
Lygo
,
Y.
Chen
,
H.
Zheng
,
D.
Vu
,
B. L.
Wooten
,
X.
Liang
,
J. P.
Heremans
,
S.
Stemmer
, and
B.
Liao
, “
Extraordinary thermoelectric properties of topological surface states in quantum confined Cd3As2 thin films
,”
Adv. Mater.
36
,
2311644
(
2024
).
39.
K.
Shrestha
,
M.
Shi
,
B.
Regmi
,
T.
Nguyen
,
D.
Miertschin
,
K.
Fan
,
L. Z.
Deng
,
N.
Aryal
, and
S.-G.
Kim
, “
High quantum oscillation frequencies and nontrivial topology in kagome superconductor KV3Sb5 probed by torque magnetometry up to 45 T
,”
Phys. Rev. B
107
,
155128
(
2023
).
40.
S.
Froude-Powers
,
S.
Kim
,
J.
Gordon
,
H.-Y.
Kee
,
Y.-J.
Kim
, and
S. R.
Julian
, “
Static and fluctuating zigzag order and possible signatures of Kitaev physics in torque measurements of α−RuCl3
,”
Phys. Rev. B
110
,
134439
(
2024
).
41.
F.
Yang
,
S.
Li
,
S.
Chi
,
X.
Wang
,
S.
Jiang
,
H.
Zuo
,
L.
Zhao
,
G.
Xu
, and
Z.
Zhu
, “
Quasilinear magnetoresistance and de Haas van Alphen quantum oscillations in a LuPb2 single crystal
,”
Phys. Rev. B
108
,
035137
(
2023
).
42.
N.
Matsuyama
,
T.
Nomura
,
S.
Imajo
,
T.
Nomoto
,
R.
Arita
,
K.
Sudo
,
M.
Kimata
,
N. D.
Khanh
, and
R.
Takagi
, “
Quantum oscillations in the centrosymmetric Skyrmion-hosting magnet GdRu2Si2
,”
Phys. Rev. B
107
,
104421
(
2023
).
43.
Y.
Nie
,
W.
Tu
,
Y.
Yang
,
Z.
Chen
,
Y.
Wang
,
S.
Pan
,
M.
Mei
,
X.
Zhu
,
W.
Lu
,
W.
Ning
, and
M.
Tian
, “
Quantum oscillations and nontrivial topological properties of layered metal SrAg4Sb2
,”
Appl. Phys. Lett.
123
,
163101
(
2023
).
44.
S.
Uji
,
T.
Konoike
,
Y.
Hattori
,
T.
Terashima
,
T.
Oguchi
, and
T.
Yamada
, “
Anomalous diamagnetic torque signals in topological nodal-line semimetal NaAlSi
,”
J. Phys. Soc. Jpn.
92
,
074703
(
2023
).
45.
K.
Shrestha
,
B.
Regmi
,
G.
Pokharel
,
S.-G.
Kim
,
S. D.
Wilson
,
D. E.
Graf
,
B. A.
Magar
,
C.
Phillips
, and
T.
Nguyen
, “
Electronic properties of kagome metal ScV6Sn6 using high-field torque magnetometry
,”
Phys. Rev. B
108
,
245119
(
2023
).
46.
E.
Rosenberg
,
J. M.
DeStefano
,
Y.
Lee
,
C.
Hu
,
Y.
Shi
,
D.
Graf
,
S. M.
Benjamin
,
L.
Ke
, and
J.-H.
Chu
, “
Probing the van Hove singularity of the kagome metal YV6Sn6 through quantum oscillations
,”
Phys. Rev. B
110
,
035119
(
2024
).
47.
Y.
Zhang
,
M.-H.
Gao
,
G.
Liu
,
L.
Cao
,
Y.-Y.
Lv
,
S.
Pan
,
J.
Zhang
,
L.
Pi
,
S.-H.
Yao
et al, “
Fermiology and Zeeman splitting of the topological metal β-ReO2 probed by de Haas van Alphen quantum oscillations under high magnetic fields
,”
Phys. Rev. B
110
,
205109
(
2024
).
48.
J. M.
Ziman
,
Principles of the Theory of Solids
(
Cambridge University Press
,
1972
).
49.
P.
Drude
, “
Zur elektronentheorie der metalle
,”
Ann. Phys.
306
,
566
–
613
(
1900
).
50.
N. W.
Ashcroft
and
N. D.
Mermin
,
Solid State Physics
(
Holt, Rinehart, and Winston
,
New York
,
1976
).
51.
V. J.
Easterling
and
H. V.
Bohm
, “
Magnetoacoustic measurements in silver at 230 Mc/sec and 4.2 K
,”
Phys. Rev.
125
,
812
(
1962
).