Quantum transport in topological semimetals under magnetic fields (III)

doi:10.1007/s11467-023-1259-5

Front. Phys.

2023, Vol. 18

Issue (2) : 21307 https://doi.org/10.1007/s11467-023-1259-5

TOPICAL REVIEW

Quantum transport in topological semimetals under magnetic fields (III)

Lei Shi^1,², Hai-Zhou Lu^1,²(

)

¹. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
². Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China

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Abstract

We review our most recent research on quantum transport, organizing the review according to the intensity of the magnetic field and focus mostly on topological semimetals and topological insulators. We first describe the phenomenon of quantum transport when a magnetic field is not present. We introduce the nonlinear Hall effect and its theoretical descriptions. Then, we discuss Coulomb instabilities in 3D higher-order topological insulators. Next, we pay close attention to the surface states and find a function to identify the axion insulator in the antiferromagnetic topological insulator MnBi₂Te₄. Under weak magnetic fields, we focus on the decaying Majorana oscillations which has the correlation with spin−orbit coupling. In the section on strong magnetic fields, we study the helical edge states and the one-sided hinge states of the Fermi-arc mechanism, which are relevant to the quantum Hall effect. Under extremely large magnetic fields, we derive a theoretical explanation of the negative magnetoresistance without a chiral anomaly. Then, we show how magnetic responses can be used to detect relativistic quasiparticles. Additionally, we introduce the 3D quantum Hall effect’s charge-density wave mechanism and compare it with the theory of 3D transitions between metal and insulator driven by magnetic fields.

Keywords topological semimetal topological insulator axion insulator nonlinear Hall effect (NHE) quantum oscillation quantum Hall effect (QHE) charge density wave (CDW)

Corresponding Author(s): Hai-Zhou Lu

Issue Date: 10 April 2023

Cite this article:

Lei Shi,Hai-Zhou Lu. Quantum transport in topological semimetals under magnetic fields (III)[J]. Front. Phys. , 2023, 18(2): 21307.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1259-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I2/21307

Fig.1 This picture shows the method of Hall effect measurement. The lock-in technique is used to amplify the nonlinear Hall signal. An input ultralow-frequency current

I ω

produces a response transverse voltage

V 2 ω

. The NHE can be generalized by substituting another response stimulus for the electric driving field [51-58]. Reproduced from Ref. [16].

Fig.2 (a) A bilayer WTe

2

device with dual-gated. (b) The different

I

–

V

curves due to the measurement from different electrodes. (c) The black line shows the Hall voltage

V b a a 2 ω

, the red line depicts resistance

R

. Abscissa axis is charge density. The blue (red) area marks the negative (positive) voltage

V b a a 2 ω

. Reproduced from Ref. [18].

Fig.3 (a) and (e) are diagrams of the intrinsic contribution. (b) and (f) are diagrams of the side-jump contribution. (c) and (g) are diagrams of intrinsic skew-scattering. (d) and (h) are diagrams of extrinsic skew-scattering. More diagrams can be found in the supplementary section of Ref. [15]. Reproduced from Ref. [15].

Fig.4 The left diagram is a 3D second-order TIs. When Coulomb interaction exists, this system may transition to a TI or a trivial insulator. Reproduced from Ref. [20].

Fig.5 For MnBi

2

4

, (a) a Chern insulator is formed from odd septuple layers, (b) an axion insulator is formed from even septuple layers. (c) The normal insulator. (d, e) The nonlocal surface measuring device. The thickness of the thick electrodes is

n t

. The phase of a MnBi

2

4

can be known by measuring its Hall conductance

σ x y

. Reproduced from Ref. [22].

Fig.6 (a) The superconductor–semiconductor nanowire island [149, 159-162]. (b–d) As a function of the B, the hybridization energy

E 0

oscillates in experiments with a rising period and diminishing amplitude. However, these experimental observations contradict the theory of MBSs, which predicts that

E 0

oscillates with increasing amplitude induced Zeeman energy

V Z

[157]. Reproduced from Refs. [23, 159].

Fig.7 (a) Energy band schematic for a Weyl semimetal. (b, c) The schematic of Fermi-arc surface states and corresponding one-sided hinge states under magnetic field

B

. (d, e) The schematic of hinge states on both sides in Dirac semimetals. We have shown that in Dirac semimetal the Fermi energy (Fig.8) and slanted magnetic field may produce one-sided, highly tunable hinge states. Reproduced from Ref. [24].

Fig.8 (a₁) The Dirac semimetal’s energy spectrum, when

B y = 15

and (

θ = 0

). (a₂–a₅) The distributions of wave functions for the states indicated in (a

1

) by horizontal dashed lines. (a₆) illustrates the position hinge states at

E F = − 4.5

meV. (a₇) shows the Fermi surface when only taking the magnetic field’s Zeeman effect into account. (a₈) shows the state indicated by the star’s wave function dispersion in (a₇). (b₁–b₈)

θ = 5 ∘

. (c₁–c₇)

θ = − 5 ∘

. Reproduced from Ref. [24].

Tab.1 Recent experimental studies of the QHE in the topological semimetal Cd

3

2

: slab growth direction, thickness, and mechanistic explanation.

Fig.9 (a) The schematic of helical edge states. The different colour represent different spin polarizations and directions of propagation. (b) The green line shows the spin Chern number

C s

. The red line is the confinement-induced energy gap. (c) The Hall conductance. (d) The Hall conductance as a function of thickness and field. Reproduced from Ref. [25].

Fig.10 (a−d) Non-relativistic fermion. (a) The energy bands without magnetic field. (b) The Landau bands. (c) Parallel magnetization

M / /

. (d) Effective transverse magnetization (

M T

). (e−h) Schematic of Weyl fermion same with (a−d). Reprocuced from Ref. [27].

Fig.11 (a)

γ = 2

, (b)

γ = 0.002

. The effective electron− phonon and electron−electron interactions are measured by

β

and

u

, respectively.

γ = | v b / v F |

. (c) The diagram without electron–phonon coupling. This picture shows double non-Gaussian points at (

u ∗, Δ b ∗

) = (0, 1/4) and (1/2, 1/2). The red line separates between a Wigner crystal and a disordered metal with zero electron−electron interaction on the left. (d−f)

u

β

, and

u / β

as a functiong of

ℓ

for various

u

starting values. Reproduced from Ref. [29].

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