Proposal for valleytronic materials: Ferrovalley metal and valley gapless semiconductor

doi:10.1007/s11467-023-1334-y

Front. Phys.

2024, Vol. 19

Issue (2) : 23302 https://doi.org/10.1007/s11467-023-1334-y

RESEARCH ARTICLE

Proposal for valleytronic materials: Ferrovalley metal and valley gapless semiconductor

San-Dong Guo¹(

), Yu-Ling Tao¹, Guangzhao Wang², Shaobo Chen³, Dong Huang¹, Yee Sin Ang⁴

¹. School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
². Key Laboratory of Extraordinary Bond Engineering and Advanced Materials Technology of Chongqing, School of Electronic Information Engineering, Yangtze Normal University, Chongqing 408100, China
³. College of Electronic and Information Engineering, Anshun University, Anshun 561000, China
⁴. Science, Mathematics and Technology (SMT), Singapore University of Technology and Design (SUTD), 8 Somapah Road, Singapore 487372, Singapore

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Abstract

Valleytronic materials can provide new degrees of freedom to future electronic devices. In this work, the concepts of the ferrovalley metal (FVM) and valley gapless semiconductor (VGS) are proposed, which can be achieved in valleytronic bilayer systems by electric field engineering. In valleytronic bilayer systems, the interaction between out-of-plane ferroelectricity and A-type antiferromagnetism can induce layer-polarized anomalous valley Hall (LP-AVH) effect. The K and −K valleys of FVM are both metallic, and electron and hole carriers simultaneously exist. In the extreme case, the FVM can become VGS by analogizing spin gapless semiconductor (SGS). Moreover, it is proposed that the valley splitting enhancement and valley polarization reversal can be achieved by electric field engineering in valleytronic bilayer systems. Taking the bilayer $R u B r 2$ as an example, our proposal is confirmed by the first-principle calculations. The FVM and VGS can be achieved in bilayer $R u B r 2$ by applying electric field. With appropriate electric field range, increasing electric field can enhance valley splitting, and the valley polarization can be reversed by flipping electric field direction. To effectively tune valley properties by electric field in bilayer systems, the parent monolayer should possess out-of-plane magnetization, and have large valley splitting. Our results shed light on the possible role of electric field in tuning valleytronic bilayer systems, and provide a way to design the ferrovalley-related material by electric field.

Keywords valleytronics electric field bilayer

Corresponding Author(s): San-Dong Guo

Issue Date: 13 September 2023

Cite this article:

San-Dong Guo,Yu-Ling Tao,Guangzhao Wang, et al. Proposal for valleytronic materials: Ferrovalley metal and valley gapless semiconductor[J]. Front. Phys. , 2024, 19(2): 23302.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1334-y
https://academic.hep.com.cn/fop/EN/Y2024/V19/I2/23302

Fig.1 Schematic diagrams of energy bands of ferrovalley semiconductor (a), half-valley-metal (b), quasi-half-valley-metal (c) and ferrovalley metal (d). The horizontal red lines mean Fermi level.

Fig.2 Schematic diagram of the analogy between spin gapless semiconductor (a, c) and valley gapless semiconductor (b, d). The spin-up/spin-down is equivalent to −K/K valley. The green arrows mean spin, and the horizontal red lines mean Fermi level.

Fig.3 (a) The distribution of Berry curvature, and Berry curvature only occurs around −K and K valleys with opposite signs and unequal magnitudes. Under an in-plane longitudinal electric field

E

: (b) for VGS-1, the electron carriers of −K valley turn towards one edge of the sample, while the hole carriers of −K valley move towards the other edge of the sample, producing measurable valley Hall voltage; (c) for FVM and VGS-2, the electron carriers of −K valley and hole carriers of K valley move towards the same edge of the sample, producing non-measurable valley Hall voltage.

Fig.4 (a) The schematic diagram of a bilayer lattice with AB pattern, and the red, blue and green arrows represents spin, electric polarization

P

and external electric field

E p

(positive

z

direction) and

E n

(negative

z

direction). The energy level of −K and K valleys without (b) and with external electric field

E p

E p c

(c) and

E p

>

E p c

(d). The red (blue) energy levels are from up-layer (dn-layer).

Fig.5 For AB-stacked bilayer

R u B r 2

, (a) the energy band structures; (b) layer-characters energy band structures; (c) Ru-

d

-orbital projected energy band structures.

Fig.6 The energy band structures of AB-stacked bilayer

R u B r 2

at representative

E

= ±0.10, ±0.20, ±0.30 and ±0.40

V / Å

Fig.7 The related band gaps including the global gap [

G T

] and gaps of −K and K valleys [

G − K

and

G K

] (a) and valley splitting for both valence [

V

] and condition [

C

] bands (b) of AB-stacked bilayer

R u B r 2

as a function of

E

Fig.8 The Berry curvatures of AB-stacked bilayer

R u B r 2

in BZ at representative

E

= +0.10

V / Å

(a) and −0.10

V / Å

(b).

Fig.9 At

a / a 0

= 0.95, the energy band structures of AB-stacked bilayer

R u B r 2

with intrinsic out-of-plane magnetization at representative

E

Fig.10 Under an in-plane longitudinal electric field

E

(black circles), for bilayer system with suitable out-of-plane electric field (red arrows) producing FVM or VGS-2, (a) the electron carriers of one valley and hole carriers of another valley move towards the same edge of the sample in different layer, which should produce measurable valley Hall voltage with opposite sign in different layer; (b) when the out-of-plane electric field direction is flipped, the electron carriers of one valley and hole carriers of another valley move towards the opposite edge of the sample in different layer, and the electron and hole carriers will exchange between up and dn layers.

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