Stacking order and interlayer coupling tuning the properties of charge density

2025-04-15 0 0 1.69MB 13 页 10玖币

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waves in layered 1T-NbSe2

Tao Jiang1, Haotian Wang1, Heng Gao1, Qinghe Zheng3, Zhenya Li1 and

Wei Ren1,2,*

1 Physics Department, International Center for Quantum and Molecular Structures,

Shanghai Key Laboratory of High Temperature Superconductors, Shanghai

University, Shanghai 200444, China

2 State Key Laboratory of Advanced Special Steel, Materials Genome Institute,

Shanghai University, Shanghai 200444, China

3 School of Materials Science and Engineering, Shanghai University, Shanghai

200444, China

* Email: renwei@shu.edu.cn

ABSTRACT

Layered transition metal dichalcogenide 1T-NbSe2 is a good candidate to explore

the charge density wave (CDW) and Mott physics. However, the effects of stacking

orders and interlayer coupling in CDW 1T-NbSe2 are still less explored and understood.

Using density functional theory calculations, we present a systematic study of the

electronic and magnetic properties of monolayer and layered CDW 1T-NbSe2. Our

results indicate that monolayer CDW 1T-NbSe2 is a magnetic insulator with

√13 × √13 periodic lattice modulation. Nevertheless, the magnetic properties of

bilayer CDWs 1T-NbSe2 are found stacking orders dependence. The mechanism is

understood by the changes of local magnetic moments in each layer due to spin charge

transfer between interlayers. Furthermore, the bulk CDW 1T-NbSe2 opens a band gap

with 0.02 eV in 1×1×2 supercell due to the interlayer spin coupling. We also discover

that the electronic structures of layered 1T-NbSe2 show a strong dependence on

stacking configurations and dimensionality.

I. INTRODUCTION

During the past decades, the charge density wave (CDW) in transition-metal

dichalcogenides (TMDs) including TaS2 and TaSe2 have been extensively studied

involving Mott insulators [1-4], superconductivity [5-8], and promising applications [9-

12] in their two-dimensional [9,13-17] and bulk [18-23] cases. For instance, bulk 1T-

TaS2 undergoes a series of structural transitions including first-order and second-order

transitions during temperature declining process. Below 180 K, it forms the

commensurate charge density wave (CCDW) characterized by 13 Ta atoms

accumulating in a √13 ×√13 “Star of David” pattern. The periodic lattice modulation

leads to the significant change of the electronic structures, resulting in an insulating

ground state of 1T-TaS2. Due to the half-filled nonbonding state of center Ta atom, such

an insulating state is usually ascribed as a Mott insulator [2,24,25]. Besides, the

interlayer dimerization and stacking order have been proved to be indispensable to

understand the insulating state of CDW in TaS2 [17,19,26]. Besides, the CDW in two-

dimension (2D) exhibits unique properties different from the corresponding bulk cases.

For example, 1T-TaS2 undergoes a series of metastable states when the thickness is

reduced down to nanometer scale [9]. A robust Mott insulating state induced by

Coulomb correlation effect was found in monolayer 1T-TaSe2 with special orbital

texture [4].

However, 1T-NbSe2, as a member of CDWs in TMDs, has been paid less attention

either in 2D or bulk cases. As a matter of fact, 2H-NbSe2 is usually easier to be

fabricated than 1T phase, thus the 2H phase has been intensively investigated for its

CDWs [27-36]. Bulk 2H-NbSe2 undergoes the nearly commensurate charge density

wave (NCCDW) phase at 33 K with a 33 periodic superlattice, which shows the

independence of temperature [34]. With the temperature decreasing to 7 K, it hosts the

coexistence of superconductivity and incommensurate charge density wave (ICCDW)

[25,27]. And the CDW transition temperature was enhanced to 145 K from 33 K when

NbSe2 was exfoliated into monolayer [30], indicating the enhancement the critical

temperature of CDW order in 2D case. Recently, monolayer 1T-NbSe2 film was firstly

synthesized on bilayer graphene, and found to be a Mott insulator with a band gap of

0.4 eV [37]. Liu et al. [38] reported that the Mott upper Hubbard band of monolayer

1T-NbSe2 is distributed away from the center dz2 orbital in the √3 × √3 R30

periodicity. It has been proved that different stacking types of CDWs could also have

an impact on the metal-insulator transition and insulating phase, accompanied with an

interlayer Peierls dimerization [19]. And a possible metal-insulator transition was

observed when the interlayer antiferromagnetic order and electronic correlation effects

were taken into account in bulk 1T-NbS2 [39]. However, less attention has been paid to

the stacking effects and interlayer coupling in layered 1T-NbSe2.

In this work, we use the first-principles calculations to investigate the monolayer,

bilayer, and bulk 1T-NbSe2, especially to concentrate on the influence of stacking and

interlayer coupling towards the properties of CDW. The monolayer 1T-NbSe2 shows

metallicity in normal structure but insulator in the CDW phase using both PBE and PBE

+U methods. Each Star of David has 1 B total magnetic moment contributed mainly

by the central Nb atoms. Then we construct five different stacking orders bilayer 1T-

NbSe2 and find that the interlayer spin charger transfer can effectively influence the

local magnetic moments of bilayer CDW. In bulk case, the results indicate the CDW

phase is an out-of-plane metal without the consideration of interlayer magnetic order,

which is same as the first-principles results of bulk 1T-TaS2 [13,14,26,40]. Interestingly,

when the interlayer antiferromagnetic order is considered, the band structure opens a

gap, possibly making the system a Mott insulator. Moreover, by comparing five

stackings of bilayer and bulk CCDW, we elucidate the stacking dependence of the

electronic structure of 1T-NbSe2. Our work shows the mechanisms of interlayer

coupling and stacking order modulate the electronic structure and magnetic properties

of 1T-NbSe2, suggesting the critical role of interlayer coupling and stacking order in

understanding the magnetic properties in CDW materials.

II. COMPUTATIONAL METHODS

The density functional theory (DFT) calculations were performed with the

projector augmented wave (PAW) [41] method implemented in the Vienna Ab initio

Simulation Package (VASP) [42,43]. Within the generalized gradient approximation

(GGA) [44], we employed Perdew-Burke-Ernzerhof (PBE) exchange and correlation

functional. The energy cutoff of 520 eV was chosen throughout all calculations. For the

undistorted structure and √13 ×√13 CDW phases, 12 ×12 × 1 and 4 × 4 × 1 -

centered Monkhorst-Pack k meshes were used in geometry optimization and self-

consistent calculations. On the other hand, 12 ×12 × 8 and 4×4×8 k meshes were

used for bulk in geometry optimization and self-consistent calculations. The structure

relaxation was achieved by converging all the forces and energies within 0.01 eV/Å and

10−6 eV, respectively. For Nb 4d orbitals, an effective Hubbard U = 2.95 eV [45] was

adopted to treat the Coulomb interaction. For bilayer and bulk 1T-NbSe2, a van der

Waals (vdW) correction [46] was adopted to reproduce the experimental lattice

constants. In monolayer and bilayer, we employed a vacuum layer of 18 Å between the

periodic images.

III. TWO-DIMENSIONAL CDW

TABLE I. Lattice parameters, relative energy, band gap, and total magnetic moment of

monolayer 1T-NbSe2 for normal and CDW phases calculated by using PBE and PBE+U

methods.

Methods

Phase

a (Å)

∆E (meV)

Eg (eV)

Mag (B)

PBE

3.48

CCDW

12.60

-52.78

0.05

0.92

PBE+U

3.53

0.19

CCDW

12.72

-54.76

0.35

We begin our discussions from the normal state of monolayer 1T-NbSe2 and

corresponding √13 ×√13 CDW phase. The normal state of monolayer 1T-NSe2

crystalizes D3d point group with octahedral coordination of Nb atom, and the Se-Nb-Se

atomic planes are arranged by ABC stacking order. TABLE I lists the structural

parameters and electronic properties of normal and CDW phases of monolayer 1T-

NbSe2 which are calculated by PBE and PBE+U methods, respectively. The lattice

constants of normal and CDW phases monolayer 1T-NbSe2 are 3.48 Å and 12.60 Å

which are slightly larger than that of PBE +vdW results (3.45 Å and 12.46 Å).

Comparing the energies between normal phase and √13 ×√13 CDW phase of

monolayer 1T-NbSe2, we find that the lattice reconstruction in CDW phase lowers the

energy by about 54.8 meV per formula unit (f.u.) than normal phase. It indicates that

CDW phase is more energetic stable. Then we turn to the electronic structures of

monolayer 1T and CDW phases as shown in Fig. 1. The PBE band structure of normal

phase show metallicity without band splitting and the band structures are slightly

changed in the present of spin-orbital coupling (SOC) effect. While the band structure

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摘要：

Stackingorderandinterlayercouplingtuningthepropertiesofchargedensitywavesinlayered1T-NbSe2TaoJiang1,HaotianWang1,HengGao1,QingheZheng3,ZhenyaLi1andWeiRen1,2,*1PhysicsDepartment,InternationalCenterforQuantumandMolecularStructures,ShanghaiKeyLaboratoryofHighTemperatureSuperconductors,ShanghaiUniversit...

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