1 First -psrncrpletF S udyF of FPhononF L rfe rmeF andF LowFLa rceF ThesmalF Conduc rvr y FofFMonolayesF

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First -psrncrpletF S udyF ofF PhononF Lrfe rmeF andF

LowFLa rceFThesmalFConduc rvr yFofFMonolayesF

γ-GeSe:FAFCompasa rveFS udy

Bowen Wang1, Xuefei Yan1,2,3, Xiangyue Cui1, Yongqing Cai1, *

1Joint Key Laboratory of the Ministry of Education, Institute of Applied Physics and

Materials Engineering, University of Macau, China

2School of Microelectronics Science and Technology, Sun Yat-sen University, Zhuhai

519082, China;

3Guangdong Provincial Key Laboratory of Optoelectronic Information Processing

Chips and Systems, Sun Yat-sen University

E-mail: yongqingcai@um.edu.mo

ABSTRACTFGermanium selenide (GeSe) is a unique two-dimensional (2D) material

showing various polymorphs stable at ambient condition. Recently, a new phase with a

layered hexagonal lattice (γ-GeSe) was synthesized with ambient stability and

extraordinary electronic conductivity even higher than graphite while its monolayer is

semiconducting. In this work, via using first-principles derived force constants and

Boltzmann transport theory we explore the lattice thermal conductivity (𝜅𝑙 ) of the

monolayer γ-GeSe, together with a comparison with monolayer α-GeSe and β-GeSe.

The 𝜅𝑙 of γ-phase is relatively low (5.50 W/mK), comparable with those of α- and β-

phases. The acoustic branches in α-GeSe are well separated from the optical branches,

limiting scattering channels in the phase space, while for β-GeSe and γ-GeSe the

acoustic branches are resonant with the low-frequency optical branches facilitating

more phonon-phonon scattering. For γ-GeSe, the cumulative 𝜅𝑙 is isotropic and

phononic representative mean free path (rMFP) is the shortest (17.07 nm) amongst the

three polymorphs, indicating that the 𝜅𝑙 of the γ phase is less likely to be affected by

the size of the sample, while for α-GeSe the cumulative 𝜅𝑙 grows slowly with mean

free path and the rMFP is longer (up to 20.56 and 35.94 nm along zigzag and armchair

direction, respectively), showing a stronger size-dependence of 𝜅𝑙. Our work suggests

that GeSe polymorphs with overall low thermal conductivity are promising contenders

for thermoelectric and thermal management applications.

KEYWORDS: phonon lifetime, GeSe, low thermal conductivity, representative mean

free path, thermoelectric applications

3 
 
I. INTRODUCTION 
The  remarkable  thermoelectric,  electrical,  and  optical  properties  [1-6]  of  two-
dimensional (2D) materials have triggered extensive interest in recent years. Among 
the various 2D materials, group IV-VI compounds monochalcogenides (GeS, GeSe, 
SnS, SnSe, etc.) are a unique family with rich ambient stable phases and polar vibrations 
allowing potential optoelectronic applications [7-11]. The IV-VI monochalcogenides 
normally have a puckered layered structure similar to phosphorene and show versatile 
thermoelectric  and  ferroelectric  transitions  [12-15].  Meanwhile,  due  to  the  large 
structural  space  and  sp3  hybridization,  the  IV-VI  chalcogenides  have  been 
experimentally demonstrated for fabricating phase change memory devices[16, 17]. 
As a member  of the  family of  IV−VI monochalcogenides,  germanium  selenide 
(GeSe) normally adopts a typical puckered layered lattice (α-GeSe) and was fabricated 
for  photodetector  with  a  marked  photoresponse  to  near  infrared  light  illumination. 
Monolayer α-GeSe semiconductor was predicted with an anisotropic and low thermal 
conductivity[18,  19]  and  the  phonon  thermal  transport  of  these  puckered  layered 
structures was widely studied[20, 21]. In addition to the puckered layered structure, a 
six-membered-ring  structure  of  GeSe  (β-GeSe)  with  uncommon  boat  conformation 
with Pmn21 symmetry (Fig. 1) was synthesized at high pressure and temperature and is 
stable under ambient conditions [22]. More recently, another phase of GeSe (γ-GeSe) 
with  a  four-atomic-thick  hexagonal  structure  was  predicted[23]  and  later 
synthesized[24]. The point group and space group of identified bulk  γ-GeSe are C6v 
(6mm) and P63mc respectively, while those are C3v (3m) and P3
̅m1 for monolayer γ-
GeSe.  Interestingly,  γ-GeSe  in  bulk  form  possesses  a  small  band  gap  but  with  an 
electronic conductivity even higher than graphite[23]. This high conductivity was found 
to  be  appealing  for  applications  in  lithium  ion  batteries,  and  Li  atoms  show  a  fast 
intercalation allowing for chemically exfoliation of γ-GeSe nanosheet[25]. Meanwhile, 
the electrical conductivity is several times higher than other 2D layered crystals which 
is highly promising for thermoelectric applications. For this novel hexagonal phase, 
many mysteries still remain unexplored. Besides the electronic properties, the thermal 

properties such as thermal conductivity of γ-GeSe, extremely important for the thermal

management and application, are still unknown. Actually, except for monolayer α-GeSe,

the phonon transport parameters of experimentally identified GeSe phases are still

missing. Comparable studies of the various polymorphs of GeSe and the knowledge of

the underpinning phonon transport features are the key to expanding the spectrum of

their applications in optoelectronics and thermoelectric.

In this work, focusing on the new member of GeSe, we aim to investigate the

phonon thermal properties of different experimentally identified phases of GeSe in the

monolayer limit. Through deriving the Grüneisen parameter (ζ) and phonon lifetime,

anharmonicity of phonons and scattering due to phonon-phonon interactions are

obtained. We find that for α-GeSe the acoustic phonons contribute about ~80% to the

thermal conductivity while its contribution reduces for β-GeSe (~60%) and γ-GeSe

(~70%). The magnitude of the thermal conductivity from large to small follows α-GeSe

(zigzag) > γ-GeSe > β-GeSe (zigzag) > β-GeSe (armchair) > α-GeSe (armchair). For all

the three GeSe phases, their thermal conductivities are overall lower than many other

2D materials, such as MoS2, MoSe2, silicene, WS2, h-BN and black phosphorene.

Finally, we provide some hints about the size-limited thermal conductivity which is

critical for nanostructured materials and devices.

II. COMPUTATIONALFMETHOD

First-principles calculations based on the density functional theory (DFT) in

conjunction with projector-augmented-wave (PAW) pseudopotentials [26] were

performed using the Vienna ab initio simulation package (VASP) [27]. The exchange-

correlation functional was treated using Perdew-Burke-Ernzerhof (PBE) type [28] of

generalized gradient approximation (GGA). We used the same calculation settings as

follows for all the three different phases of GeSe. The plane-wave energy cutoff was

set as 400 eV. Along the out-of-plane direction, a necessary 20 Å thickness of vacuum

space was used to avoid interactions between layers. A well-converged Monkhorst–

Pack k-point grid 21 × 21 ×1 was taken to sample the Brillouin Zone. The convergence

threshold was set as 10−8 eV for structural relaxation and electronic self-consistent

calculations, and the cell volume and shape were fully optimized until the force

tolerance is no larger than 10-4 eVÅ-1.

Due to the semiconducting nature of the three phases in the monolayer [22, 23],

phonons are the primary heat carriers and dominate the total thermal conductivity.

Therefore, we mainly focus on the lattice thermal conductivity in this work. We have

calculated the lattice thermal conductivity of different phases of monolayer GeSe by

solving the linearized phonon Boltzmann transport equation (BTE) based on an

adaptive smearing approach to the conservation of energy [29]. A full iterative

solution[30] with ShengBTE code [31] was used.

The lattice thermal conductivity can be expressed as [31, 32]

1( 1)( )

ff ћvF

k T N

  

  











(1)

where kB, T, Ω, N and ℏ is the Boltzmann constant, temperature, volume of the unit cell,

regular grid of q points and Planck constant respectively. f0 is the distribution of

phonons based on Bose-Einstein statistics and λ is a phonon mode comprises branch

index p as well as a wave vector q. α and β are Cartesian index. ωλ and vλ are the angular

frequency and group velocity along α direction. Considering two- and three- phonon

scattering as only scattering source, the linearized BTE 𝐹

𝜆

𝛽 can be written as

0()Fv



   





(2)

Here 𝜏𝜆

0 is phonon lifetime of mode λ and Δ𝜆 is corrective term from iteration can be

expressed as

' '' ' '' '

()

      

    

   



  

  

  

(3)

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1First-psrncrpletFSudyFofFPhononFLrfermeFandFLowFLarceFThesmalFConducrvryFofFMonolayesFγ-GeSe:FAFCompasarveFSudyBowenWang1,XuefeiYan1,2,3,XiangyueCui1,YongqingCai1,*1JointKeyLaboratoryoftheMinistryofEducation,InstituteofAppliedPhysicsandMaterialsEngineering,UniversityofMacau,China2SchoolofMicroelect...

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