Room temperature bound exciton with long lifetime in monolayer GaN

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Room temperature bound exciton with long lifetime in monolayer GaN Bo Peng, Hao Zhang, Hezhu Shao, Ke Xu, Gang Ni, Liangcai Wu, Jing Li, Hong-Liang Lu, Qingyuan Jin, and Heyuan Zhu ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00757 • Publication Date (Web): 09 Sep 2018 Downloaded from http://pubs.acs.org on September 9, 2018

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ACS Photonics

Room temperature bound exciton with long lifetime in monolayer GaN Bo Peng,† Hao Zhang,∗,†,‡ Hezhu Shao,¶ Ke Xu,† Gang Ni,† Liangcai Wu,§ Jing Li,† Hongliang Lu,k Qingyuan Jin,† and Heyuan Zhu† †Key Laboratory of Micro and Nano Photonic Structures (MOE), Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China ‡Key Laboratory for Information Science of Electromagnetic Waves, Fudan University, Shanghai 200433, China ¶Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China §College of Science, Donghua University, Shanghai 201620, China kState Key Laboratory of ASIC and System, Institute of Advanced Nanodevices,School of Microelectronics, Fudan University, Shanghai 200433, China E-mail: [email protected]

Abstract The synthesis of 2D GaN offers new opportunities for this important commercial semiconductor in optoelectronic devices because the extreme quantum confinement enables additional control of its optical properties. Using first-principles calculations based on many-body Green’s function theory, we demonstrate that in monolayer GaN, a large band gap of 5.387 eV is governed by enhanced electron-electron correlations. Strong electron-hole interactions due to weak screening lead to strongly bound excitons with a large binding energy of 1.272 eV. These tightly bound excitons result in

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strong absorption peaks in middle ultraviolet region. The dynamical screening between electron-hole pairs is totally different from bare Coulomb interaction. Long quasiparticle (quasielectron, quasihole and exciton) lifetimes are observed as a result of the many-body interactions. Due to the large binding energies, long exciton lifetimes and large quantum degeneracy, an excitonic Bose-Einstein condensate can be observed experimentally. Our results indicate the importance of many-body effects in exploring the optical performance of novel GaN optoelectronic nanodevices.

Keywords first-principles, electron-electron correlations, electron-hole interactions, dynamical screening, excitonic Bose-Einstein condensate

Introduction Excellent electronic and optical properties of GaN have made it an important commercial semiconductor for optoelectronic applications in the visible and near ultraviolet (UV) spectrum. 1 In exploring the novel GaN optoelectronic devices, various experimental and theoretical investigations have been carried out to understand the optical properties, especially many-body excitations, of GaN. 2–7 Recently, 2D GaN has been synthesized via a migration-enhanced encapsulated growth technique utilizing epitaxial graphene. 8 Although the crystal structure of free-standing monolayer GaN is in debate, 9–16 most studies favour a planar, honeycomb structure with novel electronic, optical and thermal properties. 17–21 However, the many-body effects in monolayer GaN, which play a vital role in determining the performance of GaN electronic and optoelectronic devices, remain a mystery to the community. After photoexcitation, an electron is excited from valence band into conduction band, leaving behind a positively charged hole. This single-particle excitation cannot be described

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by non-interacting particles with infinite lifetime. Due to interactions with other particles, the excited electrons and holes become quasiparticles with finite lifetimes. This acquires a self-energy to account for all the electron-electron interactions such as Hartree, exchange and correlation effects. 22 These interactions strongly modify the band gap. In addition, the negatively charged quasielectron is attracted by the quasihole, stabilizing the electronhole pair and forming a new quasiparticle, an exciton. Moreover, the electron-hole pairs are weakened by the screening of the electronic system. Therefore, three steps are required to account for self-energy, excitonic, and other many-electron interaction effects: 23 (i) Preparation of a starting electronic structure; (ii) Taking the formation of quasiparticles (quasielectrons and quasiholes) into account; (iii) Inclusion of electron-hole attraction that requires a two-particle approach on top of the quasiparticle picture. For monolayer GaN, the electron-electron correlations are enhanced as a result of quantum confinement, which may lead to large quasiparticle effects. In addition, the reduced dielectric constant in lowdimensional structures 24 poorly screens the electron-hole pair. Thus further questions need to be answered: (i) What is the role of electron-electron correlations in the band structure and screening of monolayer GaN? (ii) Are electron-hole interactions as important as for other 2D materials such as graphane and silicene 25,26 ? (iii) How do these many-body interactions influence the quasiparticle lifetime? Here, we address these issues by first-principles many-body Green’s function approach. Based on the quasiparticle picture, the role of dynamical screening is evaluated in describing accurately the band structure of monolayer GaN. We demonstrate that the optical properties of monolayer GaN are dominated by strong electron-hole interactions. The oscillator strength, binding energy and lifetime of the electron-hole pairs are also calculated to understand these many-body effects quantitatively. Finally, we examine the possibility of realizing excitonic Bose-Einstein condensation in monolayer GaN by continuous pumping of excitons by light.

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Computational details First-principles calculations are performed using the Vienna ab-initio simulation package (VASP) based on density functional theory (DFT). 27 The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) parameterization for the exchange-correlation functional is used. A plane-wave basis set is employed with kinetic energy cutoff of 800 eV. We use the projector-augmented-wave (PAW) potential with 3d electrons of Ga described as valence. A 15×15×1 k-mesh is used during structural relaxation for the unit cell until the energy differences are converged within 10−6 eV, with a Hellman-Feynman force convergence threshold of 10−4 eV/Å. We maintain the interlayer vacuum spacing larger than 10 Å to eliminate interactions between adjacent layers. Spin-orbit coupling has negligible influence on the electronic structure. The harmonic interatomic force constants are obtained by density functional perturbation theory (DFPT) using a 5×5×1 supercell. The phonon dispersion is calculated using the PHONOPY code. 28,29 Born effective charges are also computed using the perturbative approach to account for the LO-TO splitting. 30 Subsequent to the standard-DFT results, self-consistent GW0 corrections are undertaken 31–33 with eight iterations of G. The energy cutoff for the response function is set to be 300 eV. For the Wannier band structure interpolation, 34 s and p orbitals of Ga and s and p orbitals of N are chosen for initial projections with 80,000 iterations. More accurate self-consistent quasiparticle GW (QPGW) calculations 35,36 are also performed where G and W are iterated twelve times. To compute the QPGW optical properties, a total of 24 (valence and conduction) bands are used with a Γ-centered k-point sampling of 16 × 16 × 1. The convergence of our calculations has been checked carefully from 12 × 12 × 1 to 24 × 24 × 1 k-point sampling. The Bethe-Salpeter equation (BSE) is carried out on top of QPGW calculation with the Tamm-Dancoff approximation to include excitonic effects, 4,37,38 which delivers more accurate excited-state energies and oscillator strengths than GW0 +BSE. 39 The eight highest valence bands and the eight lowest conduction bands are included as basis for the excitonic state 4


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to compute the dielectric function. The convergence of our calculations has been checked carefully from 12 × 12 × 1 to 24 × 24 × 1 k-point sampling as well. Hybrid functional methods based on the Heyd-Scuseria-Ernzerhof method are also adopted. 40–42 In the HSE03/HSE06 approach, a fraction of the exact screened Hartree-Fock (HF) exchange is incorporated into the PBE exchange using a mixing parameter α = 0.25/0.3. Timedependent Hartree-Fock (TDHF) calculations are used to calculate the response function including excitonic effects on top of HSE06 calculations. Although TDHF sometimes fails in charge transfer excitations, 39 we still use this approach for comparison with the QPGW+BSE results to understand the dynamical screening properties in monolayer GaN. Such comparisons allow not only to grasp the key ideas behind the GW and BSE methods, but also to provide a potential direction for improving DFT and TDHF techniques.

Results and Discussion Monolayer GaN crystallizes in the space group P -6m2 with planar structure. The optimized lattice constant of 3.21 Å is in good agreement with previous results. 43 As shown in Figure 1(a), each Ga atom is surrounded by three N atoms. To examine the stability of atomically thin 2D GaN, we calculate the phonon dispersion in Figure 1(b). A material is dynamically stable when no imaginary phonon frequencies exist. 44,45 The phonon dispersion shows real frequencies across the Brillouin zone, indicating that monolayer GaN is kinetically stable at 0 K. The HSE06 band structure of monolayer GaN is shown in Figure 2(a). The valence band maximum (VBM) occurs at the K point, while the conduction band minimum (CBM) occurs at the Γ. The VBM is primarily composed of N pz orbitals, while the CBM is a hybridization of Ga s and N s states. The energy band calculated by HSE06 marks an indirect band gap of 3.687 eV. This is a dramatic deviation from the experimental value of 4.76-5.44 eV. 46 To understand the origin of the band gap problem, we calculate the electronic structure

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(a) b cc

a

(b)

Γ

M

K

Γ

Figure 1: (a) Top view of the optimized crystal structure of monolayer GaN. The green (blue) ball denotes gallium (nitrogen) atom. (b) Phonon dispersion of monolayer GaN. of monolayer GaN using PBE, HSE03, partially self-consistent GW0 , and self-consistent QPGW approaches, as listed in Table 1. The PBE band gap of 2.158 eV is much smaller than the experimental band gap, because DFT significantly underestimates the band gap. The HSE03 band gap is increased to 3.177 eV, but is still smaller than the experimental value. Table 1: Calculated band gap (eV) of monolayer GaN using PBE, HSE03, HSE06, GW0 , and QPGW approaches. Values obtained from the previous theoretical studies and experiments are also included in parentheses for comparison. PBE 2.158 (2.16 43 )

HSE03 HSE06 3.177 3.687

GW0 4.382

QPGW Experiment 5.387 (4.76-5.44 46 )

The band structure is further improved by GW calculations. As shown in Table 1, the partially self-consistent GW0 approach gives a band gap of 4.382 eV, while self-consistent QPGW gives 5.387 eV. As shown in Figure 2(b), for both GW0 and QPGW band structures, the VBM is still located at the K point, while the CBM at the Γ point. The GW band structures remain similar to the HSE results, but are different in band gap. 6


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(a)

Γ

M

K

Γ

(b)

π π

π*

π

σ*

Γ

M

K

σ*

Γ

Figure 2: (a) Projected orbital character of HSE06 band structure. (b) Quasiparticle band structure using GW0 (grey line) and QPGW (orange line) approaches. The dark cyan and wine arrows represent the π → σ ∗ and π → π ∗ interband transitions contributing to the QPGW peak located at 8.792 eV, respectively. The radius of circles represents the electron hole coupling coefficient Aλvck of the λth excitonic wave function. The green circles correspond to the 1st exciton wave function (BSE eigenvalue: 4.343 eV) with the second largest oscillator strength. The blue circles correspond to the 18th exciton wave function (BSE eigenvalue: 6.087 eV) with the largest oscillator strength. The red circles correspond to the 22th exciton wave function (BSE eigenvalue: 6.159 eV) with the third largest oscillator strength. The calculations suggest that the QPGW can describe the system much better. To understand the key ideas behind different methods, we underline the differences between HSE and GW formalisms. We start with the Hartree-Fock eigenvalue equation 47

h0 (r) + V H (r) φn (r) +

Z

dr0 ΣX (r, r0 )φn (r0 ) = n φn (r),

(1)

where h0 is the independent-electron Hamiltonian, V H is the classical Hartree potential, and

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ΣX is the exact exchange operator i Σ (r, r ) = −γ(r, r )ν(r, r ) = 2π 0

X

0

0

Z

+

dω eiω0 G(r, r0 ; ω)ν(r, r0 ),

(2)

where γ is the density matrix, ν is the bare Coulomb potential, and G is, in lieu of the density matrix, one-body Green’s function. For its GW analog, the eigenvalue equation becomes h0 (r) + V H (r) φn (r) +

Z

dr0 ΣXC (r, r0 ; n )φn (r0 ) = n φn (r),

(3)

where ΣXC is the exchange-correlation self-energy that contains all the electron-electron interactions (Hartree, exchange and correlation)

Σ

XC

i (r, r ; n ) = 2π 0

Z

+

dω eiω0 G(r, r0 ; ω + n )W (r, r0 ; ω),

(4)

where W is the dynamically screened Coulomb interaction evaluated by multiplying the bare Coulomb kernel ν with the inverse dielectric matrix , i.e. W ∝ −1 ν. 31 The DFT exchange-correlation potential contains electronic interactions beyond the classical Hartree potential V H , which generally yields much too small band gaps, and in specific cases, even the wrong band order. 36 For HSE, screened short-range Hartree-Fock exchange is employed instead of the full exact exchange, and the electronic correlation is represented by the corresponding part of the PBE density functional. 42 The difference between HSE and GW is that the screened interaction W between quasielectrons and quasiholes is replaced by the Coulomb kernel ν “screened” by a mixing parameter of 0.25-0.3 that determines how much of the nonlocal exchange is included. 38 Obviously, in monolayer GaN the HSE functional is inadequate to account for the dynamically screened interaction. We then compare GW0 and QPGW calculations: The GW0 result is obtained by iterating only the eigenvalues (i.e. G), while the input DFT eigenvectors (and W ) are frozen. As for

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QPGW, both eigenstates and eigenvalues are updated. As such, the QPGW band gap agrees much better with the experimental result. 46 In bulk GaN, the GW0 band gap (3.30 eV) agrees very well with the QPGW one (3.27 eV), both in good agreement with the experimental value (3.20 eV). 36 The QPGW method usually yields systematically improved band structures for large-gap materials. 36 This results from a cancellation of errors in GW0 - too small DFT band gap and neglect of electron-hole interactions. In monolayer GaN, after considering the self-determined screening properties, the band gap increases from 4.382 to 5.387 eV, reaching better agreement with the experimental band gap. For low-dimensional systems, quantum confinement significantly enhances electron-electron correlations, leading to large quasipartical corrections. In QPGW, the inclusion of many-electron vertex corrections in W yields excellent band gap. This has been observed in other large-gap materials such as ZnO, BN and LiF, 36 verifying the QPGW as a consistent calculation with a precision approaching experimental method. Now we understand how QPGW improves the description of the band gap in monolayer GaN, we further show whether these improvements carry over to the description of electronhole interaction and related properties such as optical absorption spectra. Figure 3 shows the imaginary part of the dielectric function of monolayer GaN for in-plane polarization obtained from QPGW and QPGW+BSE. The blue curve represents the QPGW result. The QPGW spectrum provides accurate occupied and virtual energy levels. The peak located at 8.792 eV originates from the π → σ ∗ and π → π ∗ interband transitions between two parallel bands along the Γ-M/K-Γ and M-K high-symmetry direction, respectively, as denoted by the dark cyan and wine arrows in Figure 2(b). This parallel band effect is also observed in h-BN. 48 However, the spectrum resulting from the interband transitions shows systematic deviations from the BSE results (red open circles in Figure 3). The GW quasiparticle spectrum represents electron removal or addition charged excitations that can be directly compared to experimental electron removal or addition energies. These quasiparticle excitations are

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Infrared

Visible

NUV

MUV

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FUV

Eg

Figure 3: Imaginary part of the dielectric function of monolayer GaN for in-plane polarization obtained from QPGW, QPGW+BSE, and TDHF. physically distinct from neutral optical excitations because they miss the electron-hole interaction. 49 Quasiparticle excitations are accompanied by the rearrangement of the remaining electrons in a solid, and the optically excited quasielectron-quasihole pairs show additional interactions that could be introduced only at the level of the BSE. 50,51 Comparing to the independent-particle spectrum, a systematic variation in the QPGW+BSE results (red open circles) reveals a global red-shift of the whole spectrum. From the difference between the QPGW and QPGW+BSE levels in Figure 3, one can see the importance of the electron-hole interaction. When the electron-hole interaction is included, the dielectric function exhibits two prominent structures located at 4.341 eV and 6.096 eV, respectively. These peaks are in the middle UV region (4.13-6.20 eV, as denoted by “MUV” in Figure 3). Wavelengths in the MUV region are particularly sensitive to changes in ozone concentration and are responsible for much of the biological activity of solar UV radiation. The strong absorption in the MUV region indicates that monolayer GaN is a promising potential candidate for efficient deep-UV optoelectronic devices such as UV lasers, light emitting diodes, and photodetectors. The large excitonic effects arise from dynamically screened interaction between electronhole pairs. We further investigate whether this interaction can be mimicked by the HSE functional. The green open circles in Figure 3 represents the TDHF result. The excitonic

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peaks become much weaker than the BSE results at low frequencies, and the position of the two pronounced peaks (4.211 eV and 6.231 eV) differs slightly from the BSE results (4.341 eV and 6.096 eV). These differences can be traced to the BSE and TDHF formalisms for bound electron-hole pair excitations. The excitonic Hamiltonian in Tamm-Dancoff approximation reads 47,49

RAλ = E λ Aλ ,

(5)

where R is the Hamiltonian corresponding to the resonant parts of the single-electron transitions between occupied and virtual orbitals (v → c), 52 Aλ is the electron-hole amplitude of the λth excitonic wave function

Ψλ (re , rh ) =

X

Aλvc φv (rh )φc (re ),

(6)

vc

and E λ is the pair excitation energy. Focusing on singlet excitations, the BSE Hamiltonian reads

BSE GW Rvc,v −GW )− φc (r)φv (r0 )W (r, r0 )φc0 (r)φv0 (r0 ) +2 φc (r)φv (r)ν(r, r0 )φc0 (r0 )φv0 (r0 ) , 0 c0 = δvv 0 δcc0 (c v (7) and its TDHF counterpart reads

T DHF HF 0 0 0 0 0 0 Rvc,v −HF 0 c0 = δvv 0 δcc0 (c v )− φc (r)φv (r )ν(r, r )φc0 (r)φv 0 (r ) +2 φc (r)φv (r)ν(r, r )φc0 (r )φv 0 (r ) . (8) As shown by the comparison between these formalisms, the BSE scheme adds 2ν − W elements to the GW occupied/unoccupied electronic energy levels, while the TDHF approach uses the bare Coulomb potential ν within HSE. The differences between BSE and TDHF is then reduced to whether the HSE functional approximates the dynamically screened Coulomb potential W well.

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As mentioned above, W ∝ −1 ν. Table 2 presents the static dielectric constant. In monolayer GaN, is roughly 2, and at least half of the Coulomb kernel is required to approximate W . However, the HSE functional approximates W by only 25-30% of the bare Coulomb kernel ν, which is necessarily insufficient. Similar results are observed in systems with relatively weak screening (static dielectric constant smaller than 4) such as LiF and ZnO. 33,53 The smaller the static dielectric function, the larger the excitonic effects because of the poorer screening of the electron-hole interaction. Consequently, the dynamic screening properties are worse captured by the HSE functional. Table 2: Calculated static dielectric constant using PBE (both dynamic dielectric function and ion-clamped dielectric function using DFPT 30 ), HSE06 (dynamic and TDHF), and QPGW (dynamic and BSE) approaches. PBE HSE06 QPGW dynamic DFPT dynamic TDHF dynamic BSE 1.796 1.786 1.924 2.028 1.752 2.023 To visualize the bound electron-hole pair excitations, a typical approach is to explicitly calculate the electron-hole amplitudes Aλvck . 37,54 As shown in Figure 2(b), the open circles with three colors correspond to three strongest bound excitons. Each color represents a BSE eigenvalue with a number of electron-hole pairs in the BSE basis, and the radius of circles represents the absolute value of electron-hole amplitude Aλvck . The larger the radius, the more a electron-hole pair contributes to a particular BSE eigenstate. The eigenstates of the three strongest bound excitons (with strongest oscillator strength) are very localized at the Γ point. The first bright exciton locates at 4.343 eV with a large binding energy of 1.272 eV, which is in nature of the σ → σ ∗ transitions from the top two valence bands to the bottom of the conduction band at the Γ point. The Coulomb interaction of excited electrons and holes leads to a redistribution of oscillator strength, giving rise to a strongly bound exciton with a BSE eigenvalue much lower than the direct band gap at the Γ point (5.615 eV). The second and third strongest excitons are formed between the same valence band and the second conduction band at the Γ point. These two excitons are nearly 12


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degenerate.

Eg

Figure 4: Dark, partially dark, and bright excitons (corresponding to zero, small, and large oscillator strength, respectively) with different binding energies via QPGW+BSE for monolayer GaN. For the bright excitons, the radius of circles represents the oscillator strength. Furthermore, we plot the first 150 excitons and their energy distribution in Figure 4. For the bright excitons, the radius of circles represents the oscillator strength. The larger the radius, the stronger the oscillator strength. Our results indicate a drastic redistribution of oscillator strength in monolayer GaN. We also plot their binding energies Eb . The binding energies characterize the stability of excitons. Even at 300 K, the binding energy is much larger than kB T , implying the stability of these tightly bound excitons. In addition, the energy scale of the longitudinal optical phonon mode, 100 meV as shown in Figure 1(b), is much lower than Eb , indicating the negligible influence of ionic screening. 54 Thus the unusual strong binding of excitons is mainly a result of a reduced electronic screening in low dimensions and a weak ionic screening. Such strong excitonic effects have also been theoretically predicted for silicane, which is due to the quantum confinement and the less efficient screening as well. 26 To understand the hot carrier dynamics after photoexcitation, we calculate the electron electron relaxation time from the imaginary part of the electron-electron self-energy Im Σnk at band n and k point in the Brillouin zone 55

τnk =

h ¯ . 2Im Σnk 13


(9)

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Figure 5: Relaxation times calculated from the electron-electron self-energy. Our data in Figure 5 indicate that the hole-hole relaxation near the band edges is characterized by relaxation times of 50-70 fs, while relaxation times of more than 100 fs are found for electrons. The calculated electron-electron relaxation times are comparable to the electron-phonon relation times near the band edges for Si and bulk GaN, 55,56 indicating that the electron-electron interactions cannot be neglected in monolayer GaN. To investigate the quasiparticle shifts in monolayer GaN, we also plot the DFT energies in cyan circles for comparison.

Eg

Figure 6: Calculated exciton lifetimes in monolayer GaN. Using the relaxation time of quasielectrons and quasiholes produced by optical excitation, we derive the many-body contributions to the lifetime of the λth exciton 57 X 1 Aλvck 2 ( 1 + 1 ). = λ λ τλ τvk τck vck 14


(10)

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The calculated lifetime arising from electron-electron interactions is present in Figure 6. The color and radius of circles represent the binding energy. The larger the radius, the redder the color, the stronger the binding energy. The radiative lifetime of the first exciton is more than 20 ps, larger than the lifetime of the excitons in graphane. 25 Due to the large binding energy and long exciton lifetime, it is tempting to investigate theoretically the possibility of realizing Bose-Einstein condensation of optically pumped excitons. Using room temperature as the degeneracy temperature T0 of a 2D Bose gas, the quantum degeneracy can be calculated as 58

N=

kB T0 Mex , 2π¯ h2

(11)

where Mex = mv + mc is the excitonic mass. The calculated density reaches 5.92×1012 cm−2 , which is comparable to that in graphane where Bose-Einstein condensation has been predicted, and two orders of magnitude smaller than the Mott critical density from the gas of excitons to a gas or liquid of unbound electrons and holes. 25 Thus the Bose-Einstein condensation of strongly bound excitons in GaN deserves further experimental studies. Because 3D layered GaN does not exist in nature, free-standing monolayer GaN cannot be exfoliated, and experimentally, it has to be grown on a substrate. Layers grown on substrates are affected by the presence, as well as the structure, of the latter, and hence the properties calculated for monolayer GaN might undergo modifications. 14 However, when monolayer GaN is grown on specific metallic and semiconducting substrates such as 3D layered blue phosphorus, the substrate-layer interaction is weak, preserving the physical properties predicted for free-standing GaN. 43 Besides, 2D materials such as graphene 59 and MoS2 60 appear to be ideal substrates to grow monolayer and multilayer GaN. These materials do not possess any dangling bonds and the surfaces are chemically passive, thus minimizing the chemical interaction between the substrate and GaN. Therefore, growing such structures experimentally allows the physical properties predicted for free-standing monolayer GaN, for

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instance realizing the excitonic Bose-Einstein condensation, to be preserved.

Conclusion In conclusion, we investigate the many-body effects (electron-electron and electron-hole interactions) in monolayer GaN. Electron-electron correlations strongly modify the band gap. Enhanced self-energy effects and strong electron-hole interactions give rise to the strongly bound excitons with considerable binding energies. The excitonic effects dominate the optical response of GaN and result in strong absorption in the middle UV region, indicating the potential of monolayer GaN as a promising candidate for efficient deep-UV optoelectronic devices such as UV lasers and light emitting diodes. The excitonic effects arise from the dynamically screened interaction between electron-hole pairs that cannot be described by the HSE functional due to the reduced screening. The bound exciton with a large bind energy of 1.272 eV primarily originates from the σ → σ ∗ transitions at the Γ point. Due to the large binding energies, the ionic screening effects can be neglected. Moreover, the electron-electron/hole-hole relaxation times are investigated to understand the hot carrier dynamics and to evaluate the exciton lifetimes in GaN. Due to their large binding energies and long lifetimes, the Bose-Einstein condensation of strongly bound excitons in monolayer GaN is an interesting possibility. Our findings provide fundamental understandings of manybody interactions in monolayer GaN, which may guide further theoretical and experimental studies in exploring novel GaN electronic and optoelectronic nanodevices.

Acknowledgement We acknowledge helpful discussions with Prof. Chunxiao Cong from Fudan University. This work is supported by the National Natural Science Foundation of China under Grants No. 11374063 and 11404348, and the National Basic Research Program of China (973 Program) under Grant No. 2013CBA01505. 16


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Graphical TOC Entry E

- - Coulomb +

+

-

-

-

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+

-

- -+ - -

EF Screening Propagator

Room temperature bound exciton with long lifetime in monolayer GaN Bo Peng, Hao Zhang, Hezhu Shao, Ke Xu, Gang Ni, Liangcai Wu, Jing Li, Hongliang Lu, Qingyuan Jin, and Heyuan Zhu Monolayer GaN is a promising potential candidate for efficient deep-UV optoelectronic devices such as UV lasers, light emitting diodes, and photodetectors using first principles calculations. The electron-electron correlations are enhanced as a result of quantum confinement, leading to a large band gap of 5.387 eV. Strong electron-hole interactions due to reduced screening lead to strongly bound excitons with a large binding energy of 1.272 eV. These tightly bound excitons result in strong absorption peaks in middle ultraviolet region. Long quasiparticle lifetimes are observed. An excitonic Bose-Einstein condensate can be realized by continuous pumping of excitons by light. Our results indicate the importance of many-body effects in exploring the optical performance of novel GaN optoelectronic nanodevices.

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(a)

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(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Γ

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M

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Page 27 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Infrared

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ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

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ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Eg


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Room temperature bound exciton with long lifetime in monolayer GaN

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