## Introduction

Quantum information science (also known as quantum information studies) is an emerging interdisciplinary research field of science and technology, which is primarily concerned with analysis, processing, storage, retrieval and secure transmission of information through the set of quantum mechanical principles. The information in quantum science is inscribed using various physical properties of quantum elementary particles such as spin of an electron (spintronics) and polarization of a single photon (photonics) etc.

Integrated quantum photonics is a sub-field of QIS (quantum information science), which uses photonic integrated circuits to architect quantum states of photons for intersecting the quantum applications.

### What is a single photon emitter?

In a broad perspective, a single photon is attained by two main mechanisms such as excitation and followed by spontaneous emission. The elementary particle, electron either in a molecule or in atom always tends to exist in ground state (un-excited state).

When this electron in ground state is excited (absorbs energy), moves to higher energy state (excited state) as shown in Fig. 1a, b. This energy absorption can be accomplished either by photoexcitation (ground state electron absorbs a photon of light and gains its energy) or electrical excitation (ground state electron absorbs energy from another excited electron).

This excited electron stays not more than few nanoseconds in higher energy state (excited state) and spontaneously return back to lower energy state (ground state). During this decay, the electron emits the absorbed energy in the form of radiation as shown in Fig. 1c.

This subtler process is called spontaneous emission which leads to emit a single photon and the quantum level light sources which emits a single photon (elementary particle of light) per one excitation cycle (combination of one excitation and spontaneous emission) is called single photon emitters often called as quantum emitters.

### Why single photon emitter?

The numerous scientists and engineers working in the domain of quantum photonics and Integrated quantum photonics, worldwide predicted and proved that these quantum technologies would overcome the limitations1,2 of classical computing and data communications technologies. Quantum computers enhance the processing speed and efficiency than classical computing using qubits3. For quantum information processing, in optical systems, the unit of light ‘photon’ is used to represent a qubit.

Secure information transfer by quantum communication (in particular, quantum cryptography technique) is highly in demand for defense organizations and financial institutions4. These computing and communication techniques employs polarize states of single photons to encode the information.

### State-of-the-art single photon emitters in 2D materials

However, traditional single photon emitters in three dimensional materials limits the photon extraction efficiency and integration ability to photonic circuits due to high refractive index.

The discovery of 2D materials from insulating hBN (hexagonal boron nitride), semiconducting TMDs (transition metal dichalcogenides) to semi metallic graphene exhibits exceptional properties such as Quantum confinement in the direction perpendicular to 2D plane leads to novel electronic and optical properties. These novel properties significantly different from their bulk counterpart5,6,7,8. These naturally passivated 2D materials, without any dangling bonds, makes it easier to integrate with photonic structures such as waveguides9,10,11,12 and cavities13,14,15,16,17. Another notable property of these materials is that these materials strongly interacts with light18.

The single photon emission in TMDs was initiated by exciton formation (bound state of a free electron and an electron–hole, attracted to each other by electrostatic force) generated by either optical or electrical excitation and a single photon is emitted during recombination of this electron hole pair.

Generally the excitons formed in TMDs are of wannier–mott kind, which tend to diffuse (not localized) across lattice. The point defects and crystal imperfections in the TMDs (WSe2, WS2, MoSe2, and Mos2) and GaSe19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,46, found to trap and localize the excitons at particular location, which in turn leads to localized single photon emission at cryogenic temperatures.

Particularly, in case of WSe2, intentionally induced strain gradients (by nanopillars) are used to funnel the excitons for effective single photon emission47,48. Electrostatic potentials in moiré patterns leads to effective exciton trapping, which in turn leads to single photon emission in bilayer TMDs, as observed in ref49,51,52,53,53.

On the other hand, in wideband semiconductors like hBN, the point defects acts as flawless single photon emitters. These point defects tend to exhibit intermediate energy states (un-occupied and electron occupied energy levels) in between the conduction band edge and valence band edge of the energy bandgap of the material and the electrons in occupied energy levels found to exist in paramagnetic form. Due to optical excitation, these paramagnetic electrons excites to higher un-occupied energy states and results in spontaneous single photon emission at wide range of temperatures54,55, which founds to be more suitable for quantum applications.

Particularly, in hBN, enhancement of single photon emission was studied via external electric fields in ref56 and via external magnetic fields in ref57. Tunable quantum emission from very recent 2D heterogeneous structures such as graphene/hBN/Wx2 or Mox2/hBN/graphene (where x = Se or S) opens the door for fascinating applications like quantum memory58, quantum imaging and metrology59,61,61.

Achieving bright and stable single photon emitters in a single chip, which covers the emission range from UV to IR spectrum and works over a wide range of temperatures is really significant because each range of SPS (single photon source) have their own on-demand unique applications.

Among various luminescent point defects predicted (more details given in Fig. 11)62, the schematic representation of three main (CN, NBVN and VBO2) point defects, hosts in hBN are shown in Fig. 2. These point defects covers the emission range from UV to near IR region as listed in Table 1 and these also consistent with experimental studies performed as given in references63,65,66,66.

This Review provides a snapshot of current research on single photon emitters hosts in hBN as well as other 2D materials, their functionalities, potential quantum applications and limitations to overcome.

## Salient features of hexagonal boron nitride and single photon emitter

### Hexagonal boron nitride

hBN is an isostructural material to graphite. Layered hBN also known as white graphene due to its highly transparent nature and the first known natural hyperbolic material, i.e. in-plane bonds are stronger than out-of-plane bonds.

Alternating boron (B) and nitrogen (N) atoms in its crystal structure, monolayer hBN is a sp2 bonded layer material. In (bulk or multilayer) hBN, these layers are arranged either with AA' stacking (B atoms of one layer are positioned above the N atoms of another layer or vice versa for N atoms of one layer w.r.t B atoms of another layer) as shown in Fig. 3a, b or AB stacking (B and N atoms of one layer are translated w.r.t another layer) configuration as shown in Fig. 3c, d.

These individual layers are packed together by weak van der Waals forces. The inter layer interactions affects the band structure of material and the variation in electronic band structure of monolayer and bulk hBN is shown in Fig. 3e, f. The monolayer hBN is a direct bandgap semiconductor material with 7.25 eV at high symmetry K point. As the number of layers increases, it becomes optically inactive (bulk) semiconductor with indirect bandgap of 5.79 eV with conduction band minimum at M and valence band maximum at K points.

The variation in bandgap of hBN and their corresponding Raman shifts essentially depends on interlayer interactions and number of individual layers stacked. Owing to larger bandgap, hBN exhibits high transparency of electromagnetic spectrum. hBN also exhibits relatively high refractive index and other electrical/optical/crystal properties of hBN were listed in Fig. 3g.

### Single photon emitter

The single photon emitter is a non-classical light source, emits only one photon per excitation cycle, observed experimentally using a Hanbury, Brown and Twiss (HBT) interferometer76 as shown in Fig. 4a. The elementary particle ‘photon’ cannot split further after passing through 50:50 beam splitter (as conventional light do), will be detected at any of the APD (avalanche photodiode) in HBT interferometer.

At zero delay time, the second order autocorrelation curve dips below 0.5 indicates the characteristics of a single photon emitter.

The single photon purity (represented by autocorrelation function g2 (τ)) is the main characteristic of a quantum emitter and other important features of an ideal single photon source (quantum emitter) to be considered while developing for quantum applications is listed in Fig. 4b and experimentally observed some of the quantum emitter characteristics of luminescent point defects in hBN are listed in Fig. 4c.

Luminescent point defects in hBN acts as excellent single photons emitters, can be described as an artificial atom having ground and excited states within the host bandgap as shown in Fig. 4d.

The nature of luminescent point defects can be precisely understood by study of additional photophysical characteristics as listed in Table 2 and corresponding values observed in hBN quantum emitters were listed in Table 3.

Polarization measurements for 103 isolated luminescent point defects in hBN (Zero Phonon Line (ZPL) range of 550–740 nm), revealed that the absorption and emission dipoles are frequently misaligned. This dipole misalignment is framed as:

{\text{Dipole}}\;{\text{misalignment}}\;\Delta\uptheta = {\text{ZPL}}\;\left( {{\text{energy}}} \right){-}{\text{exciting}}\;{\text{light}}\;{\text{energy}}\;\left( {\Delta {\text{E}}} \right).

The possible range of dipole misalignments, responsible mechanisms and their influence on light absorption are listed in Table 4.

## Contrasting hBN quantum emission characteristics with other 2D materials and encapsulation of existing and emerging single photon sources

The comparison of some of the quantum emitter characteristics among hBN and 2D TMDs were listed in Table 5. Among all the atomically thin materials, hBN found to one step ahead in furnishing supreme quantum emitters close to ideal characteristics.

The advantages and drawbacks of existing, emerging single photon sources from single atom to very recent TMDs and 2D heterostructures are represented in Table 6.

## Fabrication and activation processes of quantum emitters in hBN

### Bulk hBN

In bulk hBN96, emitters are found to be activated by annealing the samples for 30 min at 850 °C under 0.5 or 1 torr of argon. The argon gas is selected to prevent oxidation. Annealing at different temperatures found that fluorescence intensity is maximum at 850 °C.

To date, no superior techniques were experimented to fabricate the new emitters in bulk hBN, as the emitters in bulk hBN faces the disadvantages as listed in Table 10.

### CVD grown and exfoliated multi, single hBN layers

hBN multilayers grown using low-pressure chemical vapor deposition (LPCVD) technique97, found to host stable quantum emitters around 200 (per 10 × 10 µm2 area) at room temperature. The growth technique was performed in quartz tube as schematic shown in Fig. 5. This LPCVD grown hBN multilayers are usually 1.4 nm (3 to 4 monolayers) thickness.

More than 85% of emitters exhibit ZPL around 580 nm, with single photon purity $$g^{2} \left( 0 \right)$$ less than 0.5 and absolute photostability. No post growth annealing was performed for emitter activation or stabilization which is contrast to the emitter fabrication techniques observed in exfoliated multilayer hBN flakes98.

Other robust methodologies determined to fabricate quantum emitters in CVD grown multilayer and exfoliated multilayer hBN flakes are electron beam irradiation, laser irradiation, ion implantation65,98 and Ar plasma etching66 and their corresponding processing details were listed in Table 7. The stable emitters localize at flake edges after ion implantation and subsequent annealing is shown in Fig. 6 and the comparison for photostability of emitters formed due to various ion implantations and activated through only annealing is shown in Table 8.

Quantum emitters are engineered in CVD grown multilayer hBN and exfoliated multilayer hBN flakes, by performing stable emitter fabrication techniques as described in Table 8.

To date, no supreme emitter fabrication techniques were experimentally demonstrated for bulk (except annealing for emitter activation) and monolayer hBN and no annealing is performed to activate emitters in monolayer hBN as64,99 surface states are often unstable and modifies upon annealing. An important analysis from emitter formation and activation process are listed in Table 9.

In exfoliated multilayer hBN flakes, Ar plasma etching and subsequent annealing in argon produces emitters with emission wavelength greater than 700 nm66 and cathodoluminescence analysis of exfoliated multilayer flakes found single photon emission in the UV region63 with a ZPL at around ~ 302 nm.

## Photophysics of hBN quantum emitters

In traditional materials like diamond and silicon carbide, colour centres have similar spectral properties in both bulk and nano dimensional forms. But, in case of van der Waals crystals, the optical properties of 2D materials are different from their bulk102 structures. Due to this reason, we present the quantum emission properties of hBN material in bulk, multi and mono layer form.

### Optical characterization of hBN quantum emitters

#### Bulk hBN

Optical characterization of quantum emitters in bulk hBN96 was performed by complete optical characterization setup (Confocal photoluminescence (PL) setup couple to HBT interferometer) as shown in Fig. 7a.

The PL map of bulk hBN shown in Fig. 7b represents an isolated single photon emitter (circled in red colour) along with other ensemble emissions. The corresponding PL spectrum and second order correlation measurements were shown in Fig. 7c, d.

The red dots in second order autocorrelation graph, shown in Fig. 7d, represent experimental data and the solid red line is a fit by using a three level model:

$$g^{2} \left( \tau \right) = 1 - \left( {1 + a} \right)e^{{\frac{ - \left| \tau \right|}{{\tau^{1} }}}} + ae^{{\frac{ - \left| \tau \right|}{{\tau^{2} }}}}$$
(1)

where $$\tau^{1}$$ = lifetime of excited state, $$\tau^{2}$$ = lifetime of metastable state and a = bunching factor.

The emission from the defect bleaches after several minutes of excitation with 532 nm laser source. To obtain additional insight about luminescent point defect detection and its bleaching affect, the optical characterization was performed by replacing the 532 nm laser with another excitation laser of long wavelength (675 nm).

As similar to the emitter highlighted in Fig. 7b, an isolated emission with ZPL 760 nm, which satisfying the single photon emission characteristics is found. However, Bleaching is not observed for 675 nm excitation but another effect blinking is observed. This blinking behaviour of defect is clearly observed, for different excitation powers as shown in Fig. 7e–g.

Although, the emitters in bulk crystals are brightest and most stable103,105,105 but has the disadvantages as listed in Table 10, which can be overcome by using atomically thin 2D hBN.

Specifically emitters reported in 2D hBN has PL spectra, photostability and photodynamic characteristics which are significantly different from their bulk counterpart96,102.

#### CVD grown and exfoliated multi, single hBN layers

Optical characterization of emitters from CVD grown hBN multi, single layer and exfoliated multilayer flakes were analyzed and it was noted that their PL spectrum exhibiting ZPL at ~ 580 nm to 623 nm.

The emission lines in multilayer are narrower than monolayer as observed in ref64 and the emitter in hBN multilayer exhibits a stable fluorescence without any blinking or bleaching (at excitation power: 1mW, Time: 10 min). But in case of hBN monolayer the emitter blink and bleach for continuous excitation.

The creation and characterization of single photon emitters in a suspended, single crystal hBN film and free from substrate interactions were recently studied as in ref106. The emitters detected exhibits ZPL range from 550 to 700 nm with better single photon purity.

A significant difference in brightness was observed for the emitters detected in freely suspended hBN film compared to the emitters detected in substrate supported hBN, which provides a breakthrough advances in fabricating quantum photonic circuits.

Fluorescence measurements from traditional ensemble emitters were limited due to heterogeneity of emitters and individual defect-by defect studies are impractical. New techniques were proposed to quickly and accurately characterize the emission from ensemble emitters as experimented in ref107.

### Optical stability of hBN quantum emitters towards wide range of temperatures and various annealing environments

Quantum emitters in hBN multilayer exhibits absolute thermal stability, optically stable even when operated upto 800 K54, capable to withstand aggressive annealing treatments in both oxidizing and reducing environments without any change in spectral properties65.

The emitters’ stability towards temperature variation, annealing treatments in various gaseous environments is shown in Fig. 8a–f and in particular the variation in PL spectrum55 of an emitter observed from cryogenic to room temperature is shown in Fig. 8g. An important analysis related to nature of emitters obtained from various annealing environments is summarized in Table 11.

### Emission wavelength range of hBN quantum emitters

Quantum emitters in hBN multilayers exhibit a broad range of UV to near IR single photon emission63,65,66,66 as listed in Table 1, which is in contrast to colour centers and quantum dots (emission at a particular wavelength or over a narrow spectral range).

Emitters in hBN multilayer are classified into two groups based on Zero phonon line (ZPL) and phonon sideband (PSB) shapes. Emitters in group 1 have broad ZPLs along with PSBs and energies ranging from 576 nm (2.15 eV) to 652 nm (1.90 eV). Emitters in group 2 have narrow symmetric ZPLs with weak PSBs and energies ranging from 681 nm (1.82 eV) to 762 nm (1.63 eV).

In a survey of ~ 40 emitters, 70% belongs to group 1 and rest 30% of emitters belongs to group 2. The variation in ZPL of emitters in both the groups is due to variations in local strain and dielectric environment65.

The autocorrelation function measurements over a long time scale 65,96 of 0.1 s as shown in Fig. 9a provides an information about the presence of metastable states with decay times110,112,112. The presence of fewer metastable states with shorter life time makes the emitter brighter than the emitter having more metastable states with long lifetimes.

## Modulation of emission characteristics of hBN quantum emitters (mechanical, optical, magnetic and electrical tuning)

However, robust, optically strong and thermally stable single photon emitters are detected in hBN, these emitters faces the limitations of moderate emitter brightness (fluorescence intensity), non-ideal single photon purity, more emitter lifetime, spectral diffusion at cryogenic temperatures and inhomogeneous emission distribution over a large spectral band. These limitations create a central problem for fabricating identical single photon emitters with ideal characteristics, which strengthen to fabricate the efficient quantum applications.

Many new techniques are proposed and proved to overcome these limitations and enhance the emission characteristics of hBN quantum emitters as explained below:

### Simultaneous excitation with two laser beams of different wavelengths

Excitation of hBN quantum emitters with single laser (either with longer wavelength (675 nm) and high power (300 µW) or with mid-wavelength (532 nm) and low power (10 µW)), exhibits the photoluminescence measurements having moderate or less fluorescence intensity and photon emission rate.

Autocorrelation measurements of quantum emitters (over a long time scale) revealed existence of a fast decaying intermediate state and a long-lived metastable state within the transition energy gap as shown in Fig. 9a and the electron decay from this long-lived metastable state leads to poor antibunching factor, low photon emission rate and needs high laser excitation power (to saturate emission intensity).

By employing simultaneous both red laser (675 nm and 300 µW) and green laser (532 nm and 10 µW) excitations113 as shown in Fig. 9c, the enhancement in fluorescence intensity was observed due to certainty that the electrons are reverted from long-lived intermediate state to excited state, which leads to repopulation of excited state (terminating the electron decay from long-lived metastable state) as shown in Fig. 9b and the corresponding enhancement in emitter fluorescence intensity is shown in Fig. 9d.

The intensified photo physical characteristics of emitter due to two laser excitation in comparison with single laser excitation were listed in Table 13. It is noted that there is an enhancement in emitter fluorescence intensity and reduction of excitation saturation power, which are desirable, for two laser excitation in comparison to single laser excitation technique.

### Enhancing quantum emission due to coupling with plasmonic nanoparticle or via external magnetic field inducement

#### Coupling with plasmonic nanoparticle

Another superior technique to enhance the quantum emitter characteristics rather than simultaneous exciting with two laser beams is coupling the quantum emitters with plasmonic nanoparticles like gold, silver and platinum etc.

Overall photon emission rate enhancement is made possible by combination of both excitation enhancement and spontaneous enhancement rate. Coupling the gold nanospheres to the emitters in exfoliated flake edges as observed in ref114, enhances the excitation rate due to surface Plasmon resonance and spontaneous emission rate enhancement by Purcell effect (enhancement by environment).

Using AFM tip, the gold nanospheres are positioned to close proximity of emitters as shown in Fig. 9e, made to align with transition dipole angle of emitter in order to increase the plasmonic coupling effect and this transition dipole angle was deduced from flake orientation. The enhancement in quantum emitter characteristics due to single and double nanospheres coupling were listed in second row of the Table 13.

#### External magnetic field inducement

An effective alternate to plasmonic coupling enhancement is by inducing external magnetic field.

It is a known fact that electronic structure of defects in wide band semiconductors possess both electron un-occupied and occupied states in between the conduction and valence band edges of the energy gap. These occupied electrons exists in paramagnetic form (possibly with up ↑ or down ↓ spins). By inducing external magnetic field, these occupied energy states split up due to Zeeman effect (let's say one occupied state with a paramagnetic electron split up into two higher and lower energy states with energy difference (ΔE) and this paramagnetic electron prefers to sit in lower energy state).

When this lower energy paramagnetic electron absorbs a photon with energy = ΔE, then it jumps to higher energy state and emits the photon (with same or different energy) while relaxing back to lower energy state. This spin-dependent inter-system crossing (ISC) transition found to exhibit an anisotropic fluorescence response for applied magnetic field as experimented in ref57.

The schematic representation of inducing external magnetic field to the hBN film and simultaneous optical excitation is shown in Fig. 9f, where β represents angle made by horizontally applied external magnetic field w.r.t $${\hat{\text{x}}}$$ plane and α (ε) represents absorption (emission) dipole w.r.t $$\widehat{{\text{x}}} - \widehat{{\text{y}}}$$ plane.

The variation in PL spectrum with and without magnetic field is shown in Fig. 9g. The quantum emitter fluorescence emission found to increase monotonically for particular combination of applied magnetic field angle and absorption dipole angles as listed in Table 12.

### Resonant excitation technique

At cryogenic temperatures, the ZPL shape of emitters was influenced and broadened due to spectral diffusion115, which leads to erroneous ZPL measurements.

This spectral diffusion is observed in off-resonant excitation (electron is excited to higher vibronic energy levels of excited state and this excited electron should vibrationally relax to minimum energy level of excited state and followed by spontaneous emission to emit a single photon). The control of ZPL broadening (even when emitters experience spectral diffusion) is observed in on-resonant excitation116 (electron is excited directly to minimum of excited state and then follows spontaneous emission).

This off- resonant excitation occurs when excitation energy (hf) is more than luminescent point defect ZPL energy (ΔEZPL) and on-resonant excitation occurs when hf = ΔEZPL. The controlled photophysical characteristics of emitters due to on resonant excitation is shown in third row of the Table 13 and the variation in PL maps due to Off and On resonant excitations is shown in Fig. 9h–j.

### Enhancement of single photon purity

Second order correlation values found to vary around 0.5 and this deviation from $$g^{2} \left( 0 \right)$$ = 0 (ideal value) is due to high residual background emission, which leads to decrease in single photon purity.

Emitters found in the He+ ion implanted area with subsequent annealing with argon (shown as a dark region) exhibits correlation value $$g^{2} \left( 0 \right)$$ = 0.077 (indicated by blue arrow), reduced by five-fold78 (indicating the reduction of background fluorescence) compared to the emitters found in non-irradiated area exhibiting $$g^{2} \left( 0 \right)$$ = 0.263 (indicated by white dashed arrow) as shown in Fig. 9k. The corresponding PL spectrum is shown in right to PL map.

### Tuning the quantum emission through external strain inducement or external electric field inducement or through ionic liquid devices

Emitters in hBN multilayers exhibit different emission energies (ZPL) over a large spectral band (inhomogeneous spectral distribution)65 due to variations in local strain and dielectric environment, which creates a central problem for fabricating identical single photon emitters.

Tuning the quantum emitters (having uneven ZPL emission energies), through external strain inducement or through external electric field via stark effect or electrostatic tuning through ionic liquid devices, leads to increase the probability of multiple uneven emitters (different ZPL energies) to have the same emission energy (ZPL), which further tends to fabricate identical quantum emitters with necessary emission wavelength.

#### External strain inducement

Controllable external strain can be induced to the emitters in hBN film by placing on a 1.5 mm thick bendable polycarbonate (PC) beam78 as shown in Fig. 9l and corresponding ZPL energy shifts of emitters due to variation in applied strain is shown in Fig. 9m. Tunability range observed for three different emitters (with different ZPL energies) are −3.1 meV/% (green), + 3.3 meV/% (yellow) and + 6 meV/% (red) respectively.

Similar experimental approach was observed in ref117 for deterministic single photon emitter formation by a combination of nanoscale strain engineering and charge trapping.

#### External electric field inducement

Quantum emitters in hBN are expected to lie within the plane, which creates an in-plane dipole. By inducing an out-of-plane electric field through graphene gates, electrical tuning of quantum emission (via stark effect) from luminescent point defects hosts in hBN was observed in ref118. The schematic representation of multilayer hBN between top and bottom graphene electrodes (for electric field inducement) is shown in Fig. 9n.

#### Electrostatic tuning of quantum emission through ionic liquid devices

The quantum emission from luminescent point defects in hBN can also be tuned by placing the hBN sample in ionic liquid devices97 as shown in Fig. 9o, in which poly (ethylene oxide) mixed with lithium perchlorate (PEO: Li-ClO4) is used as an electrolyte.

By applying positive (negative) gate voltages, the ZPL emission is found to be blue shifted (red shifted) by around 15 nm as shown in Fig. 9p. Tuned ZPL emissions are found to be stable and does not exhibit spectral diffusion.

### Other recent advances in modulation of emission from 2D hBN quantum emitters

Contemporary exploration on hBN integration with photonic microstructures like circular Bragg grating (CBG) was found to be eminent and rooted out the second harmonic generation119 (absorbs two photons of same frequency and generates a single photon of twice the frequency absorbed) in exfoliated multilayer hBN as shown in Fig. 10. Some of the investigative explorations probe that this second harmonic generation (SHG) could be associated to defects120.

Novel techniques to enhance the quantum emission from hBN single photon sources is by coupling the quantum emitters with photonic crystal cavities from silicon nitride (Si3N4)121 and Al nano-antenna122, which revealed a 6-fold and 10 to 15 fold enhancement in photoluminescence measurements of a hBN quantum emitter at room temperature respectively.

Due to high transmittance and poor reflectance of monolayer hBN, it was found to be invisible under white light which leads to utmost difficulties in experimental works like transferring methods and fabrication of 2D heterostructures.

It was Serendipity, that hBN was found to enhance the contrast on transparent substrates123 (polymer based interfacial layer on a polydimethylsiloxane (PDMS) substrate) and similar investigation was performed on other 2D TMDs and disseminate that TMDs exhibit significant difference in contrast on transparent substrates than opaque substrates.

The simulation results also reveal that contrast of hBN is high under shorter wavelength light than longer wavelength. Finally it was negotiated that selecting an appropriate substrate for optical experimentation is very crucial.

Tuning of quantum emission spectrum is found to feasible with externally applied tensile strain and present day a record tuning of 65 meV124 was observed in hBN layers.

## Prediction of emitter defect structures and applications of quantum emitters

### Prediction of defect structures using first principle calculations

A list of 35 different possible luminescent point defects of hBN (based on most likely forming impurities incorporate during hBN growth and while annealing on substrate), as shown in Fig. 11, were examined by Density Functional Theory (DFT) calculations using Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA)125 and Vienna Ab initio Simulation Package (VASP)126 on the basis of generalized gradient approximation by Perdew, Burke and Ernzerhof (PBE) functionals127.

Based on experimental observations, three main conditions, as shown in Table 14, were applied to authenticate a luminescent point defect as an effective potential quantum emitter.

Among the 35 luminescent point defects, NBVN, OBOBVN and CBVN are the defect structures found to satisfy the rules listed in Table 14 and their corresponding ZPL energies are 2.01 eV, 1.85 eV and 1.33 eV respectively (obtained through VASP calculations).

The Emitters detected in experimental studies (emission in visible region) whose ZPL is around ~ 2 eV, predicted to have NBVN64 defect structure and simulated (using VASP) electronic structure of NBVN defect in hBN monolayer is shown in Fig. 12a.

The electronic structure of VBO2 defect (obtained using VASP simulations) in hBN monolayer is shown in Fig. 12b. Among various oxygen related defects66 examined by DFT using hybrid functionals (HSE06), found that B-vacancy with two oxygen atoms (VBO2) defect structure as shown in Fig. 12c, is the most likely defect for emission in longer wavelength. The emission energy of VBO2 defect (theoretically calculated) found to be consistent with experimental ZPL energy of near IR emitters fabricated using Ar plasma etching.

Recent studies reveal that boron and nitrogen dangling bonds as shown in Fig. 12d, e as another source of single-photon emission around 2 eV, which is described in ref131.

Numerous DFT calculations anticipate that single photon emission in UV region is due to carbon substitutional defects like CN defect (nitrogen atom is replaced with carbon) and CB defect132 (boron atom is replaced with carbon). Their quantum emission (theoretical) was observed ~ 4.1 eV, which were consistent with experimental works as described in ref63.

By using Finite Difference Time Domain (FDTD) simulations as demonstrated in ref114, the enhancement of single photon source emission characteristics due to coupling with gold nanospheres was investigated as shown in Fig. 12f. The simulated spontaneous enhancement rate was consistent with experimental studies. X-polarized emitters which are perpendicular to the gold metal surface exhibits higher enhancement rates than y-polarized emitters.

Strain tunable quantum emission from NBVN defect structure as shown in Fig. 12g, was studied using DFT calculations by PBE approximation. Four strain directions were considered in simulations78 to create similar effects of strain, induced using polycarbonate (PC) beam in experimental works.

The quantum emission from NBVN defect is observed ~ 2.01 eV (black peak), when no strain was applied (zero strain). When tensile strain is applied along ZZ1 direction, the emission peaks were tunable towards lower wavelengths (blue tones) and similarly, when tensile strain applied along AC2 direction, the emission peaks were tunable towards higher wavelengths (red tones).

### Applications of quantum emitters

Many applications of quantum emitters have been proposed and demonstrated in literature. Some major applications of quantum emitters are discussed here:

1. i.

Quantum computing,

2. ii.

Quantum cryptography (Quantum communication),

3. iii.

Quantum imaging and metrology and

4. iv.

Other fascinating applications

#### Quantum computing

In classical computing, a conventional bit can be either a 0 or 1. Quantum computer provides a breakthrough revolution, in which a qubit can be both 0 and 1 at the same time on the basis of superposition principle.

In optical quantum computing, the single photons are considered as qubits. Initially, these single photons generated from single photon emitters can be either horizontally polarized (considered as logic 0) or vertically polarized (considered as logic 1). Then processing of qubits like creating superposition state (both logic 0 and 1 at same time) and flipping of qubits (logic 0→logic 1 or logic 1→logic 0) can be created using quantum gates like Hadamard (H) gate and Pauli-X gate etc. respectively. These quantum gates are developed using set of birefringent wave plates and the encrypted qubits finally accumulated using single photon detectors.

The schematic representation of a quantum photonic circuit in a quantum computer, constructed using single photon source, set of quantum gates and polarized beam splitters (PBS) and single photon detectors as shown in Fig. 13a, in this particular example quantum dot (QD) based single photon sources133,135,136,136 are used for discussion.

#### Quantum cryptography (quantum communication)

Quantum cryptography technique is used to encrypt the key by using quantum effects (polarized photons) for secure communication and the complete quantum communication137 setup is shown in Fig. 13b.

The quantum communication setup in which the single photon source (highlighted in red colour) is present at the transmitter, coupled to HBT setup for controlling the quality of source and EOM (electro optical modulator) to make photons polarized. The sender and receiver are separated by a distance of 50 m. The horizontal–vertical (H−V) and circular left–circular right (L−R) polarization basis photons were used for data encryption.

To date, Color centers in diamond87 (free space) and Quantum dots138 (optical fiber communication to a distance of 120 km) are used as single photon emitters in quantum communication systems.

#### Quantum imaging and metrology

##### Quantum imaging

Quantum imaging is a new sub-field of quantum optics, makes use of entangled photons to image the objects with higher resolution or other imaging criteria beyond the limitations of classical optics.

The simplified schematic of quantum imaging experiment is shown in Fig. 13c in which two entangled photons139,140 are generated using BBO (beta barium borate) crystal.

##### Quantum metrology

Similar to quantum imaging application, quantum metrology141,142 exploits entangled photons to make high sensitive measurements of assorted signal (weak emissions along with strong unwanted background) and physical parameters in order to avoid statistical errors. The schematic representation of quantum metrology circuit is shown in Fig. 13d.

#### Other fascination applications

##### Other fascinating applications of quantum emitters

Other fascinating quantum technology applications of single photon emitters (detected in 2D materials like hBN, WSe2, MoSe2 and MoS2 etc.) were listed in Table 15.

Surging the enhancement of emission characteristics in hBN like single photon purity, suppressing off-resonant noise, reduction of excited state lifetime and elimination of photo blinking and bleaching using Purcell effect was perceived by creating an array of plasmonic nanocavities149.

Contemporarily, the enhancement without coupling to plasmonic nanoparticles was made feasible using photonic crystal cavities143 and microcavities144, which enhances the implementation of scaled quantum photonic circuits. As similar to stark tuning of emission in hBN and graphene heterostructure, efficient spontaneous emission and enhancing photon extraction was realized through graphene-hBN hyperstructure148.

Coupling of quantum emitters in hBN to tapered optical fibers152 escalates the application of on-demand quantum repeaters, but the collection efficiency was observed around 10%.

Deposition of TMDs like WSe2 material on plasmonic nanopillars150, originates simultaneous exciton trapping and enhancement in emission characteristics. Recently coupling the WSe2 material to silicon nitride145,146 nanochip and waveguide found to increase photon extraction efficiency. Tunable quantum emission due to electric and magnetic fields and control of emitter lifetime in TMDs were also observed31,147 as similar to spectral tuning observed in hBN57,118. Particularly, the graphene/hBN/TMDs heterostructure facilitated the controlled charge trapping of excitons58.

##### Implementation of qubits (single photons) using various 2D materials and heterostructures

The implementation of qubits using various 2D materials and heterostructures are listed in Table 16 with relevant discussion and the corresponding figures are shown in Fig. 14.

Typical qubits (single photons) can be implemented by 2D materials using various phenomena like spontaneous emission associated to intermediate energy state transition in hBN, spontaneous emission associated to localized excitons trapped and funneled due to point defects and crystal imperfections in TMDs.

Electrostatic potential traps due to moiré patterns and intentionally induced strain gradients can also effectively tap excitons for qubits implementation.

Especially, in case of WSe2 material the crystal imperfections due to intentionally induced strain gradients by transferring on dielectric nanopillars and folding the material using gapped golden rods as shown in Fig. 14a, d, which leads to funnel and trap excitons. Optically exciting these trapped excitons leads to single photon emission. In similar fashion, an array of quantum emitters can be created by trapping the excitons using set of dielectric nanopillars as shown in Fig. 14b, the corresponding dry transfer technique of layered material on array of nanopillars in shown in Fig. 14c.

Moiré super-lattice of 2D heterobilayers structure as shown in Fig. 14g with twist angle θ leads to formation of electrostatic potential traps for effective trapping of exciton as shown in Fig. 14h.

Qubits can also be implemented by electrical excitation of excitons using 2D heterostructures like graphene/hBN/MoS2/hBN/graphene heterostructure as shown in Fig. 14e. The MoS2 acts as recombination layer, hBN as tunneling barrier and graphene as transparent electrodes. To verify the effect of charge trapping complete structure is divided into two: one with MoS2 layer (GBM) and without MoS2 layer (GB).

Energy band structure of graphene/hBN/MoS2/hBN/graphene heterostructure is shown in Fig. 14f. By increase in applied voltage, quasi fermi level of graphene (left contact) reaches minimum of conduction band of MoS2, electrons tunnel through the hBN barrier into MoS2 layer and quasi fermi level of graphene (right contact) reaches maximum of valence band of MoS2, holes tunnel through the hBN barrier into MoS2 layer. Injection of electrons and holes in MoS2 layer (recombination layer) leads to formation of exciton recombination followed by single photon emission.

Electrical manipulation of excitonic emission to generate entangled photons59,61,61 using 2D heterostructures, as similar to shown in Fig. 14e, is also realized which facilitates the application of quantum imaging and metrology.

#### Practical challenges of implementing quantum emitters and their applications

Few major challenges are noticed in fabricating hBN single photon emitters and developing towards quantum applications. The challenges associated with emitters (luminescent point defects) hosts in hBN were listed in Table 17.

One of the major challenge to be resolved is moderate single photon purity (non-ideal) due to residual background emission. In most of the experiments it was noted that emission intensity of emitters spans over a large spectral band (inhomogeneous spectral distribution) which is a central problem for developing identical single photon sources.

High refractive index of the material which makes difficult to confine the light within the hBN structure is another important problem to be addressed and finally, indistinguishability of photons from the emitter is very poor.

The challenges associated with optical quantum applications were listed in Table 18. In quantum computing, the loss of quantum coherence due to temperature fluctuations is the one major challenge to be overcome for practical implementation and another problem is influence of other electromagnetic waves and undesirable interactions with outer environment leads to collapse of quantum properties of computer.

In case of quantum communication, Security loopholes or side channels leads to in-secure quantum communication. Currently, probabilistic single photon sources are used for entangle photon generation which are not reliable for on-demand applications like quantum imaging and metrology.

The complete summary of hBN materials used and their synthesis, stable emitter formation techniques, defects consistent with experimental studies, important photophysical characteristics of emitters and their emission enhancement techniques and major applications of quantum emitters were discussed in Table 19.

## Conclusion and outlook

Single photon emission is observed from single atom in a cavity to recent 2D materials, however, each of these sources have their own constraints. However, the state-of-the-art quantum emitters in 2D materials found to be an effective alternate to traditional single photon emitters in three dimensional materials due to the disadvantage of photon extraction efficiency and external circuit coupling.

In the quest of A1 supreme quantum emitters, strong excitonic single photon emission is observed in monolayer TMDs19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,46 and in their Moiré patterns49,51,52,53,53 at cryogenic temperatures. Despite, inducing a stronger strain in TMDs is found to improve their operating temperatures22 and quantum yield47,48. It’s an auspicious that emitters observed in multilayer hBN are found to be stable at a wide range of operating temperatures, various harsh environments and found to be localized at flake edges in mechanically exfoliated flakes which enhances the device fabrication and coupling to plasmonic cavity for higher integration quantum photonic circuits.

This solid quantum emitters in hBN are found to be generated by Ion implantation, laser ablation, Ar plasma etching followed by subsequent annealing and electron beam irradiation. But, the nature of emitters formed is still under debate. The cutting-edge research is fabricating stable quantum emitters in higher order (⁓ 100–200 SPEs per 10 × 10 μm2) in large few-layer hBN fabricated with LPCVD technique, strongly publicized that more than 85% of the emitters have a ZPL at (580 ± 10) nm, which is the confined uneven spectral distribution reported to date97.

To enhance the performance of quantum photonic devices and converge to on-demand applications, fabricating the quantum emitters which covers the wide range of emission on a single platform is really worthy of attention. Significantly, hBN exhibits broad emission range from UV to near IR region and the first signature of Rabi oscillations and resonant fluorescence emission was observed from a resonantly drive hBN quantum emitter153. Contemporarily, an attractive phenomenon of second harmonic generation (SHG)119,120 was discovered in hBN multilayer coupled to circular Bragg grating (CBG) photonic microstructures which, encourages the delightful applications.

Although the emission characteristic measurements in hBN were not up to the mark, quantification enhancement techniques like Two laser excitation technique, plasmonic coupling using gold nanospheres, external strain engineering, electrostatic tuning through ionic liquid devices97 and very recently electric and magnetic field inducements57 etc., techniques found to enhance and tune the quantum emitters emission properties and control the inhomogeneous spectral distribution. To date a record tuning of quantum emission around 65 meV124 and higher rate of emission enhancement (around 6 to 15 fold) owing to coupling with photonic crystal cavities from silicon nitride (Si3N4)121 and Al nano-antenna122 was perceived. However the quantum emitters in hBN experience spectral diffusion at cryogenic temperatures, Resonant and antistokes154 excitation technique found to overcome the complication due to spectral diffusion.

Emitters in hBN are mostly stable under illumination at 532 nm. On the other facet, emitters exhibits fluorescence instability and spectral diffusion at blue laser excitation155. However employing different substrates like Al2O3 156 or InGaP157 found to reduce the random spectral fluctuations, layered hBN mounts a problem of invisibility on opaque substrates under white light illumination. Recent explorations make a Serendip that hBN was found to enhance the contrast on transparent substrates123, which makes experimental works feasible on hBN.

Efficient photon extraction and coupling to external photonic circuits and devices is at most important for practical implementation for quantum applications. Out of sort, only 10% efficiency in photon extraction using an optical fiber and coupling to an optical waveguide is achieved146 at room temperature. A waveguide of proper design is needed to improve the coupling of quantum emitters and filter the propagating laser light, to enhance the feasible implementation of quantum repeaters.

As a quantum breakthrough, tunable excitonic emission in hybrid structures initiate the development of quantum memories58. Entanglement of photons for Quantum imaging and metrology was made possible by a back-gated WSe2 monolayer, hBN and graphene heterostructure59,61,61, overcome the drawback of generating entangled photons at random process in nonlinear BBO crystal.

Several computational evidences disclose that point defects responsible for single photon emission. Investigation of 35 different likely possible point defect structures by density-functional theory (DFT) provides a strong evidence that NBVN defect structure is more consistent with the emitter responsible for visible region emission, VBO2 defect for near IR region and CN defect for UV emission. Recent theoretical studies reveal boron dangling bonds125 are also the likely source of emission around 2 eV and CB defect126 as another candidate responsible for UV emission.