We experimentally study the electronic spin transport in hBN encapsulated single layer graphene nonlocal spin valves. The use of top and bottom gates allows us to control the carrier density and the electric field independently. The spin relaxation times in our devices range up to 2 ns with spin relaxation lengths exceeding 12 $μ$m even at room temperature. We obtain that the ratio of the spin relaxation time for spins pointing out-of-plane to spins in-plane is $τ_{\bot} / τ_{||} \approx$ 0.75 for zero applied perpendicular electric field. By tuning the electric field this anisotropy changes to $\approx$0.65 at 0.7 V/nm, in agreement with an electric field tunable in-plane Rashba spin-orbit coupling.
We study fully hexagonal boron nitride (hBN)-encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes; thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from SiO2/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Furthe…
We present a thermal annealing study on single-layer and bilayer (BLG) graphene encapsulated in hexagonal boron nitride. The samples are characterized by electron transport and Raman spectroscopy measurements before and after each annealing step. While extracted material properties such as charge carrier mobility, overall doping, and strain are not influenced by the annealing, an initial annealing step lowers doping and strain variations and thus results in a more homogeneous sample. Additionally, the narrow 2D-sub-peak widths of the Raman spectrum of BLG, allow us to extract information about…
The encapsulation of graphene in hexagonal boron nitride provides graphene on substrate with excellent material quality. Here, we present the fabrication and characterization of Hall sensor elements based on graphene boron nitride heterostructures, where we gain from high mobility and low charge charier density at room temperature. We show a detailed device characterization including Hall effect measurements under vacuum and ambient conditions. We achieve a current- and voltage-related sensitivity of up to 5700 V/AT and 3 V/VT, respectively, outpacing state-of- the-art silicon and III/V Hall s…
Interference of double moire patterns of graphene (G) encapsulated by hexagonal boron nitride (BN) can alter the electronic structure features near the primary/secondary Dirac points and the electron-hole symmetry introduced by a single G/BN moire pattern depending on the relative stacking arrangements of the top/bottom BN layers. We show that strong interference effects are found in nearly aligned BN/G/BN and BN/G/NB and obtain the evolution of the associated density of states as a function of moire superlattice twist angles. For equal moire periods and commensurate patterns with $Δϕ= 0^{\cir…
Embedding a WS$_2$ monolayer in flakes of hexagonal boron nitride allowed us to resolve and study the photoluminescence response due to both singlet and triplet states of negatively charged excitons (trions) in this atomically thin semiconductor. The energy separation between the singlet and triplet states has been found to be relatively small reflecting rather weak effects of the electron-electron exchange interaction for the trion triplet in a WS$_2$ monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the h…
We investigate the impact of the encapsulation with hexagonal boron nitride (h-BN) on the Raman spectrum of few layer black phosphorus. The encapsulation results in a significant reduction of the line width of the Raman modes of black phosphorus, due to a reduced phonon scattering rate. We observe a so far elusive peak in the Raman spectra $\sim$4cm$^{-1}$ above the A$_{\text{g}}^1$ mode in trilayer and thicker flakes, which had not been observed experimentally. The newly observed mode originates from the strong black phosphorus inter-layer interaction, which induces a hardening of the surface…
We develop the device model for the proposed injection (electrically) driven thermal light emitters (IDLEs) based on the vertical Hexagonal Boron Nitride Layer/Graphene Layer/ Hexagonal Boron Nitride Layer (hBNL/GL/hBNL) heterostructures and analyze their dynamic response. The operation of the IDLEs is associated with the light emission of the hot two-dimensional electron-hole plasma (2DEHP) generated in the GL by both the lateral injection from the side contacts and the vertical injection through the hBNL (combined injection) heating the 2DEHP. The temporal variation of the injection current …
Atomically thin materials, like semiconducting transition metal dichalcogenides, are highly sensitive to the environment. This opens up an opportunity to externally control their properties by changing their surroundings. In this work, high-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer MoS$_2$ are studied with the aid of photoluminescence, photoluminescence excitation, and reflectance contrast experiments. We demonstrate that carrier concentration in MoS$_2$ monolayers, arising from charge transfer from impurities in the substrate, can be significantly tuned …
Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs display superb electronic properties due to very limited scattering from extrinsic disorder sources such as Coulomb impurities and corrugations. Such samples are therefore expected to be ideal platforms for highly-tunable low-loss plasmonics in a wide spectral range. In this Article we present a theory of collective electron density oscillations in a graphene sheet encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes. W…
Electron-electron interactions in graphene are sufficiently strong to induce a correlated and momentum-conserving flow such that charge carriers behave similarly to the Hagen-Poiseuille flow of a classical fluid. In the current work, we investigate the electronic signatures of such a viscous charge flow in high-mobility graphene FETs. In two complementary measurement schemes, we monitor differential resistance of graphene for different channel widths and for different effective electron temperatures. By combining both approaches, the presence of viscous effects is verified in a temperature ran…
We present low-temperature Raman measurements on gate tunable graphene encapsulated in hexagonal boron nitride, which allows to study in detail the Raman G and 2D mode frequencies and line widths as function of the charge carrier density. We observe a clear softening of the Raman G mode (of up to 2.5 cm$^{-1}$) at low carrier density due to the phonon anomaly and a residual G~mode line width of $\approx$ 3.5 cm$^{-1}$ at high doping. From analyzing the G mode dependence on doping and laser power we extract an electron-phonon-coupling constant of $\approx$ 4.4 $\times$ 10$^{-3}$ (for the G mode…
We present measurements of weak localization on hexagonal boron nitride encapsulated bilayer MoS$_2$. From the analysis we obtain information regarding the phase-coherence and the spin diffusion of the electrons. We find that the encapsulation with boron nitride provides higher mobilities in the samples, and the phase-coherence shows improvement, while the spin relaxation does not exhibit any significant enhancement compared to non-encapsulated MoS$_2$. The spin relaxation time is in the order of a few picoseconds, indicating a fast intravalley spin-flip rate. Lastly, the spin-flip rate is fou…
We report a proof-of-concept study of extraordinary magnetoresistance (EMR) in devices of monolayer graphene encapsulated in hexagonal boron nitride, having metallic edge contacts and a central metal shunt. Extremely large EMR values, $MR=(R(B) - R_0) / R_0\sim 10^5$, are achieved in part because $R_0$ approaches or crosses zero as a function of the gate voltage, exceeding that achieved in high mobility bulk semiconductor devices. We highlight the sensitivity, $dR/dB$, which in two-terminal measurements is the highest yet reported for EMR devices, and in particular exceeds prior results in gra…
We present a novel method to establish inner point contacts on hexagonal boron nitride (hBN) encapsulated graphene heterostructures with dimensions as small as 100 nm by pre-patterning the top-hBN in a separate step prior to dry-stacking. 2 and 4-terminal field effect measurements between different lead combinations are in qualitative agreement with an electrostatic model assuming pointlike contacts. The measured contact resistances are 0.5-1.5 k$Ω$ per contact, which is quite low for such small contacts. By applying a perpendicular magnetic fields, an insulating behaviour in the quantum Hall …
We have performed spin and charge transport measurements in dual gated high mobility bilayer graphene encapsulated in hexagonal boron nitride. Our results show spin relaxation lengths $λ_s$ up to 13~\textmu m at room temperature with relaxation times $τ_s$ of 2.5~ns. At 4~K, the diffusion coefficient rises up to 0.52~m$^2$/s, a value 5 times higher than the best achieved for graphene spin valves up to date. As a consequence, $λ_s$ rises up to 24~\textmu m with $τ_s$ as high as 2.9~ns. We characterized 3 different samples and observed that the spin relaxation times increase with the device leng…
We study the infrared cyclotron resonance of high mobility monolayer graphene encapsulated in hexagonal boron nitride, and simultaneously observe several narrow resonance lines due to interband Landau level transitions. By holding the magnetic field strength, $B$, constant while tuning the carrier density, $n$, we find the transition energies show a pronounced non-monotonic dependence on the Landau level filling factor, $ν\propto n/B$. This constitutes direct evidence that electron-electron interactions contribute to the Landau level transition energies in graphene, beyond the single-particle …
We present a fast method to fabricate high quality heterostructure devices by picking up crystals of arbitrary sizes. Bilayer graphene is encapsulated with hexagonal boron nitride to demonstrate this approach, showing good electronic quality with mobilities ranging from 17 000 cm^2/V/s at room temperature to 49 000 cm^2/V/s at 4.2 K, and entering the quantum Hall regime below 0.5 T. This method provides a strong and useful tool for the fabrication of future high quality layered crystal devices.
Devices made from graphene encapsulated in hexagonal boron-nitride exhibit pronounced negative bend resistance and an anomalous Hall effect, which are a direct consequence of room-temperature ballistic transport on a micrometer scale for a wide range of carrier concentrations. The encapsulation makes graphene practically insusceptible to the ambient atmosphere and, simultaneously, allows the use of boron nitride as an ultrathin top gate dielectric.
Devices made from two dimensional materials such as graphene and transition metal dichalcogenides exhibit remarkable electronic properties of interest to many subdisciplines of nanoscience. Owing to their 2D nature, their quality is highly susceptible to contamination and degradation when exposed to the ambient environment. Protecting the 2D layers by encapsulation between hexagonal boron nitride layers significantly improves their quality. Locating these samples within the encapsulant and assessing their integrity prior to further processing then becomes challenging. Here we show that conduct…
Devices made from two-dimensional (2D) materials such as graphene or transition metal dichalcogenides possess interesting electronic properties that can become accessible to experimental probes when the samples are protected from deleterious environmental effects by encapsulating them between hexagonal boron nitride (hBN) layers. While the encapsulated flakes can be detected through post-processing of optical images or confocal Raman mapping, these techniques lack the sub-micrometer scale resolution to identify tears, structural defects or impurities, which is crucial for the fabrication of hi…
A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called super-moiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the non-relaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the …
Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here we study moiré superlattice minibands in graphene (G) encapsulated in hexagonal boron nitride (hBN) with an almost perfect alignment with both the top and bottom hBN crystals. We show that, for such an orientation of the unit cells of the hBN layers that locally breaks inversion symmetry of the graphene lattice, the hBN/G/hBN structure features a Kagomé network of topologically protected chiral states…
More than a decade after the discovery of graphene, ballistic transport in nanostructures based on this intriguing material still represents a challenging field of research in two-dimensional electronics. The presence of rough edges in nanostructures based on this material prevents the appearance of truly ballistic electron transport as theo\-re\-tically predicted and, therefore, not well-developed plateaus of conductance have been revealed to date. In this work we report on a novel implementation of the cryo-etching method, which enabled us to fabricate graphene nanoconstrictions encapsulated…
Low frequency 1/f noise is investigated in graphene, encapsulated between hexagonal boron nitride (hBN) substrate in dual gated geometry. The overall noise magnitude is smaller as compared to graphene on Si/SiO2 substrate. The noise amplitude in the hole doped region is independent of carrier density while in the electron doped region, a pronounced peak is observed, at Fermi energy, EF ~ 90 meV. The physical mechanism of the anomalous noise peak in the electron doped region is attributed to the impurity states originating from the Carbon atom replacing the Nitrogen site in hBN crystal. Further…
The encapsulation of graphene based Hall sensors on foil is shown to be an effective method for improving the performance in terms of higher sensitivity for magnetic field detection. Two types of encapsulation were investigated: a simple encapsulation of graphene with polymethyl methacrylate (PMMA) as a proof of concept and an encapsulation with mechanically exfoliated hexagonal boron nitride (hBN). The Hall sensor with PMMA encapsulation already shows higher sensitivity compared to the one without encapsulation. However, the Hall sensor with graphene encapsulated between two stacks of hBN sho…
The excellent electronic and mechanical properties of graphene allow it to sustain very large currents, enabling its incandescence through Joule heating in suspended devices. Although interesting scientifically and promising technologically, this process is unattainable in ambient environment, because graphene quickly oxidises at high temperatures. Here, we take the performance of graphene-based incandescent devices to the next level by encapsulating graphene with hexagonal boron nitride (hBN). Remarkably, we found that the hBN encapsulation provides an excellent protection for hot graphene fi…
Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a hot spot with Berry curvature accumulating at the charge neutral point (CNP), and it…
Van der Waals heterostructures provide a rich platform for emergent physics due to their tunable hybridization of electronic orbital- and spin-degrees of freedom. Here, we show that a heterostructure formed by twisted bilayer graphene sandwiched between ferromagnetic insulators develops flat bands stemming from the interplay between twist, exchange proximity and spin-orbit coupling. We demonstrate that in this flat-band regime, the spin degree of freedom is hybridized, giving rise to an effective triangular superlattice with valley as a degenerate pseudospin degree of freedom. Incorporating el…
Hexagonal boron nitride (h-BN) encapsulation significantly improves carrier transport in graphene. This work investigates the benefit of implementing the encapsulation technique in graphene field-effect transistors (GFET) in terms of their radio frequency (RF) performance. For such a purpose, a drift-diffusion self-consistent simulator is prepared to get the GFET electrical characteristics. Both the mobility and saturation velocity information are obtained by means of an ensemble Monte Carlo simulator upon considering the relevant scattering mechanisms that affect carrier transport. RF figures…
The recently observed unconventional ferroelectricity in AB bilayer graphene sandwiched by hexagonal Boron Nitride (hBN) presents a new platform to manipulate correlated phases in multilayered van der Waals heterostructures. We present a low-energy continuum model for AB bilayer graphene encapsulated by the top and bottom layers of either hBN or graphene, with two independent twist angles. For the graphene/hBN heterostructures, we show that twist angle asymmetry leads to a layer polarization of the valence and conduction bands. We also show that an out-of-plane displacement field not only tune…
We study spin-orbit torques in two dimensional hexagonal crystals such as graphene, silicene, germanene and stanene. The torque possesses two components, a field-like term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-$k$ space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100\% by tuning the bias voltage or mag…
The relative twist angle in heterostructures of two-dimensional (2D) materials with similar lattice constants result in a dramatic alteration of the electronic properties. Here, we investigate the electrical and magnetotransport properties in bilayer graphene (BLG) encapsulated between two hexagonal boron nitride (hBN) crystals, where the top and bottom hBN are rotationally aligned with bilayer graphene with a twist angle $θ_t\sim 0^{\circ} \text{and}~ θ_b < 1^{\circ}$, respectively. This results in the formation of two moiré superlattices, with the appearance of satellite resistivity peaks at…
Opto-electronic devices utilizing graphene have already demonstrated unique capabilities, which are much more difficult to realize with conventional technologies. However, the requirements in terms of material quality and uniformity are very demanding. A major roadblock towards high-performance devices are the nanoscale variations of graphene properties, which strongly impact the macroscopic device behaviour. Here, we present and apply opto-electronic nanoscopy to measure locally both the optical and electronic properties of graphene devices. This is achieved by combining scanning near-field i…
The performance of electronic and spintronic devices based on two-dimensional semiconductors (2D SC) is largely dependent on the quality and resistance of the metal/SC electrical contacts, as well as preservation of the intrinsic properties of the SC channel. Direct Metal/SC interaction results in highly resistive contacts due to formation of large Schottky barriers and considerably affects the properties of the 2D SC. In this work, we address these two important issues in monolayer $\mathrm{MoSe_2}$ Field-Effect transistors (FETs). We encapsulate the $\mathrm{MoSe_2}$ channel with hexagonal B…
Hysteresis-Free High Mobility Graphene Encapsulated in Tungsten Disulfide
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology(光子科学研究所,巴塞罗那科学技术研究院);Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice(威尼斯大学分子科学与纳米系统系);School for Engineering of Matter, Transport and Energy, Arizona State University(亚利桑那州立大学物质、交通与能源工程学院)
Graphene has remarkable opportunities for spintronics due to its high mobility and long spin diffusion length, especially when encapsulated in hexagonal boron nitride (h-BN). Here, for the first time, we demonstrate gate-tunable spin transport in such encapsulated graphene-based spin valves with one-dimensional (1D) ferromagnetic edge contacts. An electrostatic backgate tunes the Fermi level of graphene to probe different energy levels of the spin-polarized density of states (DOS) of the 1D ferromagnetic contact, which interact through a magnetic proximity effect (MPE) that induces ferromagnet…
Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulphides and hBN are found to exhibit consistently high carrier mobilities of about 60,000 cm$^{2}$V$^{-1}$s$^{-1}$. In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper o…
Many-body effects resulting from strong electron-electron and electron-phonon interactions play a significant role in graphene physics. We report on their manifestation in low B field magneto-phonon resonances in high quality exfoliated single-layer and bilayer graphene encapsulated in hexagonal boron nitride. These resonances allow us to extract characteristic effective Fermi velocities, as high as $1.20 \times 10^6$ m/s, for the observed "dressed" Landau level transitions, as well as the broadening of the resonances, which increases with Landau level index.
We report on quantum transport measurements on etched graphene nanoribbons encapsulated in hexagonal boron nitride (hBN). At zero magnetic field our devices behave qualitatively very similar to what has been reported for graphene nanoribbons on $\text{SiO}_2$ or hBN, but exhibit a considerable smaller transport gap. At magnetic fields of around $3~$T the transport behavior changes considerably and is dominated by a much larger energy gap induced by electron-electron interactions completely suppressing transport. This energy gap increases with a slope on the order of $3-4~ $meV/T reaching value…
We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, th…
Integration of individual two-dimensional materials into heterostructures is a crucial step which enables development of new and technologically interesting functional systems of reduced dimensionality. Here, well-defined lateral heterostructures of hexagonal boron nitride and graphene are synthesized on Ir(111) by performing sequential chemical vapor deposition from borazine and ethylene in ultra-high vacuum. Low-energy electron microscopy (LEEM) and selected-area electron diffraction (μ-LEED) show that the heterostructures do not consist only of hexagonal boron nitride (an insulator) and gra…
We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase coherence times $τ_ϕ$ as well as the inter- and intra-valley scattering times $τ_i$ and $τ_*$. While $τ_ϕ$ is in qualitative agreement with an electron-electron interaction mediated dephasing mechanism, electron spin-flip scattering processes are limiting $τ_ϕ$ at low temperatures. The anal…
Ultra-clean graphene sheets encapsulated between hexagonal boron nitride crystals host two-dimensional electron systems in which low-temperature transport is solely limited by the sample size. We revisit the theoretical problem of carrying out microscopic calculations of non-local ballistic transport in such micron-scale devices. By employing the Landauer-Buttiker scattering theory, we propose a novel scaling approach to tight-binding non-local transport in realistic graphene devices. We test our numerical method against experimental data on transverse magnetic focusing (TMF), a textbook examp…
We use scanning gate microscopy to map out the trajectories of ballistic carriers in high-mobility graphene encapsulated by hexagonal boron nitride and subject to a weak magnetic field. We employ a magnetic focusing geometry to image carriers that emerge ballistically from an injector, follow a cyclotron path due to the Lorentz force from an applied magnetic field, and land on an adjacent collector probe. The local electric field generated by the scanning tip in the vicinity of the carriers deflects their trajectories, modifying the proportion of carriers focused into the collector. By measuri…
Graphene supported on a transition metal dichalcogenide substrate offers a novel platform to study the spin transport in graphene in presence of a substrate induced spin-orbit coupling, while preserving its intrinsic charge transport properties. We report the first non-local spin transport measurements in graphene completely supported on a 3.5 nm thick tungsten disulfide (WS$_2$) substrate, and encapsulated from the top with a 8 nm thick hexagonal boron nitride layer. For graphene, having mobility up to 16,000 cm$^2$V$^{-1}$s$^{-1}$, we measure almost constant spin-signals both in electron and…
Color centers in hexagonal boron nitride (hBN) show stable single photon emission even at room temperature, making these systems a promising candidate for quantum information applications. Besides this remarkable property, also their interaction with longitudinal optical (LO) phonons is quite unique because they lead to dominant phonon sidebands (PSBs), well separated from the zero phonon line (ZPL). In this work we utilize this clear spectral separation to theoretically investigate the influence of phonon decay dynamics on time-dependent photoluminescence (PL) signals. Our simulations show, t…
We report the fabrication of hexagonal-boron-nitride (hBN) encapsulated multi-terminal WSe$_2$ Hall bars with 2D/2D low-temperature Ohmic contacts as a platform for investigating the two-dimensional (2D) metal-insulator transition. We demonstrate that the WSe$_2$ devices exhibit Ohmic behavior down to 0.25 K and at low enough excitation voltages to avoid current-heating effects. Additionally, the high-quality hBN-encapsulated WSe$_2$ devices in ideal Hall-bar geometry enable us to accurately determine the carrier density. Measurements of the temperature ($T$) and density ($n_s$) dependence of …
We explore possible ways to manipulate the intrinsic edge magnetism in hexagonal graphene nanoflake with zigzag edges, using density functional theory supplemented with on-site Coulomb interaction. The effect of carrier doping, chemical modification at the edge, and finite temperature on the edge magnetism has been studied. The magnetic phase diagram with varied carrier doping, and on-site Coulomb interaction is found to be complex. In addition to the intrinsic antiferromag- netic solution, as predicted for charge neutral hexagonal nanoflake, fully polarized ferromagnetic, and mixed phase solu…
Using time-resolved optical Kerr rotation, we measure the low temperature valley dynamics of resident electrons and holes in exfoliated WSe$_2$ monolayers as a systematic function of carrier density. In an effort to reconcile the many disparate timescales of carrier valley dynamics in monolayer semiconductors reported to date, we directly compare the doping-dependent valley relaxation in two electrostatically-gated WSe$_2$ monolayers having different dielectric environments. In a fully-encapsulated structure (hBN/WSe$_2$/hBN, where hBN is hexagonal boron nitride), valley relaxation is found to…