Semi-metallic graphene and semiconducting monolayer transition metal dichalcogenides (TMDCs) are the two-dimensional (2D) materials most intensively studied in recent years. Recently, black phosphorus emerged as a promising new 2D material due to its
widely tunable and direct bandgap, high carrier mobility and remarkable in-plane anisotropic electrical, optical and phonon properties. However, current progress is primarily limited to its thin-film form, and its unique properties at the truly 2D quantum confinement have yet to be demonstrated. Here, we reveal highly anisotropic and tightly bound excitons in monolayer black phosphorus using polarization-resolved photoluminescence measurements at room temperature. We show that regardless of the excitation laser polarization, the emitted light from the monolayer is linearly polarized along the light effective mass direction and centers around 1.3 eV, a clear signature of emission from highly anisotropic bright excitons. In addition, photoluminescence excitation spectroscopy suggests a quasiparticle bandgap of 2.2 eV, from which we estimate an exciton binding energy of around 0.9 eV, consistent with theoretical results based on first-principles. The experimental observation of highly anisotropic, bright excitons with exceedingly large binding energy not only opens avenues for the future explorations of many-electron effects in this unusual 2D material, but also suggests a promising future in optoelectronic devices such as on-chip infrared light sources.
Local energy extrema of the bands in momentum space, or valleys, can endow electrons in solids with pseudo-spin in addition to real spin. In transition metal dichalcogenides this valley pseudo-spin, like real spin, is associated with a magnetic momen
t which underlies the valley-dependent circular dichroism that allows optical generation of valley polarization, intervalley quantum coherence, and the valley Hall effect. However, magnetic manipulation of valley pseudospin via this magnetic moment, analogous to what is possible with real spin, has not been shown before. Here we report observation of the valley Zeeman splitting and magnetic tuning of polarization and coherence of the excitonic valley pseudospin, by performing polarization-resolved magneto-photoluminescence on monolayer WSe2. Our measurements reveal both the atomic orbital and lattice contributions to the valley orbital magnetic moment; demonstrate the deviation of the band edges in the valleys from an exact massive Dirac fermion model; and reveal a striking difference between the magnetic responses of neutral and charged valley excitons which is explained by renormalization of the excitonic spectrum due to strong exchange interactions.
Two-dimensional (2D) materials, such as graphene1, boron nitride2, and transition metal dichalcogenides (TMDs)3-5, have sparked wide interest in both device physics and technological applications at the atomic monolayer limit. These 2D monolayers can
be stacked together with precise control to form novel van der Waals heterostructures for new functionalities2,6-9. One highly coveted but yet to be realized heterostructure is that of differing monolayer TMDs with type II band alignment10-12. Their application potential hinges on the fabrication, understanding, and control of bonded monolayers, with bound electrons and holes localized in individual monolayers, i.e. interlayer excitons. Here, we report the first observation of interlayer excitons in monolayer MoSe2-WSe2 heterostructures by both photoluminescence and photoluminescence excitation spectroscopy. The energy and luminescence intensity of interlayer excitons are highly tunable by an applied vertical gate voltage, implying electrical control of the heterojunction band-alignment. Using time resolved photoluminescence, we find that the interlayer exciton is long-lived with a lifetime of about 1.8 ns, an order of magnitude longer than intralayer excitons13-16. Our work demonstrates the ability to optically pump interlayer electric polarization and provokes the immediate exploration of interlayer excitons for condensation phenomena, as well as new applications in 2D light-emitting diodes, lasers, and photovoltaic devices.
Light-emitting diodes are of importance for lighting, displays, optical interconnects, logic and sensors. Hence the development of new systems that allow improvements in their efficiency, spectral properties, compactness and integrability could have
significant ramifications. Monolayer transition metal dichalcogenides have recently emerged as interesting candidates for optoelectronic applications due to their unique optical properties. Electroluminescence has already been observed from monolayer MoS2 devices. However, the electroluminescence efficiency was low and the linewidth broad due both to the poor optical quality of MoS2 and to ineffective contacts. Here, we report electroluminescence from lateral p-n junctions in monolayer WSe2 induced electrostatically using a thin boron nitride support as a dielectric layer with multiple metal gates beneath. This structure allows effective injection of electrons and holes, and combined with the high optical quality of WSe2 it yields bright electroluminescence with 1000 times smaller injection current and 10 times smaller linewidth than in MoS2. Furthermore, by increasing the injection bias we can tune the electroluminescence between regimes of impurity-bound, charged, and neutral excitons. This system has the required ingredients for new kinds of optoelectronic devices such as spin- and valley-polarized light-emitting diodes, on-chip lasers, and two-dimensional electro-optic modulators.
Coupling degrees of freedom of distinct nature plays a critical role in numerous physical phenomena. The recent emergence of layered materials provides a laboratory for studying the interplay between internal quantum degrees of freedom of electrons.
Here, we report experimental signatures of new coupling phenomena connecting real spin with layer pseudospins in bilayer WSe2. In polarization-resolved photoluminescence measurements, we observe large spin orientation of neutral and charged excitons generated by both circularly and linearly polarized light, with a splitting of the trion spectrum into a doublet at large vertical electrical field. These observations can be explained by locking of spin and layer pseudospin in a given valley. Because up and down spin states are localized in opposite layers, spin relaxation is substantially suppressed, while the doublet emerges as a manifestation of electrically induced spin splitting resulting from the interlayer bias. The observed distinctive behavior of the trion doublet under circularly and linearly polarized light excitation further provides spectroscopic evidence of interlayer and intralayer trion species, a promising step toward optical manipulation in van der Waals heterostructures through the control of interlayer excitons.
Monolayers of transition metal dichalcogenides (TMDCs) have emerged as new optoelectronic materials in the two dimensional (2D) limit, exhibiting rich spin-valley interplays, tunable excitonic effects, and strong light-matter interactions. An essenti
al yet undeveloped ingredient for many photonic applications is the manipulation of its light emission. Here we demonstrate the control of excitonic light emission from monolayer tungsten diselenide (WSe2) in an integrated photonic structure, achieved by transferring one monolayer onto a photonic crystal (PhC) with a cavity. In addition to the observation of greatly enhanced (~60 times) photoluminescence of WSe2 and an effectively coupled cavity-mode emission, we are able to redistribute the emitted photons both polarly and azimuthally in the far field through designing PhC structures, as revealed by momentum-resolved microscopy. A 2D optical antenna is thus constructed. Our work suggests a new way of manipulating photons in hybrid 2D photonics, important for future energy efficient optoelectronics and 2D nano-lasers.
We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {sc Test Cover} problem we are given a set $[n]={1,...,n}$ of items together with a collecti
on, $cal T$, of distinct subsets of these items called tests. We assume that $cal T$ is a test cover, i.e., for each pair of items there is a test in $cal T$ containing exactly one of these items. The objective is to find a minimum size subcollection of $cal T$, which is still a test cover. The generic parameterized version of {sc Test Cover} is denoted by $p(k,n,|{cal T}|)$-{sc Test Cover}. Here, we are given $([n],cal{T})$ and a positive integer parameter $k$ as input and the objective is to decide whether there is a test cover of size at most $p(k,n,|{cal T}|)$. We study four parameterizations for {sc Test Cover} and obtain the following: (a) $k$-{sc Test Cover}, and $(n-k)$-{sc Test Cover} are fixed-parameter tractable (FPT). (b) $(|{cal T}|-k)$-{sc Test Cover} and $(log n+k)$-{sc Test Cover} are W[1]-hard. Thus, it is unlikely that these problems are FPT.
We consider a CNF formula $F$ as a multiset of clauses: $F={c_1,..., c_m}$. The set of variables of $F$ will be denoted by $V(F)$. Let $B_F$ denote the bipartite graph with partite sets $V(F)$ and $F$ and with an edge between $v in V(F)$ and $c in F$
if $v in c$ or $bar{v} in c$. The matching number $ u(F)$ of $F$ is the size of a maximum matching in $B_F$. In our main result, we prove that the following parameterization of {sc MaxSat} (denoted by $( u(F)+k)$-textsc{SAT}) is fixed-parameter tractable: Given a formula $F$, decide whether we can satisfy at least $ u(F)+k$ clauses in $F$, where $k$ is the parameter. A formula $F$ is called variable-matched if $ u(F)=|V(F)|.$ Let $delta(F)=|F|-|V(F)|$ and $delta^*(F)=max_{Fsubseteq F} delta(F).$ Our main result implies fixed-parameter tractability of {sc MaxSat} parameterized by $delta(F)$ for variable-matched formulas $F$; this complements related results of Kullmann (2000) and Szeider (2004) for {sc MaxSat} parameterized by $delta^*(F)$. To obtain our main result, we reduce $( u(F)+k)$-textsc{SAT} into the following parameterization of the {sc Hitting Set} problem (denoted by $(m-k)$-{sc Hitting Set}): given a collection $cal C$ of $m$ subsets of a ground set $U$ of $n$ elements, decide whether there is $Xsubseteq U$ such that $Ccap X eq emptyset$ for each $Cin cal C$ and $|X|le m-k,$ where $k$ is the parameter. Gutin, Jones and Yeo (2011) proved that $(m-k)$-{sc Hitting Set} is fixed-parameter tractable by obtaining an exponential kernel for the problem. We obtain two algorithms for $(m-k)$-{sc Hitting Set}: a deterministic algorithm of runtime $O((2e)^{2k+O(log^2 k)} (m+n)^{O(1)})$ and a randomized algorithm of expected runtime $O(8^{k+O(sqrt{k})} (m+n)^{O(1)})$. Our deterministic algorithm improves an algorithm that follows from the kernelization result of Gutin, Jones and Yeo (2011).
The key feature of the improved coupling design in the Damped Detuned Structure (DDS) is focused on the four manifolds. Rectangular geometry slots and rectangular manifolds are used. This results in a significantly stronger coupling to the manifolds
compared to the previous design. We describe the new design together with its wakefield damping properties.
Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, a
nd optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable second order nonlinear susceptibility chi ^(2) once an in-plane electric field is applied. chi^(2) can be electrically tuned from 0 to ~ {10^5 pm/V}, three orders of magnitude larger than the widely used nonlinear crystal AgGaSe2. We show that the unusually large chi^(2) arises from two different quantum enhanced two-photon processes thanks to the unique electronic spectrum of BLG. The tunable electronic bandgap of BLG adds additional tunability on the resonance of chi^(2), which corresponds to a tunable wavelength ranging from ~2.6 {mu}m to ~3.1 {mu}m for the up-converted photon. Combined with the high electron mobility and optical transparency of the atomically thin BLG, our scheme suggests a new regime of nonlinear photonics based on BLG.
