Spatially indirect excitons with displaced wavefunctions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe2, by performing electric field-tunable photoluminescence measurements. Because of different out-of-plane electric dipole moments, the energy order between the three types of spatially indirect excitons can be switched by a vertical electric field. Remarkably, we demonstrate, assisted by first-principles calculations, that the observed spatially indirect excitons in bilayer WSe2 are also momentum-indirect, involving electrons and holes from Q and K/Γ valleys in the Brillouin zone, respectively. This is in contrast to the previously reported spatially indirect excitons with electrons and holes localized in the same valley. Furthermore, we find that the spatially indirect intervalley excitons in bilayer WSe2 can exhibit considerable, doping-sensitive circular polarization. The spatially indirect excitons with momentum-dark nature and highly tunable circular polarization open new avenues for exotic valley physics and technological innovations in photonics and optoelectronics.
The electronic properties of twisted bilayer graphene on SiC substrate were studied via combination of transport measurements and scanning tunneling microscopy. We report the observation of enhanced intervalley scattering from one Dirac cone to the other, which contributes to weak localization, of the twisted bilayer graphene by increasing the interlayer coupling strength. Our experiment and analysis demonstrate that the enhanced intervalley scattering is closely related to the periodic AB stacked atoms (the A atom of layer 1 and the B atom of layer 2 that have the same horizontal positions) t…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
We investigated the valley depolarization and carrier relaxation process of monolayer and bilayer WS2 at 10 K by using time-resolved Kerr rotation (TRKR) and differential reflectance measurement simultaneously. Two decay processes extracted from TRKR signals were observed on both monolayer and bilayer WS2. In monolayer WS2, the initial ultrafast decay component (less than 1 ps) was interpreted as the stimulated emission or Pauli-blocking of electrons and holes in one valley by comparing with carrier decay process. The relatively slow component was around 4 ps under low excitation energy (less …
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Λ$ point leads to a drastic reds…
Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of 2π. This nontrival topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties, such as anti-Klein tunneling, unconventional quantum Hall effect, and valley Hall effect1-6. Here we show that the quantum interference due to intervalley scattering induced by atomic defects/impurities provides further insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct v…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
We investigate the hole spin relaxation due to the Rashba spin-orbit coupling induced by an external perpendicular electric field in bilayer WSe$_2$. The Rashba spin-orbit coupling coefficients in bilayer WSe$_2$ are constructed from the corresponding monolayer ones. In contrast to monolayer WSe$_2$, the out-of-plane component of the bilayer Rashba spin-orbit coupling acts as a Zeeman-like field with opposite directions but identical values in the two valleys. For in-plane spins, this Zeeman-like field, together with the intervalley hole-phonon scattering, opens an intervalley spin relaxation …
Correlated insulators are frequently observed in magic angle twisted bilayer graphene at even fillings of electrons or holes per moiré unit-cell. Whereas theory predicts these insulators to be intervalley coherent excitonic phases, the measured gaps are routinely much smaller than theoretical estimates. We explore the effects of random strain variations on the intervalley coherent phase, which have a pair-breaking effect analogous to magnetic disorder in superconductors. We find that the spectral gap may be strongly suppressed by strain disorder, or vanish altogether, even as intervalley coher…
The variety of excitonic states in tungsten-based dichalcogenide monolayers stems from unique interplay between the spin and valley degrees of freedom. One of the exciton species is the indirect exciton (momentum or valley dark), which is responsible to a series of resonances when the monolayer is charge neutral. We investigate the short-range electron-hole exchange interaction of the indirect exciton, as well as its recombination mechanism mediated by impurities. The analysis provides thorough understanding of the energy and polarization of the zero-phonon indirect exciton resonance in the em…
We study the exciton condensate (EC) in a bilayer two-dimension-electron-gas (2DEG) adjacent to a type-II superconductor thin film with an array of pinned vortex lattices. By applying continuum low energy theory and carrying numerical simulations of lattice model within mean-field approximation, we find that if the order parameter of EC has a vortex profile, there are exact zero modes and associated \emph{rational} fractional charge for zero pseudospin potential ($μ$) and average chemical potential ($h$): $μ$=0 and $h$=0; while for $μ\mathtt{\neq}0$ and $h$=0, intervalley mixing splits the zer…
We investigate the steady-state out-of-plane spin diffusion in p-type bilayer WSe2 in the presence of the Rashba spin-orbit coupling and Hartree-Fock effective magnetic field. The out-of-plane components of the Rashba spin-orbit coupling serve as the opposite Zeeman-like fields in the two valleys. Together with the identical Hartree-Fock effective magnetic fields, different total effective magnetic field strengths in the two valleys are obtained. It is further revealed that due to the valley-dependent total effective magnetic field strength, similar (different) spin-diffusion lengths in the tw…
Electron spin relaxation due to the D'yakonov-Perel' mechanism is investigated in bilayer graphene with only the lowest conduction band being relevant. The spin-orbit coupling is constructed from the symmetry group analysis with the parameters obtained by fitting to the numerical calculation according to the latest report by Konschuh {\it et al.} [Phys. Rev. B {\bf 85}, 115423 (2012)] from first principles. In contrast to single-layer graphene, the leading term of the out-of-plane component of the spin-orbit coupling in bilayer graphene shows a Zeeman-like term with opposite effective magnetic…
Due to low dimensionality, the controlled stacking of the graphene films and their electronic properties are susceptible to environmental changes including strain. The strain-induced modification of the electronic properties such as the emergence and modulation of bandgaps crucially depends on the stacking of the graphene films. However, to date, only the impact of strain on electronic properties of Bernal and AA-stacked bilayer graphene has been extensively investigated in theoretical studies. Exploiting density functional theory and tight-binding calculation, we investigate the impacts of in…
We explore attractive dipolar interaction in indirect excitons (IXs). For one layer of IXs in a single pair of coupled quantum wells (CQW), the out-of-plane IX electric dipoles lead to repulsive dipolar interaction between IXs. The attractive dipolar interaction between IXs is realized in a 2-CQW heterostructure with two IX layers in two separated CQW pairs. We found both in experimental measurements and theoretical simulations that increasing density of IXs in one layer causes a monotonic energy reduction for IXs in the other layer. We also found an in-plane shift of a cloud of IXs in one lay…
We study direct and indirect magnetoexcitons in Rydberg states in monolayers and heterostructures of transition-metal dichalcogenices (TMDCs) in an external magnetic field, applied perpendicular to the monolayer or heterostructures. We calculate binding energies of magnetoexcitons for the Rydberg states 1$s$, 2$s$, 3$s$, and 4$s$ by numerical integration of the Schrödinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect magnetoexcitons. Latter allows understanding the role of screening in TMDCs heterostructu…
We report on spin transport features which are unique to high quality bilayer graphene, in absence of magnetic contaminants and strong intervalley mixing. The time-dependent spin polarization of propagating wavepacket is computed using an efficient quantum transport method. In the limit of vanishing effects of substrate and disorder, the energy-dependence of spin lifetime is similar to monolayer graphene with a M-shape profile and minimum value at the charge neutrality point, but with an electron-hole asymmetry fingerprint. In sharp contrast, the incorporation of substrate-induced electron-hol…
The presence of non-degenerate valley states in silicon can drastically affect electron dynamics in silicon-based heterostructures, leading to electron spin relaxation and spin-valley coupling. In the context of solid-state spin qubits, it is important to understand the interplay between spin and valley degrees of freedom to avoid or alleviate these decoherence mechanisms. Here we report the observation of relaxation from the excited valley state to the ground state in a Si/SiGe quantum dot, at zero magnetic field. Valley state read-out is aided by a valley-dependent tunneling effect, which we…
Ensembles of indirect or interlayer excitons (IXs) are intriguing systems to explore classical and quantum phases of interacting bosonic ensembles. IXs are composite bosons that feature enlarged lifetimes due to the reduced overlap of the electron-hole wave functions. We demonstrate electric Field control of indirect excitons in MoS2/WS2 hetero-bilayers embedded in a field effect structure with few-layer hexagonal boron nitrite as insulator and few-layer graphene as gate-electrodes. The different strength of the excitonic dipoles and a distinct temperature dependence identify the indirect exci…
We study the electron-phonon coupling in twisted bilayer graphene (TBG), which was recently experimentally observed to exhibit superconductivity around the magic twist angle $θ\approx 1.05^\circ$. We show that phonon-mediated electron electron attraction at the magic angle is strong enough to induce a conventional intervalley pairing between graphene valleys $K$ and $K'$ with a superconducting critical temperature $T_c\sim1K$, in agreement with the experiment. We predict that superconductivity can also be observed in TBG at many other angles $θ$ and higher electron densities in higher Moiré ba…
We present a theory of bilayer two-dimensional electron systems that host a spatially indirect exciton condensate when in thermal equilibrium. Equilibrium bilayer exciton condensates (BXCs) are expected to form when two nearby semiconductor layers are electrically isolated, and when the conduction band of one layer is brought close to degeneracy with the valence band of a nearby layer by varying bias or gate voltages. BXCs are characterized by spontaneous inter-layer phase coherence and counterflow superfluidity. The bilayer system we consider is composed of two transition metal dichalcogenide…
We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that this interaction-driven "leaky" emission dominates photoluminescence at low temperatures, with distinctive …
A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.
We report an experimental study of temperature-dependent spectral lineshapes of phonon side-band emission stemming from dark excitons in monolayer and bilayer WSe$_{2}$. Using photoluminescence spectroscopy in the range from 4 to 100K, we observe a pronounced asymmetry in the phonon-assisted luminescence from momentum-indirect exciton reservoirs. We demonstrate that the corresponding spectral profiles are distinct from those of bright excitons with direct radiative decay pathways. The lineshape asymmetry reflects thermal distribution of exciton states with finite center-of-mass momenta, charac…
Monolayer (ML) transition metal dichalcogenides (TMDs) undergo substantial changes in the single-particle band structure and excitonic optical response upon the addition of just one layer. As opposed to the single-layer limit, the bandgap of bilayer (BL) TMD semiconductors is indirect which results in reduced photoluminescence with richly structured spectra that have eluded a detailed understanding to date. Here, we provide a closed interpretation of the elementary optical responses of BL WSe$_2$ as a representative material for the wider class of TMD semiconductors. By combining theoretical c…
A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{ν}=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG…
It is shown that exciton swapping between two graphene sheets may occur under specific conditions. A magnetically tunable optical filter is described to demonstrate this new effect. Mathematically, it is shown that two turbostratic graphene layers can be described as a "noncommutative" two-sheeted (2+1)-spacetime thanks to a formalism previously introduced for the study of braneworlds in high energy physics. The Hamiltonian of the model contains a coupling term connecting the two layers which is similar to the coupling existing between two braneworlds at a quantum level. In the present case, t…
We investigate the possibility of band structure engineering in the recently predicted 2D layered form of blue phosphorus via an electric field (E$_z$) applied perpendicular to the layer(s). Using density functional theory, we study the effect of a transverse electric field in monolayer, as well as three differently stacked bilayer structures of blue phosphorus. We find that, for E$_z > 0.2$ V/Å the direct energy gap at the $Γ$ point, which is much larger than the default indirect band gap of mono- and bilayer blue phosphorus, decreases linearly with the increasing electric field; becomes comp…
Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we provide a general theory for the electric dipole superconductivity, and derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equatio…
The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the …
The ground state of two-dimensional (2D) electron systems with equal low densities of electrons and holes in nearby layers is an exciton fluid. We show that a reservoir for excitons can be established by contacting the two layers separately and maintaining the chemical potential difference at a value less than the spatially indirect band gap. Equilibration between the exciton fluid and the contacts proceeds via a process involving virtual intermediate states in which an unpaired electron or hole occupies a free carrier state in one of the 2D layers. We derive an approximate relationship betwee…
Monolayer transition metal dichalcogenides are a promising platform to investigate many-body interactions of excitonic complexes. In monolayer tungsten diselenide, the ground-state exciton is dark (spin-indirect), and the valley degeneracy allows low-energy dark momentum-indirect excitons to form. Interactions between the dark exciton species and the optically accessible bright exciton (X) are likely to play significant roles in determining the optical properties of X at high power, as well as limiting the ultimate exciton densities that can be achieved, yet so far little is known about these …
We derive an effective Bose-Hubbard model that predicts a phase transition from Bose-Einstein condensate to Mott insulator in two different systems subject to applied periodic potentials: microcavity exciton-polaritons and indirect excitons. Starting from a microscopic Hamiltonian of electrons and holes, we derive an effective Bose-Hubbard model for both systems and evaluate the on-site Coulomb interaction U and hopping transition amplitudes t. Experimental parameters required for observing a phase transition between a Bose-Einstein condensate and a Mott insulator are discussed. Our results su…
Spatially indirect excitons can be created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite Boson. Because there is no recombination pathway such excitons are long lived making them accessible to transport studies. Moreover, the ability to independently tune both the intralayer charge density and interlayer electron-hole separation provides the capability to reach the low-density, strongly interacting regime where a BEC-like phase transition into a superfluid ground state is anticipated. To date, transport signatures of the supe…
The layer interdependence of transport in an undoped electron-hole bilayer (uEHBL) device was studied as a function of carrier density, interlayer electric field, and temperature. The uEHBL device consisted of a density tunable, independently contacted two-dimensional electron gas (2DEG) and two-dimensional hole gas (2DHG) induced via field effect in distinct GaAs quantum wells separated by a 30 nm Al$_{0.9}$Ga$_{0.1}$As barrier. Transport measurements were made simultaneously on each layer using the van der Pauw method. An increase in 2DHG mobility with increasing 2DEG density was observed, w…
We study superfluid behavior of a gas of spatially indirect magnetoexcitons with reference to a system of two graphene layers embedded in a multilayer dielectric structure. The system is considered as an alternative of a double quantum well in a GaAs haterostructure. We determine a range of parameters (interlayer distance, dielectric constant, magnetic field and gate voltage) where magnetoexciton superfluidity can be achieved. Temperature of superfluid transition is computed. A reduction of critical parameters caused by impurities is evaluated and critical impurity concentration is determined.
Recent advances in the field of vertically stacked 2D materials have revealed a rich exciton landscape. In particular, it has been demonstrated that out-of-plane electrical fields can be used to tune the spectral position of spatially separated interlayer excitons. Other studies have shown that there is a strong hybridization of exciton states, resulting from the mixing of electronic states in both layers. However, the connection between the twist-angle dependent hybridization and field-induced energy shifts has remained in the dark. Here, we investigate on a microscopic footing the interplay …
We investigate the optical excitation spectra and the photoluminescence depolarization dynamics in bilayer WS$_2$. A different understanding of the optical excitation spectra in the recent photoluminescence experimentby Zhu {\em et al.} [arXiv:1403.6224] in bilayer WS$_2$ is proposed. In the experiment, four excitations (1.68, 1.93, 1.99 and 2.37 eV) are observed and identified to be indirect exciton for the $Γ$ valley, trion, A exciton and B exciton excitations, respectively, with the redshift for the A exciton energy measured to be 30$\sim$50 meV when the sample synthesized from monolayer to…
Using an external electric field, one can modulate the bandgap of Bernal stacked bilayer graphene by breaking A-~B symmetry. We analyze strain effects on the bilayer graphene using the extended Huckel theory and find that reduced interlayer distance results in higher bandgap modulation, as expected. Furthermore, above about 2.5 angstrom interlayer distance, the bandgap is direct, follows a convex relation to electric field and saturates to a value determined by the interlayer distance. However, below about 2.5 angstrom, the bandgap is indirect, the trend becomes concave and a threshold electri…
The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-va…
We probe the room temperature photoluminescence of $N$-layer molybdenum ditelluride (MoTe$_2$) in the continuous wave (cw) regime. The photoluminescence quantum yield of monolayer MoTe$_2$ is three times larger than in bilayer MoTe$_2$ and forty times greater than in the bulk limit. Mono- and bilayer MoTe$_2$ display almost symmetric emission lines at $1.10~\rm eV$ and $1.07~\rm eV$, respectively, which predominantly arise from direct radiative recombination of the A exciton. In contrast, $N\geq3-$layer MoTe$_2$ exhibits a much reduced photoluminescence quantum yield and a broader, redshifted …
Van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar manyparticle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstra…
Twist angle modifies the band alignment, screening, and interlayer (IL) coupling in twisted bilayers (tBLs) of transition metal dichalcogenides. Intermediate misorientation (twist angles > 15 degrees) bilayers (BLs) offer a unique opportunity to tune excitonic behavior within these concurrent physical mechanisms but are seldom studied. In this paper, we measure many-body excitonic complexes in monolayer (ML), natural BL, and tBL WSe2. Neutral biexciton (XX) is observed in tBL, while being undetected in nonencapsulated ML and BL, demonstrating unique effects of disorder screening in tBLs. The X…
Mo$X_2$ ($X$=S or Se) is a semiconductor family with two-dimensional structure. And a recent calculation predicted the superconductivity in electron doped MoS$_2$ monolayer. In this work, the electronic structure and lattice dynamics of Mo$X_2$ bilayers with monolayer Na intercalated, have been calculated. According to the electron-phonon interaction, it is predicted that these bilayers can be transformed from indirect-gap semiconductors to a superconductors by Na intercalation. More interestingly, the biaxial tensile strain can significantly enhance the superconducting temperature up to $\sim…
With exceptional electrical and mechanical properties and at the same time air-stability, layered MoSi2N4 has recently draw great attention. However, band structure engineering via strain and electric field, which is vital for practical applications, has not yet been explored. In this work, we show that the biaxial strain and external electric field are effective ways for the band gap engineering of bilayer MoSi$_2$N$_4$ and WSi$_2$N$_4$. It is found that strain can lead to indirect band gap to direct band gap transition. On the other hand, electric field can result in semiconductor to metal t…
Moire-Engineered Excitonic Landscape and Phonon-Mediated Recombination in Twisted WSe2 Bilayers
Indian Institute of Technology Mandi（印度技术学院曼迪分校）；CSIR-National Physical Laboratory（印度科学工业研究理事会国家物理实验室）；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）；Indian Institute of Science（印度科学学院）；National Institute of Material Science（国家物质科学研究所）
Twisted layers of atomically thin two-dimensional materials realize a broad range of novel quantum materials with engineered optical and transport phenomena arising from spin and valley degrees of freedom and strong electron correlations in hybridized interlayer bands. Here, we report experimental and theoretical studies of WSe$_2$ homobilayers obtained in two stable configurations of 2H ($60^\circ$ twist) and 3R ($0^\circ$ twist) stackings by controlled chemical vapor synthesis of high-quality large-area crystals. Using optical absorption and photoluminescence spectroscopy at cryogenic temper…
University of Maryland, College Park（马里兰大学帕克分校）；Universität Heidelberg（海德堡大学）；Laboratory for Physical Sciences（物理科学实验室）；Brookhaven National Laboratory（布鲁海文国家实验室）；National Institute for Materials Science（物质材料研究机构）
