Tunable excitons in biased bilayer graphene

Ultrafast many-body bright-dark exciton transition in anatase TiO2

The momentum-forbidden dark excitons can have a pivotal role in quantum information processing, Bose-Einstein condensation, and light-energy harvesting. Anatase TiO2 with an indirect band gap is a prototypical platform to study bright to momentum-forbidden dark exciton transition. Here, we examine, by GW plus the real-time Bethe-Salpeter equation combined with the nonadiabatic molecular dynamics (GW + rtBSE-NAMD), the many-body transition that occurs within 100 fs from the optically excited bright to the strongly bound momentum-forbidden dark excitons in anatase TiO2. Comparing with the single-particle picture in which the exciton transition is considered to occur through electron-phonon scattering, within the GW + rtBSE-NAMD framework, the many-body electron-hole Coulomb interaction activates additional exciton relaxation channels to notably accelerate the exciton transition in competition with other radiative and nonradiative processes. The existence of dark excitons and ultrafast bright-dark exciton transitions sheds insights into applications of anatase TiO2 in optoelectronic devices and light-energy harvesting as well as the formation process of dark excitons in semiconductors.

Theory of Excitons in Gated Bilayer Graphene Quantum Dots

We present a theory of excitons in gated bilayer graphene (BLG) quantum dots (QDs). Electrical gating of BLG opens an energy gap, turning this material into an electrically tunable semiconductor. Unlike in laterally gated semiconductor QDs, where electrons are attracted and holes repelled, we show here that lateral structuring of metallic gates results in a gated lateral QD confining both electrons and holes. Using an accurate atomistic approach and exact diagonalization tools, we describe strongly interacting electrons and holes forming an electrically tunable exciton. We find these excitons to be different from those found in semiconductor QDs and nanocrystals, with exciton energy tunable by voltage from the terahertz to far infrared (FIR) range. The conservation of spin, valley, and orbital angular momentum results in an exciton fine structure with a band of dark low-energy states, making this system a promising candidate for storage, detection and emission of photons in the terahertz range.

Effects of Mono-Vacancies and Co-Vacancies of Nitrogen and Boron on the Energetics and Electronic Properties of Heterobilayer h-BN/graphene

A study is carried out which investigates the effects of the mono-vacancies of boron (VB) and nitrogen (VN) and the co-vacancies of nitrogen (N), and boron (B) on the energetics and the structural, electronic, and magnetic properties of an h-BN/graphene heterobilayer using first-principles calculations within the framework of the density functional theory (DFT). The heterobilayer is modelled using the periodic slab scheme. In the present case, a 4 × 4-(h-BN) monolayer is coupled to a 4 × 4-graphene monolayer, with a mismatch of 1.40%. In this coupling, the surface of interest is the 4 × 4-(h-BN) monolayer; the 4 × 4-graphene only represents the substrate that supports the 4 × 4-(h-BN) monolayer. From the calculations of the energy of formation of the 4 × 4-(h-BN)/4 × 4-graphene heterobilayer, with and without defects, it is established that, in both cases, the heterobilayers are energetically stable, from which it is inferred that these heterobilayers can be grown in the experiment. The formation of a mono-vacancy of boron (1 V_B), a mono-vacancy of nitrogen (1 V_N), and co-vacancies of boron and nitrogen (V_BN) induce, on the structural level: (a) for 1 V_B, a contraction n of the B-N bond lengths of ~2.46% and a slight change in the interfacial distance D (~0.096%) with respect to the heterobilayer free of defects (FD) are observed; (b) for 1 V_N, a slight contraction of the B-N of bond lengths of ~0.67% and an approach between the h-BN monolayer and the graphene of ~3.83% with respect to the FD heterobilayer are observed; (c) for V_BN, it can be seen that the N-N and B-B bond lengths (in the 1 V_B and 1 V_N regions, respectively) undergo an increase of ~2.00% and a decrease of ~3.83%, respectively. The calculations of the Löwdin charge for the FD heterobilayer and for those with defects (1 V_B, 1 V_N, and V_BN) show that the inclusion of this type of defect induces significant changes in the Löwdin charge redistribution of the neighboring atoms of VB and VN, causing chemically active regions that could favor the interaction of the heterobilayer with external atoms and/or molecules. On the basis of an analysis of the densities of states and the band structures, it is established that the heterobilayer with 1 V_B and V_BN take on a half-metallic and magnetic behavior. Due to all of these properties, the FD heterobilayer and those with 1 V_B, 1 V_N, and V_BN are candidates for possible adsorbent materials and possible materials that could be used for different spintronic applications.

Intervalley Excitonic Hybridization, Optical Selection Rules, and Imperfect Circular Dichroism in Monolayer h-BN

We perform first-principles GW plus Bethe-Salpeter equation calculations to investigate the photophysics of monolayer hexagonal boron nitride (h-BN), revealing excitons with novel k-space characteristics. The excitonic states forming the first and third peaks in its absorption spectrum are s-like, but those of the second peak are notably p-like, a first finding of strong co-occurrence of bright s-like and bright p-like states in an intrinsic 2D material. Moreover, even though the k-space wave function of these excitonic states are centered at the K and K^{'} valleys as in monolayer transition metal dichalcogenides, the k-space envelope functions of the basis excitons at one valley have significant extents to the basin of the other valley. As a consequence, the optical response of monolayer h-BN exhibits a lack of circular dichroism, as well as a coupling that induces an intervalley mixing between s- and p-like states.

Theory and Ab Initio Calculation of Optically Excited States-Recent Advances in 2D Materials

Recent studies of the optical properties of 2D materials have reported unique phenomena and features that are absent in conventional bulk semiconductors. Many of these interesting properties, such as enhanced light-matter coupling, gate-tunable photoluminescence, and unusual excitonic optical selection rules arise from the nature of the two- and multi-particle excited states such as strongly bound Wannier excitons and charged excitons. The theory, modeling, and ab initio calculations of these optically excited states in 2D materials are reviewed. Several analytical and ab initio approaches are introduced. These methods are compared with each other, revealing their relative strength and limitations. Recent works that apply these methods to a variety of 2D materials and material-defect systems are then highlighted. Understanding of the optically excited states in these systems is relevant not only for fundamental scientific research of electronic excitations and correlations, but also plays an important role in the future development of quantum information science and nano-photonics.

Floquet Topological Phase of Nondriven p-Wave Nonequilibrium Excitonic Insulators

The nontrivial topology of p-wave superfluids makes these systems attractive candidates in information technology. In this work we report on the topological state of a p-wave nonequilibrium excitonic insulator (NEQ-EI) and show how to steer a nontopological band insulator with bright p excitons toward this state by a suitable laser pulse, thus achieving a dynamical topological phase transition. The underlying mechanism behind the transition is the broken gauge-symmetry of the NEQ-EI which causes self-sustained persistent oscillations of the excitonic condensate and hence a Floquet topological state for high enough exciton densities. We show the formation of Floquet Majorana modes at the boundaries of the open system and discuss unique topological spectral signatures for time-resolved ARPES experiments. We emphasize that the topological properties of a p-wave NEQ-EI arise exclusively from the electron-hole Coulomb interaction as the system is not driven by external fields.

Sizable Band Gap in Epitaxial Bilayer Graphene Induced by Silicene Intercalation

Opening a band gap in bilayer graphene (BLG) is of significance for potential applications in graphene-based electronic and photonic devices. Here, we report the generation of a sizable band gap in BLG by intercalating silicene between BLG and Ru substrate. We first grow high-quality Bernal-stacked BLG on Ru(0001) and then intercalate silicene to the interface between the BLG and Ru, which is confirmed by low-energy electron diffraction and scanning tunneling microscopy. Raman spectroscopy shows that the G and 2D peaks of the intercalated BLG are restored to the freestanding-BLG features. Angle-resolved photoelectron spectroscopy measurements show that a band gap of about 0.2 eV opens in the BLG. Density functional theory calculations indicate that the large-gap opening results from a cooperative contribution of the doping and rippling/strain in the BLG. This work provides insightful understanding on the mechanism of band gap opening in BLG and enhances the potential of graphene-based device development.

Unifying Optical Selection Rules for Excitons in Two Dimensions: Band Topology and Winding Numbers

We show that band topology can dramatically change the photophysics of two-dimensional semiconductors. For systems in which states near the band extrema are of multicomponent character, the spinors describing these components (pseudospins) can pick up nonzero winding numbers around the extremal k point. In these systems, we find that the strength and required light polarization of an excitonic optical transition are dictated by the optical matrix element winding number, a unique and heretofore unrecognized topological characteristic. We illustrate these findings in three gapped graphene systems-monolayer graphene with inequivalent sublattices and biased bi- and trilayer graphene, where the pseudospin textures manifest into nontrivial optical matrix element winding numbers associated with different valley and photon circular polarization. This winding-number physics leads to novel exciton series and optical selection rules, with each valley hosting multiple bright excitons coupled to light of different circular polarization. This valley-exciton selective circular dichroism can be unambiguously detected using optical spectroscopy.

Tunable excitons in bilayer graphene

Excitons, the bound states of an electron and a hole in a solid material, play a key role in the optical properties of insulators and semiconductors. Here, we report the observation of excitons in bilayer graphene (BLG) using photocurrent spectroscopy of high-quality BLG encapsulated in hexagonal boron nitride. We observed two prominent excitonic resonances with narrow line widths that are tunable from the mid-infrared to the terahertz range. These excitons obey optical selection rules distinct from those in conventional semiconductors and feature an electron pseudospin winding number of 2. An external magnetic field induces a large splitting of the valley excitons, corresponding to a g-factor of about 20. These findings open up opportunities to explore exciton physics with pseudospin texture in electrically tunable graphene systems​.

Two-photon absorption in gapped bilayer graphene with a tunable chemical potential

Despite the now vast body of two-dimensional materials under study, bilayer graphene remains unique in two ways: it hosts a simultaneously tunable band gap and electron density; and stems from simple fabrication methods. These two advantages underscore why bilayer graphene is critical as a material for optoelectronic applications. In the work that follows, we calculate the one- and two-photon absorption coefficients for degenerate interband absorption in a graphene bilayer hosting an asymmetry gap and adjustable chemical potential-all at finite temperature. Our analysis is comprehensive, characterizing one- and two-photon absorptive behavior over wide ranges of photon energy, gap, chemical potential, and thermal broadening. The two-photon absorption coefficient for bilayer graphene displays a rich structure as a function of photon energy and band gap due to the existence of multiple absorption pathways and the nontrivial dispersion of the low energy bands. This systematic work will prove integral to the design of bilayer-graphene-based nonlinear optical devices.

Two-Dimensional Heterojunctions from Nonlocal Manipulations of the Interactions

We propose to create lateral heterojunctions in two-dimensional materials based on nonlocal manipulations of the Coulomb interaction using structured dielectric environments. By means of ab initio calculations for MoS2 as well as generic semiconductor models, we show that the Coulomb interaction-induced self-energy corrections in real space are sufficiently nonlocal to be manipulated externally, but still local enough to induce spatially sharp interfaces within a single homogeneous monolayer to form heterojunctions. We find a type-II heterojunction band scheme promoted by a laterally structured dielectric environment, which exhibits a sharp band gap crossover within less than 5 unit cells.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

Trapping photon-dressed Dirac electrons in a quantum dot studied by coherent two dimensional photon echo spectroscopy

We study the localization of dressed Dirac electrons in a cylindrical quantum dot (QD) formed on monolayer and bilayer graphene by spatially different potential profiles. Short lived excitonic states which are too broad to be resolved in linear spectroscopy are revealed by cross peaks in the photon-echo nonlinear technique. Signatures of the dynamic gap in the two-dimensional spectra are discussed. The effect of the Coulomb induced exciton-exciton scattering and the formation of biexciton molecules are demonstrated.

Synthesis of reduced graphene oxide-anatase TiO2 nanocomposite and its improved photo-induced charge transfer properties

The construction of reduced graphene oxide or graphene oxide with semiconductor has gained more and more attention due to its unexpected optoelectronic and electronic properties. The synthesis of reduced graphene oxide (RGO) or graphene oxide-semiconductor nanocomposite with well-dispersed decorated particles is still a challenge now. Herein, we demonstrate a facile method for the synthesis of graphene oxide-amorphous TiO(2) and reduced graphene oxide-anatase TiO(2) nanocomposites with well-dispersed particles. The as-synthesized samples were characterized by transmission electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, UV-Vis absorption spectroscopy, Fourier transform infrared spectrometry, and thermogravimetric analysis. The photovoltaic properties of RGO-anatase TiO(2) were also compared with that of similar sized anatase TiO(2) by transient photovoltage technique, and it was interesting to find that the combination of reduced graphene oxide with anatase TiO(2) will significantly increase the photovoltaic response and retard the recombination of electron-hole pairs in the excited anatase TiO(2).

Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons

Significant excitonic effects were observed in graphene by measuring its optical conductivity in a broad spectral range including the two-dimensional π-band saddle-point singularities in the electronic structure. The strong electron-hole interactions manifest themselves in an asymmetric resonance peaked at 4.62 eV, which is redshifted by nearly 600 meV from the value predicted by ab initio GW calculations for the band-to-band transitions. The observed excitonic resonance is explained within a phenomenological model as a Fano interference of a strongly coupled excitonic state and a band continuum. Our experiment also showed a weak dependence of the excitonic resonance in few-layer graphene on layer thickness. This result reflects the effective cancellation of the increasingly screened repulsive electron-electron (e-e) and attractive electron-hole (e-h) interactions.

Magnetoconductance oscillations and evidence for fractional quantum Hall states in suspended bilayer and trilayer graphene

We report pronounced magnetoconductance oscillations observed on suspended bilayer and trilayer graphene devices with mobilities up to 270,000 cm²/V s. For bilayer devices, we observe conductance minima at all integer filling factors ν between 0 and -8, as well as a small plateau at ν=1/3. For trilayer devices, we observe features at ν=-1, -2, -3, and -4, and at ν∼0.5 that persist to 4.5 K at B=8 T. All of these features persist for all accessible values of Vg and B, and could suggest the onset of symmetry breaking of the first few Landau levels and fractional quantum Hall states.

Wafer scale homogeneous bilayer graphene films by chemical vapor deposition

The discovery of electric field induced band gap opening in bilayer graphene opens a new door for making semiconducting graphene without aggressive size scaling or using expensive substrates. However, bilayer graphene samples have been limited to μm(2) size scale thus far, and synthesis of wafer scale bilayer graphene poses a tremendous challenge. Here we report homogeneous bilayer graphene films over at least a 2 in. × 2 in. area, synthesized by chemical vapor deposition on copper foil and subsequently transferred to arbitrary substrates. The bilayer nature of graphene film is verified by Raman spectroscopy, atomic force microscopy, and transmission electron microscopy. Importantly, spatially resolved Raman spectroscopy confirms a bilayer coverage of over 99%. The homogeneity of the film is further supported by electrical transport measurements on dual-gate bilayer graphene transistors, in which a band gap opening is observed in 98% of the devices.

Quantum transport and field-induced insulating states in bilayer graphene pnp junctions

We perform transport measurements in high quality bilayer graphene pnp junctions with suspended top gates. At a magnetic field B = 0, we demonstrate band gap opening by an applied perpendicular electric field with an On/Off ratio up to 20,000 at 260 mK. Within the band gap, the conductance decreases exponentially by 3 orders of magnitude with increasing electric field and can be accounted for by variable range hopping with a gate-tunable density of states, effective mass, and localization length. At large B, we observe quantum Hall conductance with fractional values, which arise from equilibration of edge states between differentially doped regions, and the presence of an insulating state at filling factor v = 0. Our work underscores the importance of bilayer graphene for both fundamental interest and technological applications.