Session S17: 2D Semiconductor Physics II

Novel exciton systems in 2D TMD monolayers and heterobilayers

In this talk, two exciton systems in transition metal dichalcogenides (TMDs) monolayer and heterobilayer will be discussed. In TMD monolayers, the strong e-h Coulomb exchange interaction splits the exciton and trion dispersions into two branches with zero and finite gap, respectively \footnote{H. Yu, G.-B. Liu, P. Gong, X. Xu, and W. Yao, Nat. Commun. \textbf{5}, 3876 (2014).} \footnote{H. Yu, X. Cui, X. Xu, and W. Yao, Natl Sci Rev \textbf{2}, 57 (2015).}. Each branch is a center-of-mass wave vector dependent coherent superposition of the two valleys, which leads to a valley-orbit coupling and possibly a trion valley Hall effect. The exchange interaction also eliminates the linear polarization of the negative trion PL emission \footnote{A. Jones, H. Yu, N. Ghimire, S. Wu, G. Aivazian, J. Ross, B. Zhao, J. Yan, D. Mandrus, D. Xiao, W. Yao, and X. Xu, Nature Nanotech. \textbf{8}, 634 (2013).}. In TMD heterobilayers with a type-II band alignment, the low energy exciton has an interlayer configuration with the e and h localized in opposite layers. Because of the inevitable twist or/and lattice mismatch between the two layers, the bright interlayer excitons are located at finite center-of-mass velocities with a six-fold degeneracy \footnote{H. Yu, Y. Wang, Q. Tong, X. Xu, and W. Yao, Phys. Rev. Lett. \textbf{115}, 187002 (2015).}. The corresponding photon emission is elliptically polarized, with the major axis locked to the direction of exciton velocity, and helicity determined by the valley indices of the e and h. Some experimental results on the interlayer excitons in the WSe$_2$-MoSe$_2$ heterobilayers will also be presented. The interlayer exciton exhibits a long lifetime as well as a long depolarization time, which facilitate the observation of a PL polarization ring pattern due to the valley dependent exciton-exciton interaction induced expansion \footnote{P. Rivera, K. L. Seyler, H. Yu, J. R. Schaibley, J. Yan, D. G. Mandrus, W. Yao, and X. Xu, to be published.}.   

Engineering topological band with superlattice.

Since the discovery of the quantum Hall effect, the search for topological states has been a major subject of interest in condensed matter physics.~Here we propose a general scheme to create nontrivial Chern band by fabricating superlattice structure on a system with non-zero Berry curvature.~We analyze the topological band structure by deriving an effective Hamiltonian that incorporates the Berry curvature effect.~The Chern number is tunable by the superlattice configurations that are realizable with existing experimental technology.   

Optical properties of quantum dots in buckled graphene-like materials

The band gap of buckled graphene-like materials, such as silicene and germanene, depends on external perpendicular electric field. A specially design profile of electric field produces a quantum dot, i.e., trapping potential for electrons in such materials. We theoretically study the optical properties of such silicene/germanene quantum dots. There are two types of absorption spectra in the quantum dot: interband (optical transitions between the states of the valence and conduction bands) and intraband (transitions between the states of conduction/valence band). The interband absorption spectra have triple-peak structure with peak separation around 10 meV, while intraband absorption spectra, which depend on the number of electrons in the dot, have double-peak structure with separation between the peaks around 15meV. The interband optical spectra as a whole are red-shifted with increasing electric field in the internal region of the quantum dot, while the energy separation between the peaks depends weakly on the electric field. With increasing the size of the quantum dot, the interband and intraband absorption spectra become red shifted as well.   

Charge density wave transition in single-layer titanium diselenide

A single molecular layer of titanium diselenide (TiSe$_{\mathrm{2}})$ is a promising material for advanced electronics beyond graphene-a strong focus of current exploration. Such molecular layers are at the quantum limit of device miniaturization and can show enhanced electronic effects not realizable in thick films. We show that single-layer TiSe$_{\mathrm{2}}$ exhibits a charge density wave (CDW) transition at critical temperature T$_{\mathrm{C}}=$232 K, which is higher than the bulk T$_{\mathrm{C}}=$200 K. Angle-resolved photoemission spectroscopy measurements reveal a small absolute bandgap at room temperature, which grows wider with decreasing temperature T below T$_{\mathrm{C}}$ in conjunction with the emergence of (2x2) ordering. The results are rationalized in terms of first-principles calculations, symmetry breaking and phonon entropy effects. The observed BCS behaviour of the gap implies a mean-field CDW order in the single layer and an anisotropic CDW order in the bulk.   

Spatially Indirect Exciton Condensates in Double Bilayer Graphene

Many-body interaction effects have a strong influence on the low-energy electronic properties of graphene bilayers because of the nearly quadratic dispersion at the K/K’ band-crossing points. In the single graphene bilayer systems, the ground state has an energy gap thought to be a consequence of spin-density wave order and other competing ordered states are believed to be nearby in energy. In systems with two closely spacing bilayer, spatially indirect exciton states are expected in neutral systems with inter-bilayer charge transfer. This transfer can be achieved by applying either a vertical electrical displacement fields or an interbilayer potential bias. Here we report that the different combinations of displacement field and potential bias can give rise to different types of indirect exciton condensate states that are distinguished by the two-dimensional momentum dependence of the spontaneous inter-bilayer coherence. In general a displacement field prefers an excitonic condensate in which the phase coherence between the inner two layers of the four layer system, while the potential bias prefers momentum-independent coherence between remote layers. The complete phase diagram reported exhibits excitonic coherence states mentioned above, and more interestingly, their mixtures.   

Exciton-polariton condensation in transition metal dichalcogenide bilayer heterostructure

For the bilayer heterostructure system in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon coupling can lead to the emergence of quasiparticles consisting of the spatially indirect exciton and cavity photons known as \emph{dipolariton}, which can form the Bose-Einstein condensate above a threshold density. Additional physics comes into play when each layer of the bilayer system consists of the transition metal dichalcogenide (TMD) monolayer. The TMD monolayer band structure in the low energy spectrum has two valley components with nontrivial Berry phase, which gives rise to a selection rule in the exciton-polariton coupling, e.g. the exciton from one (the other) valley can couple only to the clockwise (counter-clockwise) polarized photon. We investigate possible condensate phases of exciton-polariton in the bilayer TMD microcavity changing relevant parameters such as detuning, excitation density and interlayer distance.   

Berry Phase Modification to the Energy Spectrum of Excitons

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other “relativistic” terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and it highlights the importance of the Berry curvature in the effective mass approximation.   

Optical and Electronic Properties of doped-MoS2: Joint Theoretical/Experimental Study

Substitutional doping of transition metal dichalcogenides (TMDs) is an attractive way of engineering their electronic properties. The dependence of optoelectronic properties of TMDs on the dopant is largely under-explored. In this work, we will discuss how different species affect the optical properties of MoS2. The electronic structure calculations of doped TMDs are carried out using Density Functional Theory with the recently developed ACBN0 functional, a pseudo-hybrid Hubbard density functional that is a fast, accurate and parameter-free alternative to traditional DFT+U and hybrid exact exchange methods [L.A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli, Phys. Rev. X 5, 011006 (2015)]. We compare our ACBN0 predictions with measurement of the electronic and optical properties of pristine and niobium doped MoS2 films synthesized via physical vapor deposition and characterized using spectroscopic ellipsometry and optical spectroscopy.   

Storing excitons in transition-metal dichalcogenides using dark states

Monolayer transition-metal dichalcogenides exhibit strongly bound excitons confined to two dimensions. One challenge in exploiting these excitons is that they have a finite life time and collapse through electron-hole recombination. We propose that the exciton life time could be extended by transitioning the exciton population into dark states. The symmetry of these dark states require the electron and hole to be spatially separated, which not only causes these states to be optically inactive but also inhibits electron-hole recombination. Based on an atomistic model we call the Triangular Lattice Exciton (3ALE) model, we derive transition matrix elements and approximate selection rules showing that excitons could be transitioned into and out of dark states using a pulsed infrared laser. For illustration, we also present exciton population scenarios based on different recombination decay constants. Longer exciton lifetimes could make these materials candidates for applications in energy management and quantum information processing.   

Excitonic effects in 2D semiconductors: Path Integral Monte Carlo approach

One of the most striking features of novel 2D semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multi-carrier bound states (e.g., excitons, trions and biexcitons), which could remain stable at near-room temperatures and contribute significantly to optical properties of such materials. In my talk, I will report on our recent progress in using the Path Integral Monte Carlo methodology to numerically study properties of multi-carrier bound states in 2D semiconductors. Incorporating the effect of the dielectric confinement (via Keldysh potential), we have investigated and tabulated the dependence of single exciton, trion and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. The implications of the obtained results and the possible limitations of the used model will be discussed. The results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.   

Theoretical ultra-fast spectroscopy in transition metal dichalcogenides

Semiconducting 2D-materials like the transition metal dichalcogenides (TMDs) MoS$_2$, MoSe$_2$, WS$_2$, WSe$_2$ are promising alternatives to graphene for designing novel opto-electronic devices. The strong spin-orbit interaction along with the breaking of inversion symmetry in single-layer TMDs allow using the valley-index as a new quantum number [1]. The practical use of valley physics depends on the lifetimes of valley-polarized excitons which are affected by scattering at phonons, impurities and by carrier-carrier interactions. The carrier dynamics can be monitored using ultra-fast spectroscopies such as pump-probe experiments. The carrier dynamics is simulated using non-equilibrium Green’s function theory in an ab-initio framework. We include carrier relaxation through electron-phonon interaction. We obtain the transient absorption spectra of single-layer TMD and compare our simulations with recent pump-probe experiments [2]. [1] D. Xiao et. al., Phys. Rev. Lett. \textbf{108}, 196802 (2012). X. Xu et. al. , Nature Physics \textbf{10}, 343 (2014). [2] Y. T. Wang, et. al. , Scientific Reports \textbf{5}, 8289 (2015).   

Interaction Induced Quantum Valley Hall Effect in Graphene

We use Pseudo Quantum Electrodynamics (PQED) in order to describe the full electromagnetic interaction of the electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator to evaluate the Kubo's formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction. We then predict the onset of an interaction-driven spontaneous Quantum Valley Hall effect by solving the Schwinger-Dyson equation. The obtained Valley-Hall conductivity is exact and universal [1]. [1] E. C. Marino, Leandro O. Nascimento, V. S. Alves, and C. Morais Smith, Phys. Rev. X {\bf 5}, 011040 (2015).   

Lateral Heterostructures of Monolayer Transition Metal Dichalcogenides: a First-principles Study

Using first-principles calculations, we investigate the electronic structure and optical properties of lateral heterostructures consisting of different monolayer transition metal dichalcogenides (TMDs). We find that the spin-orbital coupling effect plays an important role in modifying the ground-state electronic structure and excited-state properties such as optical responses. The anisotropy of optical absorption is investigated including local-field effects.