Session R13: 2D Materials (General): Transport and Optical Phenomena -- Emerging Materials

Optical conductivity of black phosphorus

Black phosphorus (BP) is a two-dimensional layered material composed of phosphorus atoms. Recently, it was demonstrated that external perturbations such as electric field close the band gap or even induce a band inversion in few-layer BP, resulting in the insulator phase with a finite energy gap or the Dirac semimetal phase characterized by two separate Dirac nodes. At the transition between the two phases, a semi-Dirac state appears in which energy disperses linearly along one direction and quadratically along the other direction. In this work, we study the optical conductivity of few-layer BP using a lattice model and the corresponding continuum model, incorporating the effects of an external electric field and finite temperature. We find that the low-frequency optical conductivity scales as a different power-law depending on the phase, which can be used as an experimental signature. We also demonstrate the change of the material parameters as an external field increases and its consequence on the power law behavior of the optical conductivity.   

Bright Mid-Infrared Photoluminescence in Thin-Film Black Phosphorus

In this work, we report bright mid-infrared photoluminescence (PL) emission from thin-film black phosphorus (BP). The intensity of the PL emission from a 46-nm thick BP is only seven times weaker than that of an indium arsenide (InAs) multiple quantum well (MQW) structure grown by molecular beam epitaxy, in which the total thickness of the quantum wells is of similar thickness to BP. The PL emission is further tunable by the temperature and layer number of thin-film BP. In the 46-nm thick BP, the PL spectra indicates a bandgap of 0.334±0.003 eV at 300 K, which decreases to 0.308±0.003 eV at 80K. The anomalous redshift of the BP bandgap with decreasing temperature agrees with previous theoretical and experimental results, while the overall energy shift is about 60% of the previously reported value obtained from photocurrent spectroscopy. We also measure the layer number dependence of PL spectra of the thin-film BP (6-to 46-nm), and we show that the emission peaks from around 3.3 to 4 mm at 80 K. Our results reveal the promising future of thin-film BP in mid-infrared light emitting and lasering applications.   

Barkhausen effects in the first order structural phase transition in type-II Weyl semimetal MoTe2

We report the first observation of the non-magnetic Barkhausen effect in van der Waals layered crystals, specifically, between the T_d and 1T' phases in type-II Weyl semimetal MoTe₂. Thinning down the MoTe₂ crystal from bulk material to about 25nm results in a drastic strengthening of the hysteresis in the phase transition, with the difference in critical temperature increasing from ~40K to more than 300K. The Barkhausen effect appears for thin samples and the temperature range of the Barkhausen zone grows approximately linearly with reducing sample thickness, pointing to a surface origin of the phase pinning defects. The distribution of the Barkhausen jumps shows a power law behavior, with its critical exponent α = 1.27, in good agreement with existing scaling theory. Temperature-dependent Raman spectroscopy on MoTe₂ crystals of various thicknesses shows results consistent with our transport measurements.
Reference: C. Cao et al., 2D Materials 5, 044003 (2018)   

Ferroelectric switching of a two-dimensional metal

In its 3D form the semimetal WTe₂ has a polar space group, whereas an isolated monolayer of WTe₂ is centrosymmetric. We find that when exfoliated down to two- or three-layer thickness, WTe₂ exhibits a spontaneous out-of-plane electric polarization, while the monolayer does not. The polarization persists to room temperature and can be switched by a perpendicular electric field using graphite gate electrodes located above and below the sheet. We directly detect and quantify the polarization using graphene as an electric-field sensor. The polarization state can also be distinguished via the in-plane conductivity. The ferroelectricity persists even when the material is metallic in the plane; this is possible because the few-layer WTe₂ is so thin that the applied electric field penetrates it.   

Nonlinear imaging of grain boundaries in monolayer semiconducting transition metal dichalcogenides

Locating and imaging defects in two-dimensional (2D) materials is a key challenge to probe the material quality for different target applications. Recently, second harmonic generation (SHG) has been used to characterise different 2D materials and defective regions like grain boundaries [1]. However it has been shown that these grain boundaries were revelled by interference between the two neighbouring domains, leading to a dark region (no SHG emission) between then [1]. Here we implemented a nonlinear dark-field SHG microscopy setup to accurately probe grain boundaries and edges from semiconducting transition metal dichalcogenide monolayers. The dark-field SHG efficiently separates the spatial components of the emitted light and accurately locates grain boundaries and edges as bright patterns. The far field SHG pattern is calculated considering the interference between two second harmonic dipoles, which is in agreement with our experimental finding. Therefore the dark field second harmonic imaging open new opportunities to characterize defects in 2D materials [2].
[1] X.Yin et. al, Science 344, 488, 2014.
[2] Bruno Carvalho et al., submitted (2018).   

Tightly Coulomb-bound four- and five-particle intervalley states in monolayer tungsten diselenide

Tightly-bound excitonic complexes in atomically-thin semiconducting transition metal dichalcogenides (TMDCs) provide an appealing platform for studying many-body correlations. Here, we present the observation of the Coulomb-bound four-particle biexciton and five-particle exciton-trion in monolayer tungsten diselenide by the photoluminescence (PL) measurements. The ultrahigh quality sample enables us to resolve and assign several intrinsic emission features in the energy window right below the bright neutral exciton emission. Interestingly, we discover that the biexciton consists of a spin-zero bright exciton in one valley and a spin-one ‘‘dark’’ exciton in the other, which is confirmed by the magneto-PL measurements. The binding energy of these multi-particle states are further estimated as 18–23 meV and 13–20 meV for the biexciton and the exciton-trion, respectively, by charge doping and thermal activation measurements. The tightly bound nature of the multi-particle states in atomically-thin TMDCs offer opportunities for understanding many-body physics and for realizing interesting applications such as Bose-Einstein condensation, and quantum communication and teleportation.

Reference: Chen et al, NATURE COMMUNICATIONS | (2018)9:3717   

Layer number dependent barrier height of MoS2 on ultra-flat conducting surfaces

Transition metal dichalcogenides (TMDs) are layered semiconducting van der Waal crystals and promising materials for wide range of electronic and optoelectronic devices. Realizing practical device application requires an understanding of nanoscale local electronic and optoelectronic properties on layered TMDs on a conducting metal surface. In this work, we have used conducting atomic force microscopy (CAFM) of layered MoS2 (1-5 layers) immobilized on two different ultra-flat conducting surfaces (RMS surface roughness <0.2 nm) Au and indium tin oxide (ITO) forming metal (conductive-tip)-semiconductor-metal devices. First, we have found that the edges of the different layers are insulating. Second, the current increases as the layer number increases. By applying Fowler-Nordheim tunneling theory, we have determined the barrier heights for different layers and observed that the barrier height decreases as the number of layers increases. Our study provides a fundamental understanding of the local electronic behavior of TMD depending on layer numbers and may pave an avenue toward developing nanoscale electronic devices with tailored properties of different layers.   

Second-harmonic generation in strained transition metal dichalcogenide monolayers

Second-harmonic generation (SHG) is a powerful measurement technique to analyze the symmetry properties of crystals. Mechanical strain can reduce the symmetry of a crystal and even weak strain can have an immense impact on the SHG intensity along different polarization directions. The impact of strain on the SHG can be modelled with a second-order nonlinear photoelastic tensor. We determined the photoelastic tensors for four different transition metal dichalcogenide (TMD) monolayers: MoS₂, MoSe₂, WS₂ and WSe₂. We find that the photoelastic tensors depend highly on the excitation wavelength. Therefore, we identified the fundamental energies where strain has the highest impact on the SHG. This allows for highly sensitive, noninvasive strain matrix imaging at the submicron scale in all investigated TMDs.   

Computing nonlinear response to arbitrary order in the presence of electronic interactions via time-domain integration of polarizability

We describe a theoretical approach to study the nonlinear optical response of electronic systems based on a real-time solution of the electronic dynamics in the presence of time-dependent electromagnetic fields. Using accurately parameterized tight-binding models and electronic interactions, this allows expedite and accurate calculations of the nonlinear response to arbitrary order for realistic systems. We demonstrate its capabilities by computing the excitonic spectrum and high-harmonic generation (SHG, THG, FHG) in MoS$_2$ and BN monolayers. The linear optical conductivity is seen to reproduce exactly the Kubo-formula perturbative results based on the Bethe-Salpeter equation and, moreover, reproduces very well the experimental traces. Such benchmark against experiments in linear order allows us to confidently predict the frequency dependence of the higher-harmonic susceptibilities which, within our scheme, are obtained with no additional effort, in contrast to an order-by-order perturbative approach.
  

Growth of self-assembled graphene nanoribbons on SiC substrates.

Graphene nanoribbons (GNRs) hold promise for future nanoelectronics due to their unique band structure. Quantum confinement effects are observed in GNRs, and their bandgap energies increase with inverse proportionality to the GNR width. However, existing lithographic patterning methods cause disordered edges to form during the etching process creating dangling bonds that degrade the electrical properties of the GNR. To overcome these problems, structured silicon carbide (SiC) has been used as a template for selective growth of GNRs, which show outstanding ballistic transport with an electronic mean free path up to 15 μm [1, 2]. In this study, we have demonstrated the growth of narrow GNRs (~40 nm width) with improved structural properties using a surface pre-treatment. This method restrains SiC terrace edge step-flow during the annealing process, helping to form GNRs with the shape of the patterned SiC. The longitudinal and Hall magnetoresistance of GNRs are measured at low temperature using a six-terminal Hall bar geometry and the structural characteristics are demonstrated with atomic force microscopy (AFM), conductive AFM, and field emission scanning electron microscopy.

[1] Y. Hu et al., J. Phys. D: Appl. Phys. 45, 154010 (2012)
[2] J. Baringhaus et al., Nature 506, 349 (2014)   

Two-dimensional electrons electrostatically confined on the surface of graphite

In the bulk of a crystal, charge carriers are described by the Bloch states. At the crystal surface, the lattice periodicity is disrupted transforming itinerant Bloch waves to evanescent states. While easily accessible in semiconductors due to the presence of band gap, surface states are prohibited in gapless metals due to the presence of massive Fermi sea. Here, using capacitance spectroscopy, we show that two-dimensional (2D) charge carriers can be confined on the surface of graphite and electronically decoupled from the bulk simply by electrostatic gating. In the presence of a magnetic field, perpendicular to graphite basal plane, the Landau bands of bulk graphite render to evanescent Landau levels, which, in high magnetic fields, show electron-electron interactions including fractional quantum Hall states and negative electronic compressibility. Our work provides an experimentally convenient and highly tunable system for exploring bulk-surface correspondence.   

Interlayer interaction and Davydov splitting in MoS2 polytypes studied by Raman spectroscopy

The dependence of the interlayer interaction on the stacking order of MoS₂ is investigated by Raman spectroscopy using three excitation energies of 2.81, 2.41, and 1.96 eV. The low-frequency Raman spectra show distinct correlation with the stacking type [1]. The A-like intra-layer vibration mode at 405 cm^–1 exhibit Davydov splitting due to interlayer interactions when the 1.96-eV excitation is used. The positions and the relative intensities of the Davydov-split peaks depend on the stacking type as well. By using the linear-chain model, the interlayer force constants are extracted and compared for 3-layer samples with different stacking types: the 3R-types have a larger force constant than the 2H-type. For the 2H-type, Davydov splitting is analyzed as a function of the number of layers. The force constants for the second-nearest-neighbor interaction are obtained and compared with other transition metal dichalcogenides [2, 3, 4].

References
[1] J.-U. Lee et al., ACS NANO, 10, 1948 (2016).
[2] G. Froehlicher et al., Nano Lett., 15, 6481 (2015).
[3] K. Kim et al., ACS NANO, 10, 8113 (2016).
[4] W. Na et al., 2D Mater., 6, 015004 (2019).   

Current Transport and Phase Transition in MoTe2

MoTe₂ is an interesting two-dimensional (2D) material, which has small energy barrier between semiconducting 2H phase and metallic 1T′ phase, and has ambipolar transport with high carrier mobility, which makes it promising for phase-change memories and logic devices. In this work, we systematically studied the current transport and phase transition in MoTe₂. The spectral photocurrent measurement reveals that the bandgap of MoTe₂ is ~1eV. The bandgap of MoTe₂ was also extracted using temperature dependence of conductance. The mobility of MoTe₂ was characterized using Hall-bar devices. At low temperatures, the carrier mobility is limited by Columbic scattering, while at high temperatures, it is limited by phonon scattering. Vertical metal/MoTe₂/metal junctions were also fabricated. As the current or voltage applied to the junction increases, MoTe₂ exhibits two transitions: high-to-low resistance transition at medium current levels, and low-to-high resistance transition at high current levels. These two transitions in resistivity in MoTe₂ may correspond to the 2H-to-1T phase transition and 1T-to-amorphous state transition respectively.   

Impacts of h-BN Stacking Sequence and Layer Thickness on the Band Structure and Radiative Recombination

We investigated the variation of the electronic and optical properties of h-BN as a function of stacking sequence and number of layers using first-principles calculations. Our study includes bulk and bilayer structures for the five possible stacking sequences, as well as monolayer and randomly stacked bulk structures (t-BN). Variations of the band structure were studied both at the density functional theory (DFT) and GW levels, with particular focus on the band extrema. The majority of the investigated structures were found to have indirect band gaps, with a few exceptions such as the AB₁ stacking sequence and t-BN. We further calculated the phonon-assisted optical matrix elements (S) for all structures to understand how the number of layers and stacking type influence light emission. Most of the ordered bulk and bilayer structures are capable of efficient light emission with values of S² ranging from ~10-1000× that of bulk Si, indicating that efficient phonon-assisted light emission is possible even though the gap is indirect.