Session R40: 2D Materials - Electronic Structure and Transport

Vertical Tunneling in Layered Materials and Its Applications

Tunneling has to play an essential role in vertical transport in layered materials due to the van der Waals coupling between layers. The van der Waals gap can be viewed as the thinnest insulator, with a physical thickness of about 3-5 angstrom measured from the center of the nearest atomic planes separated by the van der Waals gap (not the centroid of a monolayer). When an electron wavelet moves perpendicular to this gap, is it sufficient to use the transfer-Hamiltonian method to calculate the time it takes thus calculating the magnitude of the resulting current flow? Is it possible to control tunneling with an applied electric field thus possible to generate a signal? Being one of the most sensitive transport mechanisms, it is difficult to reach very high tunneling current density. In resonant tunneling diodes, very high tunneling peak currents are achieved (\textasciitilde MA/cm$^{\mathrm{2}})$; however, the valley current increases concurrently, thus limiting the range of tunable tunneling current to a typical value of \textless 5. Finally, how is tunneling in layered materials different from 3D materials? These are the questions our group has aimed to answer [1-8]. In this talk, I will share our progress and the challenges we face in terms of preparing, characterizing these layered materials as well as pursuing their applications. \begin{enumerate} \item Mingda (Oscar) Li, Huili Grace Xing et al. \textit{Single particle transport in two-dimensional heterojunction interlayer tunneling field effect transistor}. J. Appl. Phys. 115, 074508 (2014). doi:10.1063/1.4866076 \item Shudong Xiao, Mingda Li,~Alan Seabaugh, Debdeep Jena,~Huili Grace Xing. \textit{Vertical heterojunction of MoS2 and WSe2.} IEEE Device Research Conference, University of California, Santa Barbara, June 2014. \item Debdeep Jena,~Mingda Li,~Nan Ma, Wan Sik Hwang, David Esseni, Alan~Seabaugh, and~Huili Grace Xing. \newline \textit{Electron transport in 2D crystal semiconductors and their device applications.} IEEE Silicon Nanoelectronics Workshop, Hawaii, June 2014. \item Rusen Yan, Huili Grace Xing et al.,~\textit{Esaki diodes in van der Waals heterojunctions with broken-gap energy band alignment}.~Nano Letters, 15(9), 5791-8, (2015). DOI: 10.1021/acs.nanolett.5b01792 \item Mingda (Oscar) Li, David Esseni, Gregory Snider, Debdeep Jena and~Huili Grace Xing.~\textit{Two-dimensional heterojunction interlayer tunneling field effect transistors (Thin-TFET)}~IEEE J-EDS, 3(3), 200-207 (2015). DOI:10.1109/JEDS.2015.2390643 \item ~Mingda (Oscar) Li, Rusen Yan, Debdeep Jena and Huili Grace Xing. \textit{Two-dimensional Heterojunction Interlayer Tunnel Field Effect Transistor (Thin-TFET): From Theory to Applications.} IEDM, pp.19.2/1-4, (2016) \item Mingda (Oscar) Li, Ozan Irsoy, Claire Cardie, and Huili Grace Xing. \textit{Physics-inspired neural networks (Pi-NN) for efficient device compact modeling.} IEEE J. of Exploratory Solid-State Computational Devices and Circuits (2016). \item Jimy Encomendero, Faiza Afroz Faria, S. M. Islam, Vladimir Protasenko, Sergei Rouvimov, Berardi Sensale-Rodriguez, Patrick Fay, Debdeep Jena, and Huli Grace Xing. \textit{New tunneling features in polar III-nitride resonant tunneling diodes.} Physics Review X (PRX), 7,041017 (2017).~ DOI: 10.1103/PhysRevX.7.041017 \end{enumerate}   

Electronic Band Structure Study of Millimeter-Sized Mono-Layer WSe2 using Angle-Resolved Photoemission Spectroscopy

The transition metal dichalcogenide (TMDC) semiconductors MX2 (M = Mo, W; X = S, Se) exhibit unique properties in the mono- or few-layer forms. The monolayer MX2 crystals of TMDC have also showed great potential in the next-generation electronics, optoelectronics and spintronics. Of particular interest is the monolayer WSe2 which has the largest spin-splitting in the valence band at the Brillouin zone corner among all the MX2 semiconductors. We will present electronic structure study on pristine and alkali metal-doped WSe2 monolayer by high resolution angle-resolved photoemission spectroscopy (ARPES). By utilizing an improved exfoliation method, we have prepared milimeter-sized mono-layer WSe2 with a high quality. We found experimental evidence of the direct gap transition in monolayer WSe2 as predicted by density functional theory. The observed direct gap and spin splitting of the upper valence band at K point is ~ 1.1 eV and 500 meV, respectively. We also found some additional and interesting electronic state features which are to be discussed within the frameworks of quantum well state and monolayer WSe2-substrate interaction. Our study may pave a way for engineering band structure and tuning electronic properties in mono-layer TMDC semiconductor.   

2D materials under the microscope(s)

Interest in transition metal dichalcogenides (TMDs) has been renewed by the discovery of emergent properties when reduced to single, two-dimensional (2D) layers. Here, we use a set of complementary techniques - photoluminescence, Kelvin probe, scanning tunneling and photoelectron spectroscopy – to correlate locally chemical state, electronic structure, and optical properties of 2D-TMDs. Atomic force and scanning tunneling microscopy allowed us to identify unambiguously the atomic and electronic structure of chalcogen and metal vacancies in chemical vapor deposition grown WS₂. Furthermore, we employ spatially and angle resolved photoemission spectroscopy (nano-ARPES) to map variations in band alignment and chemical composition. By correlating this information with photoluminescence data, we reveal the interplay between local material properties, such as defect density or chemical composition, and the formation of charged trions, defect-bound excitons and neutral excitons.   

Photoemission study of the electronic structure of valence band convergent SnSe

IV-VI semiconductor SnSe has been known as the material with record high thermoelectric performance. The multiple close-to-degenerate (or “convergent”) valence bands in the electronic band structure has been one of the key factors contributing to the high power factor and thus figure of merit in the SnSe single crystal. To date, there have been primarily theoretical calculations of this particular electronic band structure. In this paper, however, using angle-resolved photoemission spectroscopy, we perform a systematic investigation of the electronic structure of SnSe. We directly observe three predicted hole bands with small energy differences between their band tops and relatively small in-plane effective masses, in good agreement with the ab initio calculations and critical for the enhancement of the Seebeck coefficient while keeping high electrical conductivity. Our results reveal the complete band structure of SnSe and help to provide a deeper understanding of the electronic origin of the excellent thermoelectric performances in SnSe.   

Edge states of ABA Trilayer Graphene Nanoribbons

Due to mirror symmetry the bands of ABA stacked trilayer graphene can be identified by their parity with respect to mirror symmetry. The even parity bands exhibit gapped bilayer graphene-like dispersion, while the odd parity bands exhibit a gapped graphene-like dispersion. Using a tight binding model with Slonczewski-Weiss-McClure parameters we look at the edge states in trilayer graphene nanoribbons in the quantum hall regime. Both armchair and zigzag edge nanoribbons are analyzed. When mirror symmetry is preserved, the system exhibits quantized longitudinal conductance at charge neutrality point, due to counterpropagating even and odd parity edge modes. We study the effects of perpendicular electric field and mirror symmetry breaking disorder on the longitudinal conductance.   

Highly anisotropic characters of hole carriers in ReS2 and ReSe2

Two-dimensional (2D) materials have greatly drawn attentions in condensed matter physics, since it shows intriguing electronic structure such as the Dirac cone in graphene and valley degeneracy in MoS₂, and also often shows strong electron-electron correlation effect due to low electronic dimensionality such as in charge density wave formation in NbSe₂. Group 7 transition metal dichalcogenides, ReS₂ and ReSe₂ are recently highlighted, since layer-layer interaction is much weaker than the other 2D materials and their highly anisotropic features. Here, we perform systematic directional dependence of effective mass of hole carriers in ReS₂ and ReSe₂ using angle resolved photoemission spectroscopy (ARPES). Remarkably, observed effective masses are heavier than those from first principles calculations and the effective masses along Re chain direction show seven times lighter than the other directions which is much stronger anisotropy than predicted by first principles calculations.   

Effects of biaxial strain on the electronic structure, vibrational properties and electron-phonon coupling of silicene

We present results of ab-initio calculations for the electronic structure, vibrational properties, electron-phonon coupling, and conventional superconductivity for silicene under biaxial strain for deformations up to 18%. The calculations were performed using the Plane-Waves and Pseudopotential method, with the GGA-PBE exchange-correlation functional. Dynamical matrices and e-ph coupling properties were computed with the linear response theory. The superconducting gap and the critical temperature were calculated employing the multiband Eliashberg formalism. We found that biaxial strain shifts the sigma-band located above the Fermi level at the Gamma point to lower energies and the Dirac point is shifted above the Fermi level, producing an electronic topological transition in the Fermi surface. Thus, silicene under biaxial strain becomes metallic for deformations larger than 8%. Hence, we found that biaxial strain produces strong changes in the electronic structure that enhances the electron-phonon coupling and induce conventional superconductivity in silicene.   

Exploring electronic structure of rectangualr silicene nanoclusters

In the last years, graphene has attracted an increasing interest because it is considered the
elementary unit in modern microelectronics such as transistors, photovoltaics cells,
and even battery energy storage. Although most of the striking properties of
graphene have been predicted to occur in silicene such as Diract cone, the major advantage of investigating silicene
like nanoclusters or nanoribbons is that these can be easily incorporated into the present silicon
based microelectronic industry. In addition, silicene nanoclusters have the advantage that they all posses fine band gaps because of quantum confinement effect that is desirable for their applications. Therefore, we investigated the electronic and transport properties of silicene
nanclusters, and the eect of electron correlation using multi-referential first principal calculations
that have not been done yet until now in density functional theory publications concerning silicene. So, we demonstrated that silicene nanoclusters can exhibit two dierent states known
as ferromagnetic and antiferromagnetic. The ferromagnetic state is obtained for na > nz with
na and nz being the units on the armchair and zigzag edges of the rectangular nanoclusters.
The antiferromagnetic states is given by nz > na with nz 2 [1; 7] and na 2 [1; 9].   

Low-Lying Unoccupied Electronic States in Graphene on Ir(111) and Intercalated Interfaces by Time- and Angle-Resolved Two-Photon-Photoemission

We report experimental and theoretical work to understand how intercalation modulates unoccupied electronic states in a metal/graphene interface. We use time- and angle-resolved two-photon-photoemission spectroscopy to map the evolution of the electronic band structure and record the electron dynamics of an epitaxially grown graphene on Ir(111) as it undergoes through a cycle involving oxygen intercalation and deintercalation. Oxygen intercalation is carried out in situ and LEED is used to determine the crystallinity of the interface in the presence or absence of the intercalated adatoms. The image potential state and its electron dynamics are examined by both mono- and bi-chromatic 2PPE. The observation of an oxygen induced state is discussed and explained by DFT calculations. Furthermore, a recently proposed effective potential model at the graphene/metal interface is developed to accommodate intercalation and interpret our experimental electronic structure variation with good agreement with the model.   

Bending space to create a geometric analogue of the classical Hall effect without magnetic field

We show that it is possible to determine the sign and density of the charge carriers in a material without using magnetism. Instead of a magnetic field, we use the geometry of the wire carrying the current to measure these properties. If the wire is curved, the charge carriers must experience a centripetal force to follow the wire. The centripetal force arises from surface charges along the wire, which create a component of the electric field perpendicular to the drift velocity. This transverse electric field produces a potential difference between the sides of the wire which depends on the sign and density of the charge carriers.

We perform measurements on devices made from graphene to find experimental evidence for this effect. We measure a signal from our curved wires which is consistent with positive carriers at zero back-gate voltage, as expected in CVD graphene. However, we also find a background signal that occurs even in straight graphene wires. We investigate other possible sources of small potentials, such as the Seebeck effect, to determine the origin of this background. Our measurements provide evidence of a new classical effect, similar to the Hall effect, where geometry replaces the magnetic field as a tool for characterizing a material’s charge carriers.   

Microwave Spectroscopy of Resistive Film Gated Higfets and Mosfets

Undoped devices, such as heterojunction-insulated-gate field-effect transistors (HIGFET), can host ultrahigh quality low density two-dimensional electron system (2DES), but are nearly devoid of carriers without gating [1]. In contrast, an unbiased doped device still has carriers. Microwaves are advantageous in the study of Wigner crystals (WCs) because their conductivity vanishes at dc and they exhibit pinning modes, in which the crystal oscillates within the disorder potential. For WCs in doped samples microwave measurements have been carried out using coplanar waveguides (CPW) [2]. The CPW has a driven center conductor separated from ground planes by slots, and measures mainly the 2DES under the slots. In our devices we have placed resistive film under the CPW metal and in the slots to act as the gate. Using MOSFETS and HIGFETS we demonstrate that a CPW loaded this way by a resistive film is still sensitive to 2DES conductivity, and is hence useable for microwave spectroscopy.
[1] W. Pan, et. al., PRL 106, 206806 (2011).
[2] G. Sambandamurthy, et.al., SSC 140, 100-106 (2006).   

Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding

The photon-like propagation of the Dirac-electrons in graphene together with the record-high electronic mobility can lead to applications based on ultra-fast electronic response and low dissipation. But the chiral nature of the charge-carriers which is responsible for the high mobility also makes it difficult to control their motion and prevents electronic switching. Here we show how to manipulate the charge-carriers by using a circular p-n junction whose size can be continuously tuned from the nanometer to the micrometer scale. The junction size is controlled with a dual-gate device consisting of a planar back-gate and a point-like top-gate made by decorating an STM tip with an Au nanowire. The nanometer-scale junction is defined by a deep potential well created by the tip-induced charge. It traps the Dirac-electrons in quantum-confined states which are the graphene equivalent of the atomic collapse states predicted to occur at super-critically charged nuclei. As the junction size increases, the transition to the optical regime is signaled by the emergence of whispering-gallery modes¹.

¹Y. Jiang, et al, Nature Nanotechnology (2017) doi:10.1038/nnano.2017.181