Session L15: 2D Materials (Semiconductors) -- Quantum Interactions in Transport and Optical Phenomena

Transport theory of quantum dots based on transition metal dichalcogenides

Atomically thin transition metal dichalcogenides (TMDs) represent a conceptually new class of materials that have large bandgaps, strong spin-orbit couplings, and multiple valley degrees of freedom. One particular characteristic of TMDs is their even-odd layer-dependent band structures that have been theoretically predicted and experimentally observed. We study the transport properties of few-layer TMDs in the quantum dot geometry and predict unconventional Coulomb peaks and Kondo resonances when such a dot is tunnel coupled to two normal leads. The irrational peak ratios and fractional resonance conductances found in our study suggest that TMDs provide a unique platform for novel quantum dot physics.   

Single photon-phonon entanglement in WSe2 quantum dots

We study photoluminescence of optically active quantum dots (QDs) in monolayer WSe₂ FET at low temperature (4K) and magnetic fields up to 8T. In addition to the neutral QD emission, a 21.8 meV red-shifted peak is observed. This replica peak shows correlated spectral jitters identical to the parent peak and exhibits similar excitation power dependence and magnetic field induced Zeeman splitting. Raman spectroscopy and phonon dispersion calculations are used to assign this peak to doubly-degenerate chiral phonons. Different to linearly polarized neutral QD, the phonon replica is completely unpolarized. This unusual behavior is not expected in a coherent phonon scattering. We understand it as a result of phonon-photon entanglement resulting from two indistinguishable paths in the phonon scattering process. As the phonon part of the entanglement is never measured, the photon part gets fully unpolarized. Under magnetic field this indistinguishability is lost and the replica peak recovers its polarization, corroborating our claim. Our results highlight an intriguing feature of 2D honeycomb lattice which can host chiral phonons. This single photon-phonon entanglement can be further explored for non-reciprocal light propagation at the quantum level.   

Control of spin-valley state in a charged WSe2 quantum dot by optical helicity

We present low temperature (~4 K) photoluminescence study of positively charged quantum dots (QDs) in an ambipolar WSe₂ field effect transistor. At a negative gate voltage when the monolayer sample is lightly hole-doped, a single peak (S-peak) and a doublet (D-peak) appear simultaneously and spectrally wander in an identical manner. We thus assign S- and D-peaks originate from the same QD. D-peaks are the neutral (X⁰) QD with fine structure splitting of ~600 µeV resulting from the e-h exchange interaction. While the exchange interaction in a singly, positively charged (X⁺) QD is expected to vanish due to holes forming a singlet and Pauli blocking. We assign S-peaks to be X⁺ QD which has a binding energy of -10 meV with respect to X⁰. X⁺ QD is doubly degenerate at B = 0 T. The degeneracy of X⁺ is lifted in finite B field, allowing us to spectrally distinguish between the spin-valley states (with excess hole spin up in -K valley or spin down in K valley). By controlling the helicity of the excitation laser, we observe selective initialization of spin-valley of excess hole in X⁺ QD under small B field. Our results show that spin-valley degree is robust in charged WSe₂ QDs and enables valleytronics on single localized charge carriers.   

Potential landscape engineering in two-dimensional transition metal dichalcogenides: towards hybrid optical-electrical quantum dots

Monolayer transition metal dichalcogenides (TMDCs) have attracted recent interest due to their unique excitonic and electronic properties. As gapped, semiconducting counterparts to graphene, they show particularly strong excitonic effects, which can be exploited both in pure monolayer devices, as well as in van der Waals heterostructures where the TMDC is encapsulated between layers of insulating hexagonal boron nitride (hBN). In this work, we discuss progress towards a unique platform that exploits the strong excitonic binding energies of the TMDCs to create a hybrid, electrically controlled yet optically active quantum dot device. Further, we report on recent experiments showing optically induced current from hole-doped molybdenum diselenide to graphite or metal electrodes across over 90nm of hBN, indicating a limitation of hBN encapsulation for hybrid optical-electronic devices in TMDCs along with a method for unipolar charge injection into uncontacted TMDC layers. Finally, we discuss methods for making tunable excitonic potential landscapes in TMDC heterostructures via modulation of the dielectric environment in reconfigurable moiré structures.   

Spontaneous emission enhancement of single-layer WSe2 coupled to a microcavity

Atomically thin layers of transition metal dichalcogenides such as single-layer WSe₂ have recently attracted much attention as promising material candidates for optoelectronic applications. Engineering the spontaneous emission rate in these materials is expected to improve the performance and functionalities of optoelectronic devices. In this talk, we show the photoluminescence (PL) enhancement of mechanically exfoliated single-layer WSe₂ integrated to a microcavity. We directly contact silicon dioxide microspheres with diameters ranging from 2 to 7 μm on single-layer WSe₂ to control the enhancement rate. We found that the experimentally obtained Purcell factor agrees well with that calculated by the finite-difference time-domain (FDTD) simulation. The Purcell enhancement is further supported by the direct measurement of the radiative decay rate of WSe₂ with and without microspheres. Our finding provides a way to manipulate optical properties of single-layer semiconductors for optoelectronic applications and integrated nanophotonics.   

Room Temperature Control of Valley Coherence in Microcavity Bilayer WS2 Exciton-Polariton

Transition metal Dichalcogenides (TMD) have emerged as promising candidate for many optoelectronic and photonic applications. Their lack of inversion symmetry, presence of strong spin-orbit coupling and spin-valley locking make them ideal for realizing “Valleytronics” , a valley counterpart of spintronics. An important aspect of using the valley degree of freedom for information technology is manipulating the coherent circularly polarized photoluminescence (PL) from both valleys which is realized in experiment via the retention of linear polarization of the PL. Bare TMD however suffer from many dephasing mechanisms with electron hole exchange being the dominant one. Embedding these TMD’s in microcavities allow us to form polaritons in the strong coupling regime which is a hybrid light-matter system. We thus earn additional control knobs provided by the photon component of the quasiparticle. Also, the lifetime of the polariton species, dictated by the quality factor can be made comparable to that of the dephasing mechanisms to ease their effects. Here we report robust room temperature valley coherence from bilayer WS₂ exciton polaritons and show control of the valley coherence without the application of external magnetic field.   

Tracking the origin of single photon emitters in WSe2

Single photon emitters (SPE) in WSe₂ have been investigated in several recent publications [1, 2], receiving considerable attention in the field of two-dimensional materials. Although the origin of these emitters is generally attributed to defects and/or local strain, an exact microscopic
explanation has proven elusive.
Using a multiscale approach we established a tight-binding model capturing non-uniform strain, defects and coulomb-interactions we elucidate this mystery. Tight-binding calculations with local strain patterns and open boundary conditions for a large WSe₂ flake yield quantum-dot-like localization. Including defects we can reproduce and explain the large g-factor (≈ 9) as well as the zero field splitting, the linear polarization and the electric field dependence.
We conclude that local strain shifts excitonic energy levels into an energy of otherwise unoccupied inter-gap defect states, acting as a doorkeeper to fill these states. Together with localized
valence bands, this leads to sharp SPE.





[1] P. Tonndorf, et.al., "Single-photon emission from localized excitons in an atomically thin semiconductor", Optica, 2, 347-352, (2015).
[2] Koperski M., et.al., ”Single photon emitters in exfoliated WSe 2 structures”,Nature Nano, 10, 503-605, (2015).   

2D-MoS2 Field Effect Transistor Enable Remote Label-Free Enzyme Measurements

We have fabricated and characterized ionic liquid-gated 2D-MoS2 field effect transistors (2D-ILFETs) that operate at the quantum capacitance limit of the 2D channel material. These devices were used to measure pH with high sensitivity (~75 times higher than the Nernst value of 59 mV/pH) and low noise (~2 orders of magnitude higher signal-to-noise ratio over ion-sensitive FETs) at room temperature. This high device performance in pH sensing is attributed to the large asymmetric capacitive coupling between the top ionic liquid gate and bottom silicon gate to the 2D semiconducting channel. This behavior is fundamentally different from dual-gate silicon FET pH sensors that control two coupled channels. To demonstrate the usefulness of ultra-sensitive pH measurements based on 2D-ILFETs, we experimentally quantified the function of enzymes implicated in Alzheimer’s disease at physiological concentrations and with sufficient time-resolution to allow the estimation of both steady-state and kinetic parameters in a single experiment.   

Analysis of the Spatial Separation of Carrier Spin by the Valley Hall Effect in Monolayer WSe2 Transistors

Monolayers of semiconducting transition metal dichalcogenides (TMDCs) exhibit a valley Hall effect (VHE) in which the carriers in the K (K’) valley acquire a velocity, v(-v) perpendicular the applied electric field, E [1,2,3]. As the K and K’ bands split by spin, the resulting valley current is also a spin current. For a sample of finite width perpendicular to the direction of an applied electric field E, this leads to a steady-state accumulation of spin and valley polarized carriers at the edges. We have investigated the VHE in ambipolar WSe₂ field-effect transistors in both n- and p- type regimes using spatial imaging of the spin and valley polarization by the optical Kerr rotation (KR) at 20 K. Here we quantitatively interpret the magnitude of the measured KR through a model of the optical response for unequal carrier populations in the valleys to obtain an estimate of the experimental spin/valley imbalance. We compare our findings to predictions of a spin diffusion model. This allows us to infer a spin and valley lifetime compatible with previous time-resolved measurements of spin-polarized carriers [4].
[1] Mak et al. Science 344, 1489-92 (2014).
[2] Xiao et al. PRL 108, 196802 (2012).
[3] Lee et al. Nat. Nano. 11, 421-5 (2016).
[4] Hsu et al. Nat. Comm. 8963 (2015)
  

Theory of thermionic emission from two-dimensional conductors.

The standard theory of thermionic emission developed for three-dimensional (3D) conductors does not apply to two-dimensional (2D) materials even for making qualitative predictions because of the vanishing out-of-plane quasiparticle velocity [1]. Here, we focus on two mechanisms possibly responsible for out-of-plane electron transport in 2D-3D and 2D-2D heterojunctions. First, we consider the fundamental origin of the out-of-plane charge carrier motion in a perfect 2D conductor due to the finite quasiparticle lifetime and huge uncertainty of the out-of-plane momentum. The theory is applied to a Schottky junction between graphene and a bulk semiconductor to derive a thermionic constant, which, in contrast to the conventional Richardson constant, depends on the barrier height and Fermi level [2]. Second, we focus on electron transport from a 2D conductor to a 2D semiconductor assuming some short-range interface disorder that results in momentum randomization and interlayer hopping. The model is applied to electron transport in graphene-MoS₂ heterostructures [3].

[1] C. Crowell, Solid-State Electron. 8, 395 (1965).
[2] M. Trushin, Appl. Phys. Lett. 112, 171109 (2018).
[3] M. Trushin, Phys. Rev. B 97, 195447 (2018).   

Hall and thermoelectric measurement of Type-II Weyl semimetal TaIrTe4

Weyl semimetal has gapless band structures protected by topology and symmetry which possess many interesting properties, like Fermi arc surface states, chiral anomaly etc. Without the constraint from the Lorentz invariance, type-II Weyl semimetal has a tilted Weyl cone that electron and hole pockets exist at the node energy. TaIrTe₄ is theoretically predicted to be a type-II Weyl semimetal hosting four well-separated Weyl points which is the minimum required by the symmetry. Here, we present our study of TaIrTe₄ with Hall and thermoelectric measurement. In the Hall measurement, two pairs of electron-hole pockets with quite different mobility could be identified by fitting the Hall curves. The temperature dependence of the carrier density shows an obvious movement of the Fermi level which is quite similar to the reported temperature-induced Lifshitz transition in WTe₂. The Hall result suggests that hole-type carrier dominate the transport properties which is in the opposite to the negative Seebeck coefficient. The Nernst coefficient has the same temperature dependence as the mobility of the dominate hole band.
  

Quantum Oscillation in WTe2 Flakes

WTe₂ is theoretically predicted to have two pairs of electron and hole pockets along Γ-X direction, which have been observed in ARPES. However, ARPES also revealed an additional hole pocket which is very closed to Γ point, the center of Brillouin zone. The two predicted pairs of Fermi pockets have already been verified in transport measurements but there's few evidence of the existence of the hole pocket at Γ point. Here we report the quantum oscillations study in semimetallic WTe₂ flakes with different thickness. An oscillation signal from the hole pocket at Γ point is very likely to be observed.   

Quantum Transport in N-doped 2D Tellurene

Tellurium (Te) is a p-type narrow-bandgap high-mobility semiconductor with one dimensional van der Waals (vdW) structure. It has a unique chiral-chain crystal lattice in which individual helical chains of Te atoms are stacked together by vdW type bonds and spiral around c-axis. With recently developed solvent-based growth method, we are able to probe the magneto-transport of Te in its 2D limit, coined as tellurene. In this work, we demonstrate an effective dielectric doping technique to realize n-type tellurene. We report on the pronounced weak anti-localization, quantum Hall effect, strong Shubnikov-de Haas oscillations on n-doped tellurene with temperature down to tens of mK and magnetic fields up to 31 Tesla. Angle, electron density and temperature dependence of the oscillations were systematically measured and analysized.   

Substrate Renormalization of Quasiparticle Band Gaps, Exciton Binding Energies and Transport Properties of Quasi-2D Materials

Electrons in atomically thin quasi-2D materials, such as monolayer transition-metal dichalcogenides, are spatially confined in the out-of-plane direction and are also more weakly and differently screened than in bulk materials. Consequently, electron-electron and electron-hole interactions in quasi-2D materials are stronger and different compared to the bulk. Similarly, owing to the atomic dimension of layer thickness, quasi-2D materials are sensitive to screening environment produced by substrates, allowing one to dramatically tune their quasiparticle and optical properties. Here, we discuss a method recently developed in our group to incorporate substrate screening into the calculation of quasiparticle and optical properties of quasi-2D materials. We perform ab initio GW and GW-Bethe Salpeter equation (GW-BSE) calculations to quantify this effect on electronic and optical gaps of these systems. We will also discuss a theoretical upper bound of the screening effect. Lastly, we will show how substrate screening can be used to engineer a lateral heterojunction within homogeneous MoS₂ monolayer.   

Multiscale Modeling of 2D Materials with the Phase-Field Crystal Model

Novel 2D materials have unusual properties, many of which are coupled to their large scale mechanical and structural properties. Modeling is a formidable challenge due to a wide span of length and time scales. I will review recent progress in structural multiscale modeling of 2D materials and thin heteroepitaxial overlayers [1], and graphene and h-BN [2,3], based on the Phase Field Crystal (PFC) model combined with Molecular Dynamics and Quantum Density Functional Theory. The PFC model allows one to reach diffusive time scales at the atomic scale, which facilitates quantitative characterisation of domain walls, dislocations, grain boundaries, and strain-driven self-organisation up to micron length scales. This allows one to study e.g. thermal conduction and electrical transport in realistic multi-grain systems [3,4].
[1] K. R. Elder et al., Phys. Rev. Lett. 108, 226102 (2012); Phys. Rev. B 88, 075423 (2013); J. Chem. Phys. 144, 174703 (2016).
[2] P. Hirvonen et al., Phys. Rev. B 94, 035414 (2016).
[3] H. Dong et al., Chem. Phys. Phys. Chem. 20, 4263 (2018).
[4] Z. Fan et al., Phys. Rev. B 95, 144309 (2017); Nano Lett. 7b172 (2017); K. Azizi et al., Carbon 125, 384 (2017).