Dielectric nano-antennas for strain engineering in atomically thin two-dimensional semiconductors
Luca Sortino, Matthew Brooks, Panaiot G. Zotev, Armando Genco, Javier Cambiasso, Sandro Mignuzzi, Stefan A. Maier, Guido Burkard, Riccardo Sapienza, Alexander I. Tartakovskii
备注：
peer-reviewed version, 4 figures main text, 5 figures supporting information
Atomically thin two-dimensional semiconducting transition metal dichalcogenides (TMDs) can withstand large levels of strain before their irreversible damage occurs. This unique property offers a promising route for control of the optical and electronic properties of TMDs, for instance by depositing them on nano-structured surfaces, where position-dependent strain can be produced on the nano-scale. Here, we demonstrate strain-induced modifications of the optical properties of mono- and bilayer TMD WSe$_2 $ placed on photonic nano-antennas made from gallium phosphide (GaP). Photoluminescence (PL) from the strained areas of the TMD layer is enhanced owing to the efficient coupling with the confined optical mode of the nano-antenna. Thus, by following the shift of the PL peak, we deduce the changes in the strain in WSe$_2$ deposited on the nano-antennas of different radii. In agreement with the presented theory, strain up to $\approx 1.4 \%$ is observed for WSe$_2$ monolayers. We also estimate that $>3\%$ strain is achieved in bilayers, accompanied with the emergence of a direct bandgap in this normally indirect-bandgap semiconductor. At cryogenic temperatures, we find evidence of the exciton confinement in the most strained nano-scale parts of the WSe$_2$ layers, as also predicted by our theoretical model. Our results, of direct relevance for both dielectric and plasmonic nano-antennas, show that strain in atomically thin semiconductors can be used as an additional parameter for engineering light-matter interaction in nano-photonic devices.
We systematically measure the dielectric function of atomically thin MoS2 films with different layer numbers and demonstrate that excitonic effects play a dominant role in the dielectric function when the films are less than 5-7 layers thick. The dielectric function shows an anomalous dependence on the layer number. It decreases with the layer number increasing when the films are less than 5-7 layers thick but turns to increase with the layer number for thicker films. We show that this is because the excitonic effect is very strong in the thin MoS2 films and its contribution to the dielectric …
We have studied the elastic deformation of freely suspended atomically thin sheets of muscovite mica, a widely used electrical insulator in its bulk form. Using an atomic force microscope, we carried out bending test experiments to determine the Young's modulus and the initial pre-tension of mica nanosheets with thicknesses ranging from 14 layers down to just one bilayer. We found that their Young's modulus is high (190 GPa), in agreement with the bulk value, which indicates that the exfoliation procedure employed to fabricate these nanolayers does not introduce a noticeable amount of defects.…
Nanopores in 2D materials are highly desirable for DNA sequencing, yet achieving single-stranded DNA (ssDNA) transport through them is challenging. Using density functional theory calculations and molecular dynamics simulations we show that ssDNA transport through a pore in monolayer hexagonal boron nitride (hBN) is marked by a basic nanomechanical conflict. It arises from the notably inhomogeneous flexural rigidity of ssDNA and causes high friction $\textit{via}$ transient DNA desorption costs exacerbated by solvation effects. For a similarly sized pore in bilayer hBN, its self-passivated ato…
We have used density functional theory to calculate the anisotropic dielectric functions for ultrathin gold sheets (composed of 1, 3, 6, and 15 atomic layers). Such films are important components in nano-electromechanical systems. When using correct dielectric functions rather than bulk gold dielectric functions we predict an enhanced attractive Casimir-Lifshitz force (at most around 20%) between two atomically thin gold sheets. For thicker sheets the dielectric properties and the corresponding Casimir forces approach those of gold half-spaces. The magnitude of the corrections that we predict …
Atomically thin layers of transition metal dichalcogenides (TMDCs) exhibit exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. The van der Waals nature of interlayer coupling makes it easy to integrate TMDC layers into heterostructures with different dielectric or metallic substrates. This allows to tailor electronic and optical properties of these materials, as Coulomb interaction inside atomically thin layers is very susceptible to screening by the environment. Here we theoretically inve…
In two-dimensional van der Waals (vdWs) materials, the relative twist angle between adjacent layers not only controls their electronic properties, but also determines their stacking energy. This effect makes it much easier to realize energetically favorable configurations of the vdWs materials, for example, Bernal-stacked structure of bilayer graphene. Here we demonstrate that we can controllably tailor adhesive energy landscape of graphene nanostructures on graphene and stabilize the system with tunable twist angle by using a one-dimensional tilt grain boundary (GB). The area ratio with diffe…
We analyze optical absorption by atomically doped carbon nanotubes with a special focus on the frequency range close to the atomic transition frequency. We derive the optical absorbtion line-shape function and, having analyzed particular achiral nanotubes of different diameters, predict the effect of absorbtion line splitting due to strong atom-vacuum-field coupling in small-diameter nanotubes. We expect this effect to stimulate relevant experimental efforts and thus to open a path to new device applications of atomically doped carbon nanotubes in modern nanotechnologies.
Unique structural and optical properties of atomically thin two-dimensional semiconducting transition metal dichalcogenides enable in principle their efficient coupling to photonic cavities with optical modes volumes close to or below the diffraction limit. Recently, it has become possible to make all-dielectric nano-cavities with reduced mode volumes and negligible non-radiative losses. Here, we realise low-loss high-refractive-index dielectric gallium phosphide (GaP) nano-antennas with small mode volumes coupled to atomic mono- and bilayers of WSe$_2$. We observe a photoluminescence enhancem…
Creation of high quality p-n junctions in graphene monolayer is vital in studying many exotic phenomena of massless Dirac fermions. However, even with the fast progress of graphene technology for more than ten years, it remains conspicuously difficult to generate nanoscale and atomically-sharp p-n junctions in graphene. Here, we employ monolayer-vacancy-island engineering of Cu surface to realize nanoscale p-n junctions with atomically-sharp boundaries in graphene monolayer. The variation of graphene-Cu separations around the edges of the Cu monolayer-vacancy-island affects the positions of th…
Mott transition has been realized in atomically thin monolayer (ML) of two dimensional semiconductors (WS$_2$) via optically excited carriers above a critical carrier density through many body interactions. The above nonlinear optical transition occurs when excited electron hole pairs in ML WS2 continuum heavily interact with each other followed by transformation into a collective electron hole plasma phase (EHP), by losing their identity as individual quasiparticles. This is manifested by the alluring red-shift-blue-shift crossover (RBC) phenomena of the excitonic peaks in the emission spectr…
The 2D electrons trapped in vacuum near the atomically thin dielectric (ATD, mono- or $N$-layer film of $h$-BN or transition metal dichalcogenide) are considered. ATD is suspended above the back gate and forms the capacitor which is controlled by the biased voltage determining 2D concentration, $n_{2D}$. It is found that the leakage current through ATD is negligible and effect of the polarizability of ATD is weak if $N\leq 5$. At temperatures $T=0.1÷$15 K and $n_{2D}=5\times 10^8÷10^{10}$ cm$^{-2}$, one deals with the Boltzmann liquid of the macroscopic thickness $\sim$100 A. Due to bending of…
Atomically-thin black phosphorus (BP) is an emerging two dimensional (2D) material exhibiting bright photoluminescence in the near infrared. Coupling its radiation to photonic nanostructures will be an important step toward the realization of 2D material based nanophotonic devices that operate efficiently in the near infrared, which includes the technologically important optical telecommunication wavelength bands. In this letter, we demonstrate the optical coupling between atomically-thin BP and a 2D photonic crystal nanocavity. We employed a home-build dry transfer apparatus for placing a thi…
When continued device scaling reaches the ultimate limit imposed by atoms, technology based on atomically precise structures is expected to emerge. Device fabrication will then require building blocks with identified atomic arrangements and assembly of the components without contamination. Here we report on a versatile dry transfer technique for deterministic placement of optical-quality carbon nanotubes. Single-crystalline anthracene is used as a medium which readily sublimes by mild heating, leaving behind clean nanotubes and thus enabling bright photoluminescence. We are able to position na…
2D abrupt nano-junctions blending sp-sp2 bonds on atomically precise heterostructures
Politecnico di Milano（米兰理工大学）；Università degli Studi di Milano（米兰大学）；INFN Sezione di Milano（意大利国家核物理研究所米兰分部）；Università di Pavia（帕维亚大学）；Università Degli Studi Di Padova（帕多瓦大学）；Instituto de Nanociencia y Materiales de Aragon (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所（INMA），西班牙国家科学研究委员会-萨拉戈萨大学）
The ability to modulate light at high speeds is of paramount importance for telecommunications, information processing, and medical imaging technologies. This has stimulated intense efforts to master optoelectronic switching at visible and near-infrared frequencies, although coping with current computer speeds in integrated architectures still remains a major challenge. As a partial success, midinfrared light modulation has been recently achieved through gating patterned graphene. Here we show that atomically thin noble metal nanoislands can extend optical modulation to the visible and near-in…
The article reviews recent progress in the theoretical understanding of near-field surface electromagnetic phenomena in pristine and atomically doped carbon nanotubes. The phenomena involving strong coupling effects are outlined. They are the optical absorption by single-walled carbon nanotubes doped with single atoms or ions in the frequency range close to the atomic transition frequency, the entanglement of the pair of atomic qubits strongly coupled to a common high-finesse surface photonic mode of the nanotube, and the optical response of the strongly coupled surface exciton-plasmon excitat…
Atomically thin semiconductors such as monolayer MoS2 and WS2 exhibit nonlinear exciton-exciton annihilation at notably low excitation densities (below ~10 excitons/um2 in MoS2). Here, we show that the density threshold at which annihilation occurs can be tuned by changing the underlying substrate. When the supporting substrate is changed from SiO2 to Al2O3 or SrTiO3, the rate constant for second-order exciton-exciton annihilation, k_XX [cm2/s], is reduced by one or two orders of magnitude, respectively. Using transient photoluminescence microscopy, we measure the effective room-temperature ex…
Raman scattering and photoluminescence spectroscopy are used to investigate the optical properties of single layer black phosphorus obtained by mechanical exfoliation of bulk crystals under an argon atmosphere. The Raman spectroscopy, performed in situ on the same flake as the photoluminescence measurements, demonstrates the single layer character of the investigated samples. The emission spectra, dominated by excitonic effects, display the expected in plane anisotropy. The emission energy depends on the type of substrate on which the flake is placed due to the different dielectric screening. …
There is a great interest in the scientific community to perform calorimetry on samples having mass in the nanogram range. A detailed knowledge of the energy (heat) exchange in the fast growing family of micro- and nano-systems could provide valuable information about the chemistry and physics at the nano-scale. The possibility to have an atomically flat thermal probe represents an added value, because it provides the unique opportunity to perform Scanning Probe Microscopy (SPM) together with calorimetry. Here we report the fabrication, characterization, and calibration of atomically flat, sin…
In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electron-hole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct-gap transition by …
The discovery of graphene some ten years ago was the first proof of a free-standing two-dimensional (2D) solid phase. Here, using quantum molecular dynamics simulations of nanoscale gold patches suspended in graphene pores, we predict the existence of an atomically thin, free-standing 2D liquid phase. The liquid phase, enabled by the exceptional planar stability of gold due to relativistic effects, demonstrates extreme fluxionality of metal nanostructures and opens possibilities for a variety of nanoscale phenomena.
We show that it is possible to deposit, by mechanical exfoliation on SiO2/Si wafers, atomically thin mica flakes down to a single monolayer thickness. The optical contrast of these mica flakes on top of a SiO2/Si substrate, which depends on their thickness, the illumination wavelength and the SiO2 substrate thickness, can be quantitatively accounted for by a Fresnel law based model. The preparation of atomically thin insulating crystalline sheets will enable the fabrication of ultrathin defect-free insulating substrates, dielectric barriers or planar electron tunneling junctions. Additionally,…
The dielectric environment of thin semiconductor nanowires can affect the charge transport properties inside the wire. In this work, it is shown that Coulomb impurity scattering inside thin nanowires can be damped strongly by coating the wire with a high-k dielectric. This will lead to an increase in the mobility of free charges inside the wire.
The monolithic integration of electromechanical transduction at the nanoscale with advanced CMOS is among the most important challenges of semiconductor electronic systems to leverage the multi-domain sensing, actuation, and resonance properties of nano-mechanical systems. Here we report on the demonstration of vibrating devices enabled by atomically engineered ferroelectric Hf0.5Zr0.5O2 thin films with a variety of mechanical resonance modes with frequencies (f0) between 340kHz - 13GHz and frequency-quality (Q) factor products (f0 x Q) up to 3.97 x 10^12. Experiments based on electrical and o…
The emergence of two-dimensional crystals has revolutionized modern solid-state physics. From a fundamental point of view, the enhancement of charge carrier correlations has sparked enormous research activities in the transport- and quantum optics communities. One of the most intriguing effects, in this regard, is the bosonic condensation and spontaneous coherence of many-particle complexes. Here, we find compelling evidence of bosonic condensation of exciton-polaritons emerging from an atomically thin crystal of MoSe2 embedded in a dielectric microcavity under optical pumping. The formation o…
Atomically Thin Amorphous Carbon with an Ultralow Dielectric Constant
National University of Singapore（新加坡国立大学）；Centre for Advanced 2D materials, National University of Singapore（新加坡国立大学二维材料中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；IKERBASQUE Basque Foundation for Science（伊克尔巴斯克巴斯克科学基金会）；Freie Universität Berlin（柏林自由大学）；Leibniz Institute for Solid State and Materials Research（莱布尼茨固体与材料研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）；Joint Laboratory “Functional Quantum Materials” at BESSY II（BESSY II功能量子材料联合实验室）；Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局材料研究与工程研究所）；Sanken, Osaka University（大阪大学三冈研究所）；Nanomaterials Research Institute, National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所纳米材料研究所）；Institute for Functional Intelligent Materials, National University of Singapore（新加坡国立大学功能智能材料研究所）
Atomically thin semiconductors have dimensions that are commensurate with critical feature sizes of future optoelectronic devices defined using electron/ion beam lithography. Robustness of their emergent optical and valleytronic properties is essential for typical exposure doses used during fabrication. Here, we explore how focused helium ion bombardment affects the intrinsic vibrational, luminescence and valleytronic properties of atomically thin MoS$_{2}$. By probing the disorder dependent vibrational response we deduce the interdefect distance by applying a phonon confinement model. We show…
Interfaces of dye molecules and two-dimensional transition metal dichalcogenides (TMDCs) combine strong molecular dipole excitations with high carrier mobilities in semiconductors. Förster type energy transfer is one key mechanism for the coupling between both constituents. We report microscopic calculations of a spectrally resolved Förster induced transition rate from dye molecules to a TMDC layer. Our approach is based on microscopic Bloch equations which are solved self-consistently together with Maxwells equations. This approach allows to incorporate the dielectric environment of a TMDC se…
Photonic integrated circuits are an enabling technology in modern communications systems. The continually increasing demands for higher-speed and lower operating power devices have resulted in the continued impetus to shrink photonic components. In this work, we demonstrate a primitive nanophotonic integrated circuit element composed of a single silver nanowire and single-layer molybdenum disulfide (MoS2) flake. We show that nanowire plasmons can excite MoS2 photoluminescence via direct plasmon-to-exciton conversion along the wire and plasmon-to-photon-to-exciton conversion at the MoS2-covered…
Mechanochemical Nano-Writing of an Atomically Thin Metal
University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）；Zhejiang University（浙江大学）；University of California Merced（加州大学默塞德分校）；National Institute for Materials Science（国立材料研究所）
Atomically thin boron nitride (BN) nanosheets have many properties desirable for surface enhanced Raman spectroscopy (SERS). BN nanosheets have a strong surface adsorption capability towards airborne hydrocarbon and aromatic molecules. For maximized adsorption area and hence SERS sensitivity, atomically thin BN nanosheet covered gold nanoparticles have been prepared for the first time. When placed on top of metal nanoparticles, atomically thin BN nanosheets closely follow their contours so that the plasmonic hot spots are retained. Electrically insulating BN nanosheets also act as a barrier la…
Recent advances in guiding and localizing light at the nanoscale exposed the enormous potential of ultra-scaled plasmonic devices. In this context, the decay of surface plasmons to hot carriers triggers a variety of applications in boosting the efficiency of energy-harvesting, photo-catalysis and photo-detection. However, a detailed understanding of plasmonic hot carrier generation and particularly the transfer at metal-semiconductor interfaces is still elusive. In this paper, we introduce a monolithic metal-semiconductor (Al-Ge) heterostructure device, providing a platform to examine surface …
Invariant ionic conductance in an atomically thin polar nanopore
National Key Laboratory of Advanced Micro and Nano Manufacture Technology, School of Integrated Circuits, Peking University（北京大学集成电路学院先进微纳制造技术国家重点实验室）；Academy for Advanced Interdisciplinary Studies and Center for Nanochemistry, Beijing Science and Engineering Center for Nanocarbons, Peking University（北京大学前沿交叉学科研究院纳米化学中心北京纳米碳科学与工程研究中心）；State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室）；Oden Institute for Computational Engineering and Sciences, Walker Department of Mechanical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校沃克机械工程系奥登计算工程与科学研究所）；School of Mechanics and Engineering Science, Peking University（北京大学力学与航空航天工程学院）；Beijing Advanced Innovation Center for Integrated Circuits（北京集成电路先进创新中心）；Beijing Graphene Institute（北京石墨烯研究院）
The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and SL fabrication processes, we address the intractable tradeoff betwe…
In this work we briefly review the studies of the optical constants of monolayer transition metal dichalcogenides and few layer black phosphorus, with particular emphasis to the complex dielectric function and refractive index. Specifically, we give an estimate of the complex index of refraction of phosphorene and few-layer black phosphorus. We extracted the complex index of refraction of this material from differential reflectance data reported in literature by employing a constrained Kramers-Kronig analysis. Finally, we studied the linear optical response of multilayer systems embedding phos…
We discuss the van der Waals (Casimir) free energies and pressures of thin metallic films, consisting from one to fifteen atomic layers, with regard to the anisotropy in their dielectric properties. Both free-standing films and films deposited on a dielectric substrate are considered. The computations are performed for a Au film and a sapphire substrate. According to our results, for free-standing Au films consisting of one and three atomic layers the respective relative error arising from the use of an isotropic (bulk) dielectric permittivity is equal to 73% and 37% for the van der Waals ener…
The ability to harness light-matter interactions at the few-photon level plays a pivotal role in quantum technologies. Single photons - the most elementary states of light - can be generated on-demand in atomic and solid state emitters. Two-photon states are also key quantum assets, but achieving them in individual emitters is challenging because their generation rate is much slower than competing one-photon processes. We demonstrate that atomically thin plasmonic nanostructures can harness two-photon spontaneous emission, resulting in giant far-field two-photon production, a wealth of resonan…
We measure the energy relaxation rate of single- and few-layer molybdenum disulphide ($\mathrm{MoS_2}$) nanomechanical resonators by detecting the resonator ring-down. Recent experiments on these devices show a remarkably low quality (Q)-factor when taking spectrum measurements at room temperature. The origin of the low spectral Q-factor is an open question, and it has been proposed that besides dissipative processes, frequency fluctuations contribute significantly to the resonance line-width. The spectral measurements performed thus far however, do not allow one to distinguish these two proce…
The electron transport properties of atomically thin semiconductors such as MoS2 have attracted significant recent scrutiny and controversy. In this work, the scattering mechanisms responsible for limiting the mobility of single layer semiconductors are evaluated. The roles of individual scattering rates are tracked as the 2D electron gas density is varied over orders of magnitude at various temperatures. From a comparative study of the individual scattering mechanisms, we conclude that all current reported values of mobilities in atomically thin transition-metal dichalcogenide semiconductors …
Atomically thin semiconductors such as transition metal dichalcogenide (TMD) monolayers exhibit a very strong Coulomb interaction, giving rise to a rich exciton landscape. This makes these materials highly attractive for efficient and tunable optoelectronic devices. In this article, we review the recent progress in the understanding of exciton optics, dynamics and transport, which crucially govern the operation of TMD-based devices. We highlight the impact of hBN-encapsulation, which reveals a plethora of many-particle states in optical spectra, and we outline the most novel breakthroughs in t…
Understanding and controlling the nanoscale transport of excitonic quasiparticles in atomically thin 2D semiconductors is crucial to produce highly efficient nano-excitonic devices. Here, we present a nano-gap device to selectively confine excitons or trions of 2D transition metal dichalcogenides at the nanoscale, facilitated by the drift-dominant exciton funnelling into the strain-induced local spot. We investigate the spatio-spectral characteristics of the funnelled excitons in a WSe2 monolayer (ML) and converted trions in a MoS2 ML using hyperspectral tip-enhanced photoluminescence (TEPL) i…
Plasmon-Enhanced Second-Harmonic Generation in Atomically Thin Crystalline Silver Nanostructures
ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院，维也纳量子科学与技术中心）；Center for Nanophotonics, NWO Institute AMOLF（纳米光子学中心，NWO AMOLF研究所）；Department of Physics, Dokuz Eylül University（德古兹埃勒大学物理系）；Centro de Física de Materiales CSIC-UPV/EHU and Materials Physics Center（CSIC-巴斯克国立大学物质物理学中心和材料物理中心）
To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the qu…
Two-dimensional (2D) semiconductors are promising channel materials for continued downscaling of complementary metal-oxide-semiconductor (CMOS) logic circuits. However, their full potential continues to be limited by a lack of scalable high-k dielectrics that can achieve atomically smooth interfaces, small equivalent oxide thicknesses (EOT), excellent gate control, and low leakage currents. Here, we report liquid metal printed ultrathin and scalable Ga2O3 dielectric for 2D electronics and electro-optical devices. We directly visualize the atomically smooth Ga2O3/WS2 interfaces enabled by the c…
The observation and electrical manipulation of infrared surface plasmons in graphene have triggered a search for similar photonic capabilities in other atomically thin materials that enable electrical modulation of light at visible and near-infrared frequencies, as well as strong interaction with optical quantum emitters. Here, we present a simple analytical description of the optical response of such kinds of structures, which we exploit to investigate their application to light modulation and quantum optics. Specifically, we show that plasmons in one-atom-thick noble-metal layers can be used…
Matter-wave interferometry has become an essential tool in studies on the foundations of quantum physics and for precision measurements. Mechanical gratings have played an important role as coherent beamsplitters for atoms, molecules and clusters since the basic diffraction mechanism is the same for all particles. However, polarizable objects may experience van der Waals shifts when they pass the grating walls and the undesired dephasing may prevent interferometry with massive objects. Here we explore how to minimize this perturbation by reducing the thickness of the diffraction mask to its ul…
