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Articles de revues sur le sujet « Twistronics »

Auteur : Grafiati

Publié le 6 septembre 2023

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1

Hu, Guangwei, Cheng-Wei Qiu, and Andrea Alù. "Twistronics for photons: opinion." Optical Materials Express 11, no. 5 (2021): 1377. http://dx.doi.org/10.1364/ome.423521.

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Armghan, Ammar, Meshari Alsharari, Khaled Aliqab, Osamah Alsalman, Juveriya Parmar, and Shobhit K. Patel. "Graphene Twistronics: Tuning the Absorption Spectrum and Achieving Metamaterial Properties." Mathematics 11, no. 7 (2023): 1579. http://dx.doi.org/10.3390/math11071579.

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Graphene twistronics using multilayer graphene is presented in such a way that it provides a metamaterial effect. This manuscript also analyzes the prediction of behavior using machine learning. The metamaterial effect is achieved by twisting the graphene layers. Graphene twistronics is a new concept for changing the electrical and optical properties of bilayer graphene by applying a small angle twist between the layers. The angle twists of 5°, 10°, and 15° are analyzed for the proposed graphene twistronics design. Tuning in the absorption spectrum is achieved by applying small twists to the a

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3

Gardezi, S. Minhal, Harris Pirie, Stephen Carr, William Dorrell, and Jennifer E. Hoffman. "Simulating twistronics in acoustic metamaterials." 2D Materials 8, no. 3 (2021): 031002. http://dx.doi.org/10.1088/2053-1583/abf252.

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4

Wu, Di, Yi Pan, and Tai Min. "Twistronics in Graphene, from Transfer Assembly to Epitaxy." Applied Sciences 10, no. 14 (2020): 4690. http://dx.doi.org/10.3390/app10144690.

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The twistronics, which is arising from the moiré superlattice of the small angle between twisted bilayers of 2D materials like graphene, has attracted much attention in the field of 2D materials and condensed matter physics. The novel physical properties in such systems, like unconventional superconductivity, come from the dispersionless flat band that appears when the twist reaches some magic angles. By tuning the filling of the fourfold degeneracy flat bands, the desired effects are induced due to the strong correlation of the degenerated Bloch electrons. In this article, we review the twist

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5

Veerpal and Ajay. "Exotic Electronic Properties of Twisted Bilayer Graphene-Emergence of Twistronics." Journal of Physics: Conference Series 2518, no. 1 (2023): 012013. http://dx.doi.org/10.1088/1742-6596/2518/1/012013.

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Abstract In Twistronics we study the effect of relative twist between the layers of a material on the electronic properties of that layered materials. There are expected to be hundreds of layered materials which can give rise to thousands or even more layered materials with combination of layers and relative twist between the layers. There is a great possibility to encounter many exotic electronic properties in these rather less explored layered materials with relative twist between the layers. There is a lot to explore and understand, to unlock full potential of twistronics. A lot of theoreti

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6

Liu, Mengya, Liping Wang, and Gui Yu. "Developing Graphene‐Based Moiré Heterostructures for Twistronics." Advanced Science 9, no. 1 (2021): 2103170. http://dx.doi.org/10.1002/advs.202103170.

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Donaldson, Laurie. "Twistronics breakthrough on manipulation of 2D materials." Materials Today 44 (April 2021): 3–4. http://dx.doi.org/10.1016/j.mattod.2021.01.021.

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Kang, Peng, Wanting Zhang, Vincent Michaud-Rioux, Xin Wang, Jiangni Yun, and Hong Guo. "Twistronics in tensile strained bilayer black phosphorus." Nanoscale 12, no. 24 (2020): 12909–16. http://dx.doi.org/10.1039/d0nr02179b.

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9

Hennighausen, Zachariah, and Swastik Kar. "Twistronics: a turning point in 2D quantum materials." Electronic Structure 3, no. 1 (2021): 014004. http://dx.doi.org/10.1088/2516-1075/abd957.

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10

Ren, Ya-Ning, Yu Zhang, Yi-Wen Liu, and Lin He. "Twistronics in graphene-based van der Waals structures." Chinese Physics B 29, no. 11 (2020): 117303. http://dx.doi.org/10.1088/1674-1056/abbbe2.

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11

Craig, Steven R., Zhenglu Li, Jiawei Ruan, Steven G. Louie, and Chengzhi Shi. "Acoustic analog of twisted bilayer graphene." Journal of the Acoustical Society of America 151, no. 4 (2022): A130. http://dx.doi.org/10.1121/10.0010876.

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The emergence of twistronics in bilayer graphene has inspired the creation of new phononic structures that translate quantum effects into macro systems. Here, we introduce an acoustic analog of twisted bilayer graphene that is built with 3D-printed star arrays confined in a two-dimensional acoustic waveguide. The lattices on the top and bottom of the waveguide are coupled by spoof surface acoustic waves. Like its quantum counterpart, the twisting angle of the structure influences wave propagation within the system and its resulting band structures. In analytical models, full-wave simulations,

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12

Yang, Yaping, Jidong Li, Jun Yin, et al. "In situ manipulation of van der Waals heterostructures for twistronics." Science Advances 6, no. 49 (2020): eabd3655. http://dx.doi.org/10.1126/sciadv.abd3655.

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In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be markedly changed by a moiré pattern induced by twist angles between different layers. This process is referred to as twistronics, where the tuning of twist angle can be realized through mechanical manipulation of 2D materials. Here, we demonstrate an experimental technique that can achieve in situ dynamical rotation and manipulation of 2D materials in van der Waals heterostructures. Using this technique, we fabricated heterostructures where

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13

Kang, Peng. "Indirect-to-direct bandgap transition in bilayer InSe: roles of twistronics." 2D Materials 7, no. 2 (2020): 021002. http://dx.doi.org/10.1088/2053-1583/ab6707.

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14

Rakib, Tawfiqur, Pascal Pochet, Elif Ertekin, and Harley T. Johnson. "Moiré engineering in van der Waals heterostructures." Journal of Applied Physics 132, no. 12 (2022): 120901. http://dx.doi.org/10.1063/5.0105405.

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Isolated atomic planes can be assembled into a multilayer van der Waals (vdW) heterostructure in a precisely chosen sequence. These heterostructures feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way, due to a lattice mismatch or twist. This design-by-stacking has opened up the promising area of moiré engineering, a term that can be understood in two different perspectives, namely, (i) structural—engineering a moiré pattern by introducing twist, relative strain, or defects that affect the commensurability of the layers and (ii) functional—exploit

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15

Varma Sangani, L. D., R. S. Surya Kanthi, Pratap Chandra Adak, et al. "Facile deterministic cutting of 2D materials for twistronics using a tapered fibre scalpel." Nanotechnology 31, no. 32 (2020): 32LT02. http://dx.doi.org/10.1088/1361-6528/ab8b93.

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Brzhezinskaya, Maria, Oleg Kononenko, Victor Matveev, et al. "Engineering of Numerous Moiré Superlattices in Twisted Multilayer Graphene for Twistronics and Straintronics Applications." ACS Nano 15, no. 7 (2021): 12358–66. http://dx.doi.org/10.1021/acsnano.1c04286.

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17

Yves, Simon, Yu-Gui Peng, and Andrea Alù. "Topological Lifshitz transition in twisted hyperbolic acoustic metasurfaces." Applied Physics Letters 121, no. 12 (2022): 122201. http://dx.doi.org/10.1063/5.0107465.

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Acoustic metamaterials and metasurfaces have been explored in the past few years to realize a wide range of extreme responses for sound waves. As one remarkable phenomenon, extreme anisotropy and hyperbolic sound propagation are particularly challenging to realize compared to electromagnetic waves because of the scalar nature of airborne acoustics. In parallel, moiré superlattices and the rapidly expanding domain of twistronics have shown that large anisotropy combined with tailored geometrical rotations can enable tantalizing emerging phenomena, such as tailored phase transitions in metamater

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18

Araujo, Ravel de Moraes Telles, Juliana Zarpellon, and Dante Homero Mosca. "Unveiling ferromagnetism and antiferromagnetism in two dimensions at room temperature." Journal of Physics D: Applied Physics 55, no. 28 (2022): 283003. http://dx.doi.org/10.1088/1361-6463/ac60cd.

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Abstract The aim of this work is to present an overview and a critical discussion on two-dimensional materials and functional nanostructures exhibiting ferromagnetic and antiferromagnetic long-range ordering at or above room temperature (RT). We specially describe and discuss the series of results concerning two-dimensional magnetism originated from intrinsic and induced d magnetic moments in low-dimensional nanostructured materials. Selected materials showing two-dimensional magnetic properties close to RT are classified as atomic monolayers, natural and artificial van der Waals layers, magne

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19

Gangemi, Nicholas, Caleb F. Sieck, Joseph Vignola, et al. "Frequency-dependent surface wave suppression at the Dirac point of an acoustic graphene analog." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A362. http://dx.doi.org/10.1121/10.0019168.

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The dispersion of bound acoustic surface waves over hexagonal lattices of resonant cavities has been shown to be analogous to the dispersion of charge transport in carbon graphene. Of particular interest is the frequency range close to the acoustic Dirac point where novel physics is predicted to occur. In this study, we measure the dispersion curves of a single-layer acoustic graphene analogue with high resolution one-dimensional spatial scansand show how the curves can be suppressed (near and at the Dirac point) by strong variations in the impedance boundary conditions between the free field

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20

Chen, Yaoyao, Liwei Liu, Xuan Song, et al. "Twisted charge-density-wave patterns in bilayer 2D crystals and modulated electronic states." 2D Materials 9, no. 1 (2021): 014007. http://dx.doi.org/10.1088/2053-1583/ac427f.

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Abstract The twistronics of the atomic-thick two-dimensional (2D) van der Waals materials has opened a new venue to investigate the interlayer coupling. Till now, most studies focus on the twist of atomic lattices and the resulted moiré superstructures, while the reports about the twist of charge density waves (CDWs), the superstructures of which are from individual layers are limited. Here, using molecular beam epitaxy, we construct bilayer (BL) 1T-NbSe2 vertical structures. With high resolution scanning tunneling microscopy observations, we identify two cases of CDW twisted stacking with ato

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21

Xin, Kaiyao, Xingang Wang, Kasper Grove-Rasmussen, and Zhongming Wei. "Twist-angle two-dimensional superlattices and their application in (opto)electronics." Journal of Semiconductors 43, no. 1 (2022): 011001. http://dx.doi.org/10.1088/1674-4926/43/1/011001.

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Abstract Twist-angle two-dimensional systems, such as twisted bilayer graphene, twisted bilayer transition metal dichalcogenides, twisted bilayer phosphorene and their multilayer van der Waals heterostructures, exhibit novel and tunable properties due to the formation of Moiré superlattice and modulated Moiré bands. The review presents a brief venation on the development of “twistronics” and subsequent applications based on band engineering by twisting. Theoretical predictions followed by experimental realization of magic-angle bilayer graphene ignited the flame of investigation on the new fre

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22

Arturo Sánchez-Sánchez, Jesús, Montserrat Navarro-Espino, Yonatan Betancur-Ocampo, José Eduardo Barrios-Vargas, and Thomas Stegmann. "Steering the current flow in twisted bilayer graphene." Journal of Physics: Materials 5, no. 2 (2022): 024003. http://dx.doi.org/10.1088/2515-7639/ac4ae0.

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Abstract A nanoelectronic device made of twisted bilayer graphene (TBLG) is proposed to steer the direction of the current flow. The ballistic electron current, injected at one edge of the bottom layer, can be guided predominantly to one of the lateral edges of the top layer. The current is steered to the opposite lateral edge, if either the twist angle is reversed or the electrons are injected in the valence band instead of the conduction band, making it possible to control the current flow by electric gates. When both graphene layers are aligned, the current passes straight through the syste

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23

Zhou, Kun, Liya Wang, Ruijie Wang, Chengyuan Wang, and Chun Tang. "One Dimensional Twisted Van der Waals Structures Constructed by Self-Assembling Graphene Nanoribbons on Carbon Nanotubes." Materials 15, no. 22 (2022): 8220. http://dx.doi.org/10.3390/ma15228220.

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Twisted van der Waals heterostructures were recently found to possess unique physical properties, such as superconductivity in magic angle bilayer graphene. Owing to the nonhomogeneous stacking, the energy of twisted van der Waals heterostructures are often higher than their AA or AB stacking counterpart, therefore, fabricating such structures remains a great challenge in experiments. On the other hand, one dimensional (1D) coaxial van der Waals structures has less freedom to undergo phase transition, thus offer opportunity for fabricating the 1D cousin of twisted bilayer graphene. In this wor

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24

Shoaib, Hassan, Qing Peng, and Abduljabar Q. Alsayoud. "Atomic Insights into Fracture Characteristics of Twisted Tri-Layer Graphene." Crystals 11, no. 10 (2021): 1202. http://dx.doi.org/10.3390/cryst11101202.

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Graphene twistronics have recently gained significant attention due their superconductive behavior as a consequence of their tunable electronic properties. Although the electronic properties of twisted graphene have been extensively studied, the mechanical properties and integrity of twisted trilayer graphene (tTLG) under loading is still elusive. We investigated the fracture mechanics of tTLG with a twist angle of ±1.53° utilizing molecular dynamics simulation. This twist angle was chosen because it is known to exhibit highly superconductive behavior. The results indicate that tTLG does not p

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25

Enaldiev, V. V., F. Ferreira, S. J. Magorrian, and Vladimir I. Fal’ko. "Piezoelectric networks and ferroelectric domains in twistronic superlattices in WS2/MoS2 and WSe2/MoSe2 bilayers." 2D Materials 8, no. 2 (2021): 025030. http://dx.doi.org/10.1088/2053-1583/abdd92.

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Lei, Shiming, Jingjing Lin, Yanyu Jia, et al. "High mobility in a van der Waals layered antiferromagnetic metal." Science Advances 6, no. 6 (2020): eaay6407. http://dx.doi.org/10.1126/sciadv.aay6407.

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Van der Waals (vdW) materials with magnetic order have been heavily pursued for fundamental physics as well as for device design. Despite the rapid advances, so far, they are mainly insulating or semiconducting, and none of them has a high electronic mobility—a property that is rare in layered vdW materials in general. The realization of a high-mobility vdW material that also exhibits magnetic order would open the possibility for novel magnetic twistronic or spintronic devices. Here, we report very high carrier mobility in the layered vdW antiferromagnet GdTe3. The electron mobility is beyond

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27

McDonnell, Liam P., Jacob J. S. Viner, David A. Ruiz-Tijerina, et al. "Superposition of intra- and inter-layer excitons in twistronic MoSe2/WSe2 bilayers probed by resonant Raman scattering." 2D Materials 8, no. 3 (2021): 035009. http://dx.doi.org/10.1088/2053-1583/abe778.

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Enaldiev, Vladimir V., Fabio Ferreira, and Vladimir I. Fal’ko. "A Scalable Network Model for Electrically Tunable Ferroelectric Domain Structure in Twistronic Bilayers of Two-Dimensional Semiconductors." Nano Letters 22, no. 4 (2022): 1534–40. http://dx.doi.org/10.1021/acs.nanolett.1c04210.

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Ren, Lingling, and Baojuan Dong. "Ferroelectric Polarization in an h-BN-Encapsulated 30°-Twisted Bilayer–Graphene Heterostructure." Magnetochemistry 9, no. 5 (2023): 116. http://dx.doi.org/10.3390/magnetochemistry9050116.

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Recently, the emergent two-dimensional (2D) ferroelectric materials have provided new possibilities for the miniaturization of ferroelectric systems and the integration of novel 2D nano-electronic devices. In addition to the intrinsic ferroelectrics exfoliated from bulk, 2D heterostructures hybridized from electrically non-polarized van der Waals (vdW) materials have also been proven to be a promising platform for the construction of ferroelectricity. Here, we report 30° twisted bilayer–graphene (TBLG) incommensurate moiré superlattice encapsulated by hexagonal boron nitride (h-BN), in which r

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Nikitin, Alexey Y. "Photothermal twistronics." Nature Nanotechnology, March 29, 2021. http://dx.doi.org/10.1038/s41565-021-00890-8.

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Mizobata, William, José Sanches, Mathaus Penha, et al. "Atomic frustration-based twistronics." 2D Materials, September 16, 2021. http://dx.doi.org/10.1088/2053-1583/ac277f.

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32

Wu, Fengcheng, Rui-Xing Zhang, and Sankar Das Sarma. "Three-dimensional topological twistronics." Physical Review Research 2, no. 2 (2020). http://dx.doi.org/10.1103/physrevresearch.2.022010.

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Yu, Yun, Madeline Van Winkle, and D. Kwabena Bediako. "Tuning interfacial chemistry with twistronics." Trends in Chemistry, August 2022. http://dx.doi.org/10.1016/j.trechm.2022.07.003.

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34

Salamon, Tymoteusz, Alessio Celi, Ravindra W. Chhajlany, et al. "Simulating Twistronics without a Twist." Physical Review Letters 125, no. 3 (2020). http://dx.doi.org/10.1103/physrevlett.125.030504.

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35

Mullan, Ciaran, Sergey Slizovskiy, Jun Yin, et al. "Mixing of moiré-surface and bulk states in graphite." Nature, July 19, 2023. http://dx.doi.org/10.1038/s41586-023-06264-5.

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AbstractVan der Waals assembly enables the design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices1–9. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene10–12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures13–18 and Hofstadter’s butterfly spectra and Brown–Zak quantum oscillations in graphene superlattices19

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Angeli, Mattia, Gabriel R. Schleder, and Efthimios Kaxiras. "Twistronics of Janus transition metal dichalcogenide bilayers." Physical Review B 106, no. 23 (2022). http://dx.doi.org/10.1103/physrevb.106.235159.

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Song, Jizhe, and Mengtao Sun. "Challenging breaking thermoelectric performance limits by twistronics." Journal of Materials Chemistry A, 2023. http://dx.doi.org/10.1039/d3ta02283h.

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With today's scarce resources, the issue of energy conversion is of great concern. Thermoelectric materials are capable of converting thermal energy into electrical energy. Excellent figure of merit (ZT) requires...

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38

Yuan, Jiahao, Mengzhou Liao, Zhiheng Huang, et al. "Precisely controlling the twist angle of epitaxial MoS₂/graphene heterostructure by AFM tip manipulation." Chinese Physics B, May 23, 2022. http://dx.doi.org/10.1088/1674-1056/ac720e.

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Abstract Two-dimensional (2D) moiré materials have attracted a lot of attention and opened a new research frontier of twistronics due to their novel physical properties. Although great progress has been achieved, the inability to precisely and reproducibly manipulate the twist angle hinders the further development of twistronics. Here, we demonstrated an atomic force microscope (AFM) tip manipulation method to control the interlayer twist angle of epitaxial MoS2/graphene heterostructure with an ultra-high accuracy of below 0.1°. Furthermore, conductive AFM and spectroscopic characterizations w

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Hennighausen, Zachariah, and Swastik Kar. "Twistronics: A turning point in 2D quantum materials." Electronic Structure, January 7, 2021. http://dx.doi.org/10.1088/2516-1075/abd957.

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Liu, Diyi, Mitchell Luskin, and Stephen Carr. "Seeing moiré: Convolutional network learning applied to twistronics." Physical Review Research 4, no. 4 (2022). http://dx.doi.org/10.1103/physrevresearch.4.043224.

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Xie, Lingbin, Longlu Wang, Weiwei Zhao, Shujuan Liu, Wei Huang, and Qiang Zhao. "WS2 moiré superlattices derived from mechanical flexibility for hydrogen evolution reaction." Nature Communications 12, no. 1 (2021). http://dx.doi.org/10.1038/s41467-021-25381-1.

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AbstractThe discovery of moiré superlattices (MSLs) opened an era in the research of ‘twistronics’. Engineering MSLs and realizing unique emergent properties are key challenges. Herein, we demonstrate an effective synthetic strategy to fabricate MSLs based on mechanical flexibility of WS2 nanobelts by a facile one-step hydrothermal method. Unlike previous MSLs typically created through stacking monolayers together with complicated method, WS2 MSLs reported here could be obtained directly during synthesis of nanobelts driven by the mechanical instability. Emergent properties are found includin

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"Twistronics: A Recent Avenue in van der Waals Heterostructures." Proceedings International 2, no. 2 (2020): 44. http://dx.doi.org/10.33263/proceedings22.044044.

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Two-dimensional (2D) materials, the thinnest form of materials to ever occur in nature, have the potential to dramatically alter and revolutionize our material world. After the discovery of graphene, the most prominent representative of this class of materials, many other 2D crystals have been identified. Even if individual 2D materials own various interesting and unexpected properties, the stacking of such layers leads to ‘artificial vdW solids’ called van der Waals heterostructures (vdW HSs) that result in the emergence of new states of matter with novel functionalities. The vdW HSs not only

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Sachin, Saurav, Puja Kumari, Neelam Gupta, Shivani Rani, Subhasmita Kar, and Soumya Jyoti Ray. "Van der Waals twistronics in a MoS2/WS2 heterostructure." Computational Condensed Matter, March 2023, e00797. http://dx.doi.org/10.1016/j.cocom.2023.e00797.

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44

Ciarrocchi, Alberto, Fedele Tagarelli, Ahmet Avsar, and Andras Kis. "Excitonic devices with van der Waals heterostructures: valleytronics meets twistronics." Nature Reviews Materials, January 31, 2022. http://dx.doi.org/10.1038/s41578-021-00408-7.

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45

Nguyen, Viet-Hung, Xuan-Hoang Trinh, and Jean-Christophe Charlier. "Electronic properties of twisted multilayer graphene." Journal of Physics: Materials, May 3, 2022. http://dx.doi.org/10.1088/2515-7639/ac6c4a.

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Abstract Twisted bilayer graphene displays many fascinating properties that can be tuned by varying the relative angle (also called twist angle) between its monolayers. As a remarkable feature, both the electronic flat bands and the corresponding strong electron localization have been obtained at a specific "magic" angle (~ 1.1°), leading to the observation of several strongly correlated electronic phenomena. Such a discovery has hence inspired the creation of a novel research field called twistronics, i.e., aiming to explore novel physical properties in vertically stacked 2D structures when t

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Mannaï, Marwa, and Sonia Haddad. "Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides." Physical Review B 103, no. 20 (2021). http://dx.doi.org/10.1103/physrevb.103.l201112.

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47

Salamon, Tymoteusz, Ravindra W. Chhajlany, Alexandre Dauphin, Maciej Lewenstein, and Debraj Rakshit. "Quantum anomalous Hall phase in synthetic bilayers via twistronics without a twist." Physical Review B 102, no. 23 (2020). http://dx.doi.org/10.1103/physrevb.102.235126.

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48

Miranda, Hudson, Vitor Monken, João Luiz Campos, et al. "Establishing the excitation field in tip-enhanced Raman spectroscopy to study nanostructures within two-dimensional systems." 2D Materials, October 8, 2022. http://dx.doi.org/10.1088/2053-1583/ac988f.

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Abstract The optical field generated by a nanoplasmonic probe is revealed in tip-enhanced Raman spectroscopy – TERS – experiments. The TERS intensity profile of nano-objects smaller than the probe’s apex has a donut-like shape which resembles the magnitude of the field generated by a point-dipole source, being well described by the Dyadic Green’s function. Having prior knowledge on the excitation field generated by the TERS probe, we measured the width of shear solitons caused by lattice reconstruction in low-angle twisted bilayer graphene, a prominent platform for twistronics, and the extend

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49

Alvarado, Miguel, and Alfredo Levy Yeyati. "2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation." SciPost Physics 13, no. 1 (2022). http://dx.doi.org/10.21468/scipostphys.13.1.009.

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Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lat

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David, Alessandro, Péter Rakyta, Andor Kormányos, and Guido Burkard. "Induced spin-orbit coupling in twisted graphene–transition metal dichalcogenide heterobilayers: Twistronics meets spintronics." Physical Review B 100, no. 8 (2019). http://dx.doi.org/10.1103/physrevb.100.085412.

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