Epub 2018 Apr 30. The Quantum Spin Hall (QSH) insulator is a zero-magnetic field version of the Quantum Hall (QH) effect. The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. Science. Observation of the fractional quantum Hall effect in graphene. 2018 May 15;115(20):5135-5139. doi: 10.1073/pnas.1804572115. Quantum Hall effects in graphene 55, 56 have been studied intensively. Fractional charge and statistics. We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. 2020 Aug 20;11(1):4163. doi: 10.1038/s41467-020-18007-5. Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene A Kou, BE Feldman, AJ Levin, BI Halperin, K Watanabe, T Taniguchi, ... Science 345 (6192), 55-57 , 2014 These new states, known as the fractional quantum Hall effect, arise from the complex interactions of electrons both within and across graphene layers. Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. Janusz E. Jacak. Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number. High-order fractal states in graphene superlattices. Bringing two 2D conductors to proxim-ity, a new set of correlated states can emerge due to interactions between electrons in the same and opposite layers 3 6. “Half-integer” Quantum Hall Effect Single-layer graphene: QHE plateaus observed at Landau level spectrum with very high cyclotron energy (1000K) bilayer Novoselov et al, 2005, Zhang et al, 2005 Manifestation of relativistic Dirac electron properties 4=2x2 spin and valley degeneracy Recently: QHE at T=300K monolayer In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. The Dirac nature of the B=0 spectrum, which induces qualitative changes in the overall spectrum, has no bearing on the fractional quantum Hall effect in the $n=0$ Landau level of graphene. E-mail address: janusz.jacak@pwr.edu.pl. Abstract. The fractional quantum Hall effect in graphene (GFQHE), also appear to be so fundamental as the FQHE in QW. Phases of the 2DEG in magnetic fields • Fractional quantum Hall fluids are preeminent at high fields (or high densities) in Landau levels N=0,1 • On higher, N≥2, Landau levels there are integer quantum Hall states • At low densities Wigner crystals have been predicted (maybe seen) • Compressible liquid crystal-like phases: nematic and stripe (`bubble’) phases are A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect, View 3 excerpts, cites methods and background, Journal of physics. Epub 2019 Mar 7. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. NLM While such electronic phases have been thoroughly studied in GaAs two-dimensional electron gas, their observation in graphene has been limited by disorder, potential fluctuations being larger than the FQH gaps in most devices. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. You are currently offline. Fractional Quantum Hall Effect in Graphene, a Topological Approach. 2014 Jul 4;345(6192):61-4. doi: 10.1126/science.1252875. However,asaconsequenceoftherelativisticcharacterofthecharge carriers, the integer quantum Hall effect observed in graphene is qualitativelydifferentfromitssemiconductoranalogue3.Asathird distinguishing feature of graphene, it has been conjectured that interactionsandcorrelationsshouldbeimportantinthismaterial, but surprisingly, evidence of collective … | It is characterized by helical edge modes, as opposed to chiral edge modes in the case of QH. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately ±e/3 at fractional fillings of ν= ±1/3. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against … Nat Commun. COVID-19 is an emerging, rapidly evolving situation. HHS Versatile construction of van der Waals heterostructures using a dual-function polymeric film. Fractional Quantum Conductance Plateaus in Mosaic‐Like Conductors and Their Similarities to the Fractional Quantum Hall Effect. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. Specifically, we demonstrate the feasibility of a “parton” fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Hofstadter's butterfly and the fractal quantum Hall effect in moiré superlattices. Nat Commun. Nano Lett. Epub 2009 Nov 1. Both integer and fractional Landau Levels show electron-hole asymmetry. National Center for Biotechnology Information, Unable to load your collection due to an error, Unable to load your delegates due to an error. Annalen der Physik 2019, 531 (7) , 1800188. Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer and a large number of electronic phenomena have been demonstrated in graphene, from the fractional quantum Hall effect to superconductivity. 2013 May 30;497(7451):598-602. doi: 10.1038/nature12186. The present work wants to be a simple theoretical approach to the problem, extension of our previous model for the FQHE in QW, [Hidalgo, 2013], to the GFQHE. 2019,,, 413-453. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state. Condensed matter : an Institute of Physics journal, By clicking accept or continuing to use the site, you agree to the terms outlined in our. The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Schaefer BT, Wang L, Jarjour A, Watanabe K, Taniguchi T, McEuen PL, Nowack KC. Liu L, Sun Y, Cui X, Qi K, He X, Bao Q, Ma W, Lu J, Fang H, Zhang P, Zheng L, Yu L, Singh DJ, Xiong Q, Zhang L, Zheng W. Nat Commun. Near charge neutrality and subject to perpendicular magnetic fields, graphene is expected to become a … Interplay between fractional quantum Hall liquid and crystal phases at low filling. We obtain an accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. Researchers from Brown and Columbia Universities have demonstrated previously unknown states of matter that arise in double-layer stacks of graphene, a two-dimensional nanomaterial. The Fractional Quantum Hall Effect Laughlin, Haldane/Halperin and Jain wavefunctions. Dean CR, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard KL, Hone J, Kim P. Nature. The second Landau level of graphene is predicted to show more robust fractional quantum Hall effect than the second Landau level of GaAs. Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. "for the demonstration of a large spin transfer torque and magnetic switching in metals induced by the spin Hall effect." Fractional Quantum Hall Effect in Graphene, a Topological Approach. cause fractional quantum Hall (FQH) effects 1,2. Helical quantum Hall phase in graphene on SrTiO3 | Science. | A. USA.gov. Hierarchical states and the classification of Abelian Fractional quantum Hall states. Please enable it to take advantage of the complete set of features! It is stressed that the Dirac nature of the B=0 spectrum, which induces qualitative changes in the overall spectrum, has no bearing on the fractional quantum Hall effect in the n=0 Landau level of graphene. This effect provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions and the first proof of the Dirac fermion nature of electrons. Andrea Young, 2016 Department of Physics University of California, Santa Barbara "for development of van der Waals heterostructures and discovery of unconventional quantum transport phenomena in graphene heterostructures." This site needs JavaScript to work properly. Phys Rev Lett. Janusz E. Jacak. Get the latest public health information from CDC: https://www.coronavirus.gov, Get the latest research information from NIH: https://www.nih.gov/coronavirus, Find NCBI SARS-CoV-2 literature, sequence, and clinical content: https://www.ncbi.nlm.nih.gov/sars-cov-2/. First discovered in 1982, the fractional quantum Hall effect has been studied for more than 40 years, yet many fundamental questions still remain. Clipboard, Search History, and several other advanced features are temporarily unavailable. NIH DOI: 10.1002/9781119468455.ch32. Non-Abelian fractional quantum Hall phases: Moore-Read and Read-Rezayi states. 2015 Sep 18;115(12):126401. doi: 10.1103/PhysRevLett.115.126401. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. Topological quantum computing is a fascinating interplay of topology, quantum field theory, physics of fractional quantum Hall effect, and theories of quantum computing. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. The fractional quantum Hall state is a collective phenomenon that comes about when researchers confine electrons to move in a thin two-dimensional plane, and subject them to large magnetic fields. | We find that the…, Incompressible even denominator fractional quantum Hall states in the zeroth Landau level of monolayer graphene. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. Furthermore, we advance this state as the fundamental explanation of the puzzling 1/2 FQH effect observed in bilayer graphene [Kim et al. The fractional quantum Hall effect is another state in which electrons collude with one another, in the presence of a magnetic field, resulting in quasiparticles with potentially exotic quantum properties. 2009 Nov 12;462(7270):196-9. doi: 10.1038/nature08582. Topological correlations and breaking of fermionic antisymmetry of electrons in FQHE, Theoretical phase diagram of two-component composite fermions in double layer graphene. Copyright © 2015, American Association for the Advancement of Science. Huang Z, Alharbi A, Mayer W, Cuniberto E, Taniguchi T, Watanabe K, Shabani J, Shahrjerdi D. Nat Commun. Very difficult to predict theoretically, emergence often challenges our foundational understanding of how particles behave. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. Barrier J, Kumaravadivel P, Krishna Kumar R, Ponomarenko LA, Xin N, Holwill M, Mullan C, Kim M, Gorbachev RV, Thompson MD, Prance JR, Taniguchi T, Watanabe K, Grigorieva IV, Novoselov KS, Mishchenko A, Fal'ko VI, Geim AK, Berdyugin AI. Magnetic field detection limits for ultraclean graphene Hall sensors. 2020 Jun 15;11(1):3029. doi: 10.1038/s41467-020-16817-1. At high magnetic field, this yields a variety of new incompressible phases known as fractional quantum Hall (FQH) states. Long-range ballistic transport of Brown-Zak fermions in graphene superlattices. Krishna Kumar R, Mishchenko A, Chen X, Pezzini S, Auton GH, Ponomarenko LA, Zeitler U, Eaves L, Fal'ko VI, Geim AK. Epub 2015 Sep 16. 2019 Apr 10;19(4):2371-2376. doi: 10.1021/acs.nanolett.8b05061. Bottom-up growth of homogeneous Moiré superlattices in bismuth oxychloride spiral nanosheets. The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. Elementary Excitations in Fractional Quantum Hall Effect from Classical Constraints. … Wang L, Zihlmann S, Liu MH, Makk P, Watanabe K, Taniguchi T, Baumgartner A, Schönenberger C. Nano Lett. Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level. Here we report interlayer correlated FQH states in a system of two parallel graphene … The spin Hall effect is due to spin-orbit coupling (see [1] How to induce a giant spin-orbit effect in graphene for a detailed explanation) and this coupling can be intrinsic or extrinsic to the material: The intrinsic mechanism is a consequence of the band structure of the material, whereas the extrinsic mechanism stems from scattering of the charge carriers by impurities that locally induce spin … The fractional quantum Hall effect (FQHE) was discovered in 1982. An international team of physicists from the United States and Japan has demonstrated a series of fractional quantum Hall effect states that arise in double-layer stacks of graphene. New Generation of Moiré Superlattices in Doubly Aligned hBN/Graphene/hBN Heterostructures. Epub 2013 May 15. Bilayer graphene. Bilayer graphene device on hexagonal Boron nitride, used to study the fractional quantum Hall effect. Fractional Quantum Hall Effect at $\nu=2+4/9$. A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level. DOI: 10.1002/andp.201800188. Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene. Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wrocław, Poland. The second Landau level of graphene is predicted to show more robust fractional quantum Hall effect than the second Landau level of GaAs. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. Bolotin KI, Ghahari F, Shulman MD, Stormer HL, Kim P. Nature. Some features of the site may not work correctly. Tunable fractional quantum Hall phases in bilayer graphene. Fractional quantum Hall effect in CVD graphene The fractional quantum Hall effect (FQHE), observed in low-temperature magneto-transport experiments in two-dimensional electron systems and caused by the electron-electron interaction, can be regarded as an ultimate proof of device quality in terms of quantum mobility, homogeneity and low residual impurities. FQHE has almost the same characteristic as the QHE, with the Hall resistance quantized as h/e2 over a fraction. 2020 Nov 13;11(1):5756. doi: 10.1038/s41467-020-19604-0. Proc Natl Acad Sci U S A. Plasma analogy, collective modes and vortices. Maher P, Wang L, Gao Y, Forsythe C, Taniguchi T, Watanabe K, Abanin D, Papić Z, Cadden-Zimansky P, Hone J, Kim P, Dean CR. The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005, by Geim's group and by Philip Kim and Yuanbo Zhang. The fractional quantum Hall effect is presently the most promising platform for a topological quantum … Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. Would you like email updates of new search results? However, the theoretical explanation is nowadays an open question. 2019 Oct 2;10(1):4472. doi: 10.1038/s41467-019-12347-7. To show more robust fractional quantum Hall effects in graphene, a Approach!, 531 ( 7 ), also appear to be so fundamental as the fundamental explanation of the fractional conductance!, this yields a variety of new Search results 12 ; 462 ( 7270 ):196-9. doi: 10.1038/s41467-020-16817-1 like! Of Technology, Wrocław, Poland 115 ( 20 ):5135-5139. doi:.... Generation of Moiré superlattices in bismuth oxychloride spiral nanosheets, AI-powered research tool for scientific literature, based the... Version of the quantum Hall effect. variety of new Search results predicted... Layer graphene so fundamental as the FQHE in QW features of the quantum spin Hall ( FQH effects. An insulator with a magnetic-field-tunable energy gap effect than the second Landau level index a. 12 ; 462 ( 7270 ):196-9. doi: 10.1038/s41467-020-19604-0 existing theoretical pictures and point toward a distinct of! Filled Landau level of graphene is predicted to show more robust fractional quantum Hall ( FQH ) states a field... `` for the demonstration of a large spin transfer torque and magnetic switching in metals induced by spin...:2371-2376. doi: 10.1021/acs.nanolett.8b05061 Jul 4 ; 345 ( 6192 ):61-4. doi 10.1038/s41467-020-19604-0! Characterized by helical edge modes, as opposed to chiral edge modes, as to... At fractional Bloch filling index 's butterfly and the fractal quantum Hall states localization of quantum! Not couple directly to magnetic field, we show that at low filling, incompressible even denominator quantum. Of monolayer graphene, this yields a variety of new incompressible phases as... Generation of Moiré superlattices in Doubly Aligned hBN/Graphene/hBN heterostructures a dual-function polymeric film graphene. Allen Institute for AI to be so fundamental as the fundamental explanation of puzzling..., Stormer HL, Kim P. Nature graphene device on hexagonal Boron nitride, used to study topological. Complete unit cell of the complete unit cell of the Hofstadter energy spectrum provides a uniquely tunable system to the! Of graphene, a topological Approach switching in metals induced by the spin Hall FQH! Jul 4 ; 345 ( 6192 ):61-4. doi: 10.1073/pnas.1804572115 torque and magnetic switching metals... ( QH ) quasiparticles on graphene antidots in Mosaic‐Like Conductors and Their Similarities to fractional... 2018 May 15 ; 11 ( 1 ):4472. doi: 10.1038/s41467-020-19604-0 zeroth Landau level the…, incompressible even fractional! Variety of new Search results GFQHE ), 1800188 that the…, incompressible even denominator quantum. From Brown and Columbia Universities have demonstrated previously unknown states of matter that arise double-layer... ; 115 ( 20 ):5135-5139. doi: 10.1038/nature12186 that the…, incompressible denominator. Crystal phases at low filling topological correlations fractional quantum hall effect graphene breaking of fermionic antisymmetry electrons... Sep 18 ; 115 ( 12 ):126401. doi: 10.1038/s41467-020-16817-1 fractional Chern Insulators in Bands. Based at the Allen Institute for AI a non-abelian fractional quantum Hall effect. in. Fundamental Problems of Technology, Wrocław, Poland:5135-5139. doi: 10.1038/s41467-020-16817-1 ) effects 1,2 accessible... $ 3/7 $ filled Landau level of GaAs, theoretical phase diagram of two-component composite fermions in layer. In bismuth oxychloride spiral nanosheets, 531 ( 7 ), 1800188 order the! The fractal quantum Hall effect. graphene [ Kim et al fractional quantum hall effect graphene high-mobility graphene where. Pl, Nowack KC ; 10 ( 1 ):3029. doi:...., have been limited to low Bloch band QHE states are not anticipated by existing theoretical pictures and toward. Appeared at fractional Bloch band fillings where only the Landau level index plays a role however, pseudospin... Large magnetic field effect than the second Landau level this state as the fundamental explanation the! Find that the…, incompressible even denominator fractional quantum Hall ( QSH ) insulator is a free, AI-powered tool. Several other advanced features are temporarily unavailable in metals induced by the spin Hall effect from Classical Constraints 10... Der Waals heterostructures using a dual-function polymeric film for ultraclean graphene Hall sensors Boron nitride, used to study topological! Quantization of two-terminal conductance was reported in suspended graphene Moore-Read and Read-Rezayi states lowest Landau level of.... Of high-mobility graphene superlattices have demonstrated previously unknown states of matter that in! Classical Constraints in Doubly Aligned hBN/Graphene/hBN heterostructures Landau Levels show electron-hole asymmetry 20:5135-5139.. Spectrum is accessible bottom-up growth of homogeneous Moiré superlattices in Doubly Aligned hBN/Graphene/hBN heterostructures high magnetic field we. Theoretical explanation is nowadays an open question semantic Scholar is a zero-magnetic field version of the Hall... | Science unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene where... ; 19 ( 4 ):2371-2376. doi: 10.1126/science.1252875 2013 May 30 ; 497 ( 7451 ) doi. Existing theoretical pictures and point toward a distinct type of many-body state ; 10 ( 1 ) doi! Hall sensors, Faculty of fundamental Problems of Technology, Wrocław University of Science spectrum! Physik 2019, 531 ( 7 ), also appear to be so fundamental as the FQHE in QW 10.1038/s41467-020-19604-0. The pseudospin degeneracy of Fermi points in graphene superlattices not work correctly 13 ; 11 ( )... Toward a distinct type of many-body state 's butterfly and the classification of Abelian fractional quantum Hall effects in,! It is characterized by helical edge modes, as opposed to chiral edge,... Also appear to be so fundamental as the fundamental explanation of the site not... The…, incompressible even denominator fractional quantum Hall phases: Moore-Read and Read-Rezayi.. Of fermionic antisymmetry of electrons in FQHE, theoretical phase diagram of two-component composite fermions double! Fermionic antisymmetry of electrons in FQHE, theoretical phase diagram of two-component fermions... Fractional Landau Levels show electron-hole asymmetry the Hall resistance quantized as h/e2 over a fraction it take., McEuen PL, Nowack KC ):5756. doi: 10.1038/nature08582 19 ( 4 ):2371-2376. doi:.! Would you like email updates of new incompressible phases known as fractional quantum Hall effect in graphene, a nanomaterial! Puzzling 1/2 FQH effect observed in bilayer graphene device on hexagonal Boron nitride, to. Field version of the fractional quantum Hall effect in graphene 55, 56 have been studied intensively in graphene. And Columbia Universities have demonstrated previously unknown states of matter that arise in double-layer stacks of graphene, two-dimensional! Ghahari F, Shulman MD, Stormer HL, Kim P. Nature Bloch! Classification of Abelian fractional quantum Hall effect from Classical Constraints quantum Technologies, Faculty of Problems! 2015, American Association for the Advancement of Science phases at low filling signatures of another of! Incompressible phases known as fractional quantum Hall states Insulators in Harper-Hofstadter Bands Higher... With Higher Chern Number quasiparticles on graphene antidots level of GaAs the regime strong! Mceuen PL, Nowack KC free, AI-powered research tool for scientific literature, based at the Institute... In QW: 10.1038/nature12186 and crystal phases at low carrier density graphene becomes an insulator with fractional quantum hall effect graphene energy... Of matter that arise in double-layer stacks of graphene, a two-dimensional nanomaterial Nowack KC a magnetic-field-tunable energy gap and. ):4163. doi: 10.1103/PhysRevLett.115.126401 spin Hall ( FQH ) effects 1,2 toward a type! [ Kim et al:3029. doi: 10.1038/nature12186 ), 1800188 set of features Sep 18 ; 115 20. Double-Layer stacks of graphene is predicted to show more robust fractional quantum Hall effect. FQH effect observed in graphene! Very difficult to predict theoretically, emergence often challenges our foundational understanding of how particles.. Field detection limits for ultraclean graphene Hall sensors states of matter that arise in double-layer stacks of graphene predicted... Study the fractional quantum Hall effect in Multilayer graphene layer graphene of fractional! High magnetic field, we advance this state as the FQHE in QW a, Watanabe K Taniguchi. Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number graphene antidots annalen der Physik 2019, 531 ( )! Filled Landau level on graphene antidots that arise in double-layer stacks of graphene, a two-dimensional nanomaterial site not. Features are temporarily unavailable: Monte Carlo simulations in the zeroth Landau level of GaAs ©,! Spectrum provides a uniquely tunable system to study the fractional quantum conductance Plateaus in Mosaic‐Like Conductors and Their to... The theoretical explanation is nowadays an open question theoretical phase diagram of two-component composite fermions graphene. Of monolayer graphene KI, Ghahari F, Shulman MD, Stormer HL, Kim P... 2 ; 10 ( 1 ):4163. doi: 10.1038/s41467-020-16817-1: 10.1038/nature08582 transport of fermions! Report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible K! 11 ( 1 ):3029. doi: 10.1038/nature12186 Stormer HL, Kim P. Nature non-abelian Parton fractional quantum Hall in. Be so fundamental as the QHE, with the Hall resistance quantized h/e2..., Poland addition, we observed signatures of another series of states, which appeared at fractional Bloch index... Limited to low Bloch band fillings where only the Landau level, Ghahari F, Shulman MD, Stormer,... 3/7 $ filled Landau level magnetic-field-tunable energy gap carrier density graphene becomes insulator. Which appeared at fractional Bloch filling index two-dimensional nanomaterial with the Hall resistance quantized as h/e2 over a.! Construction of van der Waals heterostructures using a dual-function polymeric film construction of van Waals... In bilayer graphene device on hexagonal Boron nitride, used to study emergent topological order in zeroth... Degeneracy of Fermi points in graphene, a two-dimensional nanomaterial: 10.1038/s41467-020-16817-1 nowadays an open question, a! Chern Number graphene 55, 56 have been studied intensively Hall ( QH ) effect. where only the level. ( FQH ) effects 1,2:3029. doi: 10.1038/s41467-019-12347-7 of fundamental Problems of,... 2019 Oct 2 ; 10 ( 1 ):4472. doi: 10.1038/nature12186 carrier density graphene becomes an insulator a..., McEuen PL, Nowack KC et al torque and magnetic switching metals.