1
|
Yang F, Hu ZY, Shao XH. First-principles study on tuning electronic and optical properties in graphene rotation on h-BN. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
|
2
|
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. Long-range ballistic transport of Brown-Zak fermions in graphene superlattices. Nat Commun 2020; 11:5756. [PMID: 33188210 PMCID: PMC7666116 DOI: 10.1038/s41467-020-19604-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 09/30/2020] [Indexed: 11/12/2022] Open
Abstract
In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (p/q) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 106 cm2 V−1 s−1 and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field. Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 106 cm2/V s and micrometer scale ballistic transport.
Collapse
Affiliation(s)
- Julien Barrier
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - Piranavan Kumaravadivel
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - Roshan Krishna Kumar
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - L A Ponomarenko
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,Department of Physics, University of Lancaster, Lancaster, LA1 4YW, UK
| | - Na Xin
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - Matthew Holwill
- National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - Ciaran Mullan
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK
| | - Minsoo Kim
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK
| | - R V Gorbachev
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - M D Thompson
- Department of Physics, University of Lancaster, Lancaster, LA1 4YW, UK
| | - J R Prance
- Department of Physics, University of Lancaster, Lancaster, LA1 4YW, UK
| | - T Taniguchi
- National Institute for Materials Science, Ibaraki, 305-0044, Japan
| | - K Watanabe
- National Institute for Materials Science, Ibaraki, 305-0044, Japan
| | - I V Grigorieva
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - K S Novoselov
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - A Mishchenko
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - V I Fal'ko
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK
| | - A K Geim
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK.
| | - A I Berdyugin
- Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK.
| |
Collapse
|
3
|
Anđelković M, Milovanović SP, Covaci L, Peeters FM. Double Moiré with a Twist: Supermoiré in Encapsulated Graphene. NANO LETTERS 2020; 20:979-988. [PMID: 31961161 DOI: 10.1021/acs.nanolett.9b04058] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called supermoiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the nonrelaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures.
Collapse
Affiliation(s)
- Miša Anđelković
- Departement Fysica , Universiteit Antwerpen , Groenenborgerlaan 171 , B-2020 Antwerpen , Belgium
| | - Slaviša P Milovanović
- Departement Fysica , Universiteit Antwerpen , Groenenborgerlaan 171 , B-2020 Antwerpen , Belgium
| | - Lucian Covaci
- Departement Fysica , Universiteit Antwerpen , Groenenborgerlaan 171 , B-2020 Antwerpen , Belgium
| | - François M Peeters
- Departement Fysica , Universiteit Antwerpen , Groenenborgerlaan 171 , B-2020 Antwerpen , Belgium
| |
Collapse
|
4
|
Abstract
Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here, we report magnetotransport measurements that reveal second-, third-, and fourth-order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band-structure calculations.
Collapse
|
5
|
Krishna Kumar R, Chen X, Auton GH, Mishchenko A, Bandurin DA, Morozov SV, Cao Y, Khestanova E, Ben Shalom M, Kretinin AV, Novoselov KS, Eaves L, Grigorieva IV, Ponomarenko LA, Fal'ko VI, Geim AK. High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices. Science 2018; 357:181-184. [PMID: 28706067 DOI: 10.1126/science.aal3357] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Accepted: 06/09/2017] [Indexed: 11/03/2022]
Abstract
Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work hints at unexplored physics in Hofstadter butterfly systems at high temperatures.
Collapse
Affiliation(s)
- R Krishna Kumar
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK.,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,Department of Physics, University of Lancaster, Lancaster LA1 4YW, UK
| | - X Chen
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - G H Auton
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - A Mishchenko
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - D A Bandurin
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - S V Morozov
- Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, Chernogolovka 142432, Russia.,National University of Science and Technology (MISiS), Moscow 119049, Russia
| | - Y Cao
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - E Khestanova
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - M Ben Shalom
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - A V Kretinin
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,School of Materials, University of Manchester, Manchester M13 9PL, UK
| | - K S Novoselov
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - L Eaves
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK.,School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - I V Grigorieva
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - L A Ponomarenko
- Department of Physics, University of Lancaster, Lancaster LA1 4YW, UK
| | - V I Fal'ko
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - A K Geim
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. .,National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| |
Collapse
|
6
|
Hu J, Rigosi AF, Lee JU, Lee HY, Yang Y, Liu CI, Elmquist RE, Newell DB. Quantum transport in graphene p-n junctions with moiré superlattice modulation. PHYSICAL REVIEW. B 2018; 98:10.1103/PhysRevB.98.045412. [PMID: 30997442 PMCID: PMC6463535 DOI: 10.1103/physrevb.98.045412] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present simulations of quantum transport in graphene p-n junctions (pnJs) in which moiré superlattice potentials are incorporated to demonstrate the interplay between pnJs and moiré superlattice potentials. It is shown that the longitudinal and Hall resistivity maps can be strongly modulated by the pnJ profile, junction height, and moiré potentials. Device resistance measurements are subsequently performed on graphene/hexagonal- boron-nitride heterostructure samples with accurate alignment of crystallographic orientations to complement and support the simulation results.
Collapse
Affiliation(s)
- Jiuning Hu
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Albert F. Rigosi
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
| | - Ji U. Lee
- College of Nanoscale Science and Engineering, State University of New York Polytechnic Institute, Albany, New York 12203, USA
| | - Hsin-Yen Lee
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
- Theiss Research, La Jolla, California 92037, USA
| | - Yanfei Yang
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Chieh-I Liu
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
- Graduate Institute of Applied Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Randolph E. Elmquist
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
| | - David B. Newell
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
| |
Collapse
|
7
|
Luo W, Chakraborty T. Excitation gap of fractal quantum hall states in graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:015801. [PMID: 26657089 DOI: 10.1088/0953-8984/28/1/015801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.
Collapse
Affiliation(s)
- Wenchen Luo
- Departement of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | | |
Collapse
|
8
|
Slotman GJ, van Wijk MM, Zhao PL, Fasolino A, Katsnelson MI, Yuan S. Effect of Structural Relaxation on the Electronic Structure of Graphene on Hexagonal Boron Nitride. PHYSICAL REVIEW LETTERS 2015; 115:186801. [PMID: 26565485 DOI: 10.1103/physrevlett.115.186801] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 06/05/2023]
Abstract
We performed calculations of electronic, optical, and transport properties of graphene on hexagonal boron nitride with realistic moiré patterns. The latter are produced by structural relaxation using a fully atomistic model. This relaxation turns out to be crucially important for electronic properties. We describe experimentally observed features such as additional Dirac points and the "Hofstadter butterfly" structure of energy levels in a magnetic field. We find that the electronic structure is sensitive to many-body renormalization of the local energy gap.
Collapse
Affiliation(s)
- G J Slotman
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
| | - M M van Wijk
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
| | - Pei-Liang Zhao
- Department of Applied Physics, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747AG Groningen, The Netherlands
| | - A Fasolino
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
| | - M I Katsnelson
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
| | - Shengjun Yuan
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
| |
Collapse
|