1
|
Gorbar EV, Gusynin VP, Parymuda MR. Reduced QED with Few Planes and Fermion Gap Generation. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1317. [PMID: 37761616 PMCID: PMC10528318 DOI: 10.3390/e25091317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 09/05/2023] [Accepted: 09/07/2023] [Indexed: 09/29/2023]
Abstract
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of a few atomically thick layers, and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to N planes and contains N vector fields with Maxwell's action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene.
Collapse
Affiliation(s)
- Eduard V. Gorbar
- Department of Physics, Taras Shevchenko National Kyiv University, 03022 Kyiv, Ukraine; (E.V.G.); (M.R.P.)
- Bogolyubov Institute for Theoretical Physics, 03143 Kyiv, Ukraine
| | | | - Maxim R. Parymuda
- Department of Physics, Taras Shevchenko National Kyiv University, 03022 Kyiv, Ukraine; (E.V.G.); (M.R.P.)
| |
Collapse
|
2
|
Yang ZK, Pan XY, Liu GZ. A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:075601. [PMID: 36541489 DOI: 10.1088/1361-648x/aca948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 12/06/2022] [Indexed: 06/17/2023]
Abstract
In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger (DS) integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the DS equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.
Collapse
Affiliation(s)
- Zhao-Kun Yang
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Xiao-Yin Pan
- Department of Physics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | - Guo-Zhu Liu
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| |
Collapse
|
3
|
Hirata M, Kobayashi A, Berthier C, Kanoda K. Interacting chiral electrons at the 2D Dirac points: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:036502. [PMID: 33059346 DOI: 10.1088/1361-6633/abc17c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 10/15/2020] [Indexed: 06/11/2023]
Abstract
The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)2I3, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)2I3. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)2I3, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)2I3. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.
Collapse
Affiliation(s)
- Michihiro Hirata
- Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan
- MPA-Q, Los Alamos National Laboratory, NM 87545, United States of America
| | - Akito Kobayashi
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Claude Berthier
- Laboratoire National des Champs Magnétiques Intenses, UPR 3228 CNRS, EMFL, UGA, UPS and INSA, Boite Postale 166, 38042 Grenoble Cedex 9, France
| | - Kazushi Kanoda
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
4
|
Yamada R, Fujioka J, Kawamura M, Sakai S, Hirayama M, Arita R, Okawa T, Hashizume D, Hoshino M, Tokura Y. Large Variation of Dirac Semimetal State in Perovskite CaIrO_{3} with Pressure-Tuning of Electron Correlation. PHYSICAL REVIEW LETTERS 2019; 123:216601. [PMID: 31809165 DOI: 10.1103/physrevlett.123.216601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 09/16/2019] [Indexed: 06/10/2023]
Abstract
The impact of electron correlation on the Dirac semimetal state is investigated for perovskite CaIrO_{3} in terms of the magnetotransport properties under varying pressures. The reduction of electron correlation with a pressure of 1 GPa enhances the Fermi velocity as much as 40%, but it reduces the mobility by an order of magnitude by detuning the Dirac node from the Fermi energy. Moreover, the giant magnetoresistance at the quantum limit due to the one-dimensional confinement of Dirac electrons is critically suppressed under pressure. These results indicate that the electron correlation is a crucial knob for controlling the transport of a correlated Dirac semimetal.
Collapse
Affiliation(s)
- R Yamada
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
| | - J Fujioka
- Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8577, Japan
| | - M Kawamura
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - S Sakai
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - M Hirayama
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - R Arita
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - T Okawa
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
| | - D Hashizume
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - M Hoshino
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Y Tokura
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
- Tokyo College, University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
5
|
Xu X, Liu C, Sun Z, Cao T, Zhang Z, Wang E, Liu Z, Liu K. Interfacial engineering in graphene bandgap. Chem Soc Rev 2018. [PMID: 29513306 DOI: 10.1039/c7cs00836h] [Citation(s) in RCA: 63] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.
Collapse
Affiliation(s)
- Xiaozhi Xu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China.
| | | | | | | | | | | | | | | |
Collapse
|
6
|
Hirata M, Ishikawa K, Matsuno G, Kobayashi A, Miyagawa K, Tamura M, Berthier C, Kanoda K. Anomalous spin correlations and excitonic instability of interacting 2D Weyl fermions. Science 2017; 358:1403-1406. [PMID: 29242340 DOI: 10.1126/science.aan5351] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Accepted: 11/14/2017] [Indexed: 11/02/2022]
Abstract
The Coulomb interaction in systems of quasi-relativistic massless electrons has an unscreened long-range component at variance with conventional correlated metals. We used nuclear magnetic resonance (NMR) measurements to reveal unusual spin correlations of two-dimensional Weyl fermions in an organic material, causing a divergent increase of the Korringa ratio by a factor of 1000 upon cooling, in marked contrast to conventional metallic behavior. Combined with model calculations, we show that this divergence stems from an interaction-driven velocity renormalization that almost exclusively suppresses zero-momentum spin fluctuations. At low temperatures, the NMR relaxation rate shows an unexpected increase; numerical analyses show that this increase corresponds to internode excitonic fluctuations, a precursor to a transition from massless to massive quasiparticles.
Collapse
Affiliation(s)
- Michihiro Hirata
- Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan. .,Deparment of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kyohei Ishikawa
- Deparment of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Genki Matsuno
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Akito Kobayashi
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Kazuya Miyagawa
- Deparment of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Masafumi Tamura
- Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Claude Berthier
- Laboratoire National des Champs Magnétique Intenses, LNCMI-CNRS (UPR3228), EMFL, UGA, UPS, and INSA, Boîte Postale 166, 38042 Grenoble Cedex 9, France
| | - Kazushi Kanoda
- Deparment of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan.
| |
Collapse
|
7
|
Abstract
Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons–electron–hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators. It has long been anticipated theoretically that semiconductors with small band gaps may form a correlated exciton insulator phase, but it has been difficult to find material realisations. Here, the authors predict numerically that zero-gap armchair carbon nanotubes could be exciton insulators.
Collapse
|
8
|
Thermodynamic signatures of the field-induced states of graphite. Nat Commun 2017; 8:1337. [PMID: 29116084 PMCID: PMC5677099 DOI: 10.1038/s41467-017-01394-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Accepted: 09/13/2017] [Indexed: 11/08/2022] Open
Abstract
When a magnetic field confines the carriers of a Fermi sea to their lowest Landau level, electron−electron interactions are expected to play a significant role in determining the electronic ground state. Graphite is known to host a sequence of magnetic field-induced states driven by such interactions. Three decades after their discovery, thermodynamic signatures of these instabilities are still elusive. Here we report the detection of these transitions with sound velocity measurements. The evolution of elastic constant anomalies with temperature and magnetic field allows to draw a detailed phase diagram which shows that the ground state evolves in a sequence of thermodynamic phase transitions. Our analysis indicates that the electron−electron interaction is not the sole driving force of these transitions and that lattice degrees of freedom play an important role. Previous transport studies of graphite in strong magnetic fields have found a sequence of phase transitions with a still unresolved microscopic origin. Here the authors present ultrasound measurements enabling sharper resolution and demonstrating the thermodynamic nature of these transitions.
Collapse
|
9
|
Downing CA, Portnoi ME. Bielectron vortices in two-dimensional Dirac semimetals. Nat Commun 2017; 8:897. [PMID: 29026126 PMCID: PMC5638912 DOI: 10.1038/s41467-017-00949-y] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 08/08/2017] [Indexed: 11/12/2022] Open
Abstract
Searching for new states of matter and unusual quasi-particles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasi-particles which are described by ultrarelativistic Dirac-like equations, are of a significant current interest from both a fundamental and applied physics perspective. Here we show that a pair of two-dimensional massless Dirac–Weyl fermions can form a bound state independently of the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler’s inverse distance law. This leads to the emergence of a new type of energetically favorable quasiparticle: bielectron vortices, which are double-charged and reside at zero-energy. Their bosonic nature allows for condensation and may give rise to Majorana physics without invoking a superconductor. These novel quasi-particles arguably explain a range of poorly understood experiments in gated graphene structures at low doping. Two-dimensional Dirac semimetals are known to host fermionic excitations which can mimic physics usually found in ultrarelativistic quantum mechanics. Here, the authors unveil the existence of another type of quasiparticle, bielectron vortices, which are bosonic and may give rise to new types of condensates.
Collapse
Affiliation(s)
- C A Downing
- Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, Strasbourg, F-67000, France. .,School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
| | - M E Portnoi
- School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK. .,International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal-RN, 59078-970, Brazil.
| |
Collapse
|
10
|
Xu D, Gao Y, Jiang W, Wang Z. Unusual spin-polarized electron state in fullerene induced by carbon adatom defect. NANOSCALE 2017; 9:7875-7879. [PMID: 28561094 DOI: 10.1039/c7nr02335a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
First-principles calculations show that a carbon adatom defect at the Def[5, 6] site on the surface of C60 can produce a more stable spin-polarized singlet electronic state instead of a magnetic triplet state. This is clearly different from the cases of graphene and nanotubes. The mechanism results from the electron population of the adatom, which produces antiferromagnetic coupling around the C60 cage and the adatom itself. Our calculations show the same phenomenon occurs in other IPR fullerenes, such as C70 and C80. These findings extend the understanding of the magnetic origin of pure carbon structures and are valuable for research related to the spin polarization of carbon systems.
Collapse
Affiliation(s)
- Dexuan Xu
- Institute of Atomic and Molecular Physics, Jilin University, Changchun, 130012, China.
| | | | | | | |
Collapse
|
11
|
Zhang CX, Qiu XG. Optical signatures of parity anomaly in a gapped graphene-like system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:205701. [PMID: 28322214 DOI: 10.1088/1361-648x/aa6804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Parity anomaly refers to the violation of coordinate reflection symmetry induced by the quantum fluctuations. It is proposed to exist in a graphene-like system with a finite bare mass for Dirac fermions, and manifests itself as a parity-violating quantum correction to the current of each species of fermions. Coulomb interaction greatly increases the fermion mass, and produces various types of excitons. Of particular interest is the ρ-exciton, which is directly connected to parity anomaly and can be generated by absorbing a specific photon. The exciton is a particle-hole bound state, and can be regarded as condensed-matter analogue of meson composed of quark-anti-quark pair. By virtue of this correspondence, we analyze the optical conductivity and calculate the mass of ρ-exciton by employing the Shifman-Vainshtein-Zakharov sum rule method that is widely used in the studies of hadron phenomenology. We show that ρ-exciton leads to a sharp peak in the optical conductivity, which is observable in optical experiments. Moreover, we study the impact of scalar-like excitons on two-photon processes by computing the decay amplitude, and also find peaks in the Raman spectra.
Collapse
Affiliation(s)
- C X Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
| | | |
Collapse
|
12
|
Zhu Z, McDonald RD, Shekhter A, Ramshaw BJ, Modic KA, Balakirev FF, Harrison N. Magnetic field tuning of an excitonic insulator between the weak and strong coupling regimes in quantum limit graphite. Sci Rep 2017; 7:1733. [PMID: 28496192 PMCID: PMC5431932 DOI: 10.1038/s41598-017-01693-5] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Accepted: 04/03/2017] [Indexed: 11/09/2022] Open
Abstract
The excitonic insulator phase has long been predicted to form in proximity to a band gap opening in the underlying band structure. The character of the pairing is conjectured to crossover from weak (BCS-like) to strong coupling (BEC-like) as the underlying band structure is tuned from the metallic to the insulating side of the gap opening. Here we report the high-magnetic field phase diagram of graphite to exhibit just such a crossover. By way of comprehensive angle-resolved magnetoresistance measurements, we demonstrate that the underlying band gap opening occurs inside the magnetic field-induced phase, paving the way for a systematic study of the BCS-BEC-like crossover by means of conventional condensed matter probes.
Collapse
Affiliation(s)
- Z Zhu
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA. .,Wuhan National High Magnetic Field Center, School of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074, Wuhan, China.
| | - R D McDonald
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
| | - A Shekhter
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul Dirac Dr., Tallahassee, Florida, 32310, USA
| | - B J Ramshaw
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853, USA
| | - K A Modic
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strape 40, Presden, 01187, Germany
| | - F F Balakirev
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
| | - N Harrison
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.
| |
Collapse
|
13
|
Isobe H, Yang BJ, Chubukov A, Schmalian J, Nagaosa N. Emergent Non-Fermi-Liquid at the Quantum Critical Point of a Topological Phase Transition in Two Dimensions. PHYSICAL REVIEW LETTERS 2016; 116:076803. [PMID: 26943551 DOI: 10.1103/physrevlett.116.076803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2015] [Indexed: 06/05/2023]
Abstract
We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.
Collapse
Affiliation(s)
- Hiroki Isobe
- Department of Applied Physics, University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
| | - Bohm-Jung Yang
- RIKEN Center for Emergence Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 151-747, Korea
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
| | - Andrey Chubukov
- William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Jörg Schmalian
- Institutes for Theory of Condensed Matter and for Solid State Physics, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
| | - Naoto Nagaosa
- Department of Applied Physics, University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergence Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| |
Collapse
|
14
|
Sun C, Figge F, Ozfidan I, Korkusinski M, Yan X, Li LS, Hawrylak P, McGuire JA. Biexciton Binding of Dirac fermions Confined in Colloidal Graphene Quantum Dots. NANO LETTERS 2015; 15:5472-5476. [PMID: 26192636 DOI: 10.1021/acs.nanolett.5b01888] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present transient absorption measurements and microscopic theory of biexciton binding in triangular colloidal graphene quantum dots consisting of 168 sp(2)-hybridized C atoms. We observe optical transitions from the lowest orbitally dark singlet exciton states to states below the energy of an unbound dark+bright singlet-exciton pair. Through microscopic calculations of the low-energy exciton and biexciton states via tight-binding, Hartree-Fock, and configuration interaction methods, the spectra reveal a biexciton consisting primarily of a dark-bright singlet-pair bound by ∼0.14 eV.
Collapse
Affiliation(s)
- Cheng Sun
- †Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| | - Florian Figge
- †Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| | - Isil Ozfidan
- §Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Marek Korkusinski
- ‡Quantum Theory Group, Security and Disruptive Technologies, Emerging Technologies Division, National Research Council of Canada, Ottawa, Ontario, K1A OR6 Canada
| | - Xin Yan
- ∥Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Liang-shi Li
- ∥Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Pawel Hawrylak
- §Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - John A McGuire
- †Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| |
Collapse
|
15
|
Wang JR, Liu GZ, Zhang CJ. Infrared behavior of dynamical fermion mass generation inQED3. Int J Clin Exp Med 2015. [DOI: 10.1103/physrevd.91.045006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
16
|
Black-Schaffer AM, Honerkamp C. Chiral d-wave superconductivity in doped graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:423201. [PMID: 25238054 DOI: 10.1088/0953-8984/26/42/423201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
A highly unconventional superconducting state with a spin-singlet dx2-y2+/-idxy-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss the multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review the means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.
Collapse
|
17
|
Current-Perpendicular-to-Plane Magnetoresistance in Chemical Vapor Deposition-Grown Multilayer Graphene. ELECTRONICS 2013. [DOI: 10.3390/electronics2030315] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
18
|
Li JF, Feng HT, Jiang Y, Sun WM, Zong HS. Calculation of the staggered spin correlation in the framework of the Dyson-Schwinger approach. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.87.116008] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
19
|
Mayorov AS, Elias DC, Mukhin IS, Morozov SV, Ponomarenko LA, Novoselov KS, Geim AK, Gorbachev RV. How close can one approach the Dirac point in graphene experimentally? NANO LETTERS 2012; 12:4629-4634. [PMID: 22935053 DOI: 10.1021/nl301922d] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10(6) cm(2) V(-1) s(-1) and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as ≈10(8) cm(-2), allowing a neutral state with a few charge carriers per entire micrometer-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap.
Collapse
Affiliation(s)
- Alexander S Mayorov
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
| | | | | | | | | | | | | | | |
Collapse
|
20
|
Trushin M, Schliemann J. Pseudospin in optical and transport properties of graphene. PHYSICAL REVIEW LETTERS 2011; 107:156801. [PMID: 22107311 DOI: 10.1103/physrevlett.107.156801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2011] [Indexed: 05/31/2023]
Abstract
We show that the pseudospin, being an additional degree of freedom for carriers in graphene, can be efficiently controlled by means of the electron-electron interactions which, in turn, can be manipulated by changing the substrate. In particular, an out-of-plane pseudospin component can occur leading to a zero-field Hall current as well as to polarization-sensitive interband optical absorption.
Collapse
Affiliation(s)
- Maxim Trushin
- Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany
| | | |
Collapse
|
21
|
Wang JR, Liu GZ. Eliashberg theory of excitonic insulating transition in graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:155602. [PMID: 21460428 DOI: 10.1088/0953-8984/23/15/155602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semi-metal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of the vacuum polarization function. Including the fermion gap into the polarization function increases the effective strength of the Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enhancement of the dynamical fermion gap in the excitonic insulating phase. The validity of the Eliashberg theory is justified by showing that the vertex corrections are suppressed at the large N limit.
Collapse
Affiliation(s)
- Jing-Rong Wang
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | | |
Collapse
|
22
|
Lozovik YE, Ogarkov SL, Sokolik AA. Electron-electron and electron-hole pairing in graphene structures. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:5417-5429. [PMID: 21041222 DOI: 10.1098/rsta.2010.0224] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The superconducting pairing of electrons in doped graphene owing to in-plane and out-of-plane phonons is considered. It is shown that the structure of the order parameter in the valley space substantially affects conditions of the pairing. Electron-hole pairing in a graphene bilayer in the strong coupling regime is also considered. Taking into account retardation of the screened Coulomb pairing potential shows a significant competition between the electron-hole direct attraction and their repulsion owing to virtual plasmons and single-particle excitations.
Collapse
Affiliation(s)
- Yu E Lozovik
- Institute of Spectroscopy, Russian Academy of Sciences, 142190 Troitsk, Moscow Region, Russia.
| | | | | |
Collapse
|
23
|
Destruction of quasi-Landau levels in nanographene ribbons by the external electric fields. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.06.080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
24
|
Wang J, Fertig HA, Murthy G. Critical behavior in graphene with Coulomb interactions. PHYSICAL REVIEW LETTERS 2010; 104:186401. [PMID: 20482192 DOI: 10.1103/physrevlett.104.186401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2009] [Indexed: 05/29/2023]
Abstract
We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.
Collapse
Affiliation(s)
- Jianhui Wang
- Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
| | | | | |
Collapse
|
25
|
Castro EV, Novoselov KS, Morozov SV, Peres NMR, Lopes dos Santos JMB, Nilsson J, Guinea F, Geim AK, Castro Neto AH. Electronic properties of a biased graphene bilayer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:175503. [PMID: 21393670 DOI: 10.1103/revmodphys.81.109] [Citation(s) in RCA: 5782] [Impact Index Per Article: 413.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.
Collapse
Affiliation(s)
- Eduardo V Castro
- CFP and Departamento de Física, Faculdade de Ciências Universidade do Porto, P-4169-007 Porto, Portugal
| | | | | | | | | | | | | | | | | |
Collapse
|
26
|
Nandkishore R, Levitov L. Dynamical screening and excitonic instability in bilayer graphene. PHYSICAL REVIEW LETTERS 2010; 104:156803. [PMID: 20482006 DOI: 10.1103/physrevlett.104.156803] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2009] [Revised: 12/11/2009] [Indexed: 05/29/2023]
Abstract
Electron interactions in undoped bilayer graphene lead to an instability of the gapless state, "which-layer" symmetry breaking, and energy gap opening at the Dirac point. In contrast with single-layer graphene, the bilayer system exhibits instability even for an arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full account of the dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.
Collapse
Affiliation(s)
- Rahul Nandkishore
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | | |
Collapse
|
27
|
|
28
|
|
29
|
Khveshchenko DV. Massive Dirac fermions in single-layer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:075303. [PMID: 21817324 DOI: 10.1088/0953-8984/21/7/075303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Motivated by the results of recent photoemission and tunneling studies, we discuss potential many-body sources of a finite gap in the Dirac fermion spectrum of graphene. Specifically, we focus on the putative Peierls- and Cooper-like pairing instabilities, which can be driven by sufficiently strong Coulomb and electron-phonon interactions, respectively. Our results compare favorably with the available experimental and Monte Carlo data.
Collapse
Affiliation(s)
- D V Khveshchenko
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, USA
| |
Collapse
|
30
|
Drut JE, Lähde TA. Is graphene in vacuum an insulator? PHYSICAL REVIEW LETTERS 2009; 102:026802. [PMID: 19257302 DOI: 10.1103/physrevlett.102.026802] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Indexed: 05/27/2023]
Abstract
We present evidence, from lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at alpha_{g};{crit}=1.11+/-0.06, where alpha_{g} approximately 2.16 in vacuum, and alpha_{g} approximately 0.79 on a SiO2 substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors 4<N_{f};{crit}<6. Our data are consistent with a second-order transition.
Collapse
Affiliation(s)
- Joaquín E Drut
- Department of Physics, The Ohio State University, Columbus, Ohio 43210-1117, USA
| | | |
Collapse
|
31
|
Li Z, Li G, Wang NL, Luo JL. The metal-insulator-like and insulator-metal-like behaviors in antimony. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:235232. [PMID: 21694323 DOI: 10.1088/0953-8984/20/23/235232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The resistivity and Hall resistivity of semimetallic antimony were measured from 2 to 300 K in magnetic fields up to 14 T. We found that in low field, the resistivity shows metallic behavior. In a modest field, the resistivity decreases to a minimum and then increases with decreasing temperature, showing a metal-insulator-like transition. In high field, the resistivity drops at low temperatures, showing an insulator-metal-like transition. The metal-insulator-like behavior can be explained by the competition of zero field resistivity and magneto-resistance, which is reciprocal to the zero field resistivity. The insulator-metal-like behavior can be explained by the imbalance of two carrier densities which changes the magneto-resistance from being reciprocal to proportional to the zero field resistivity.
Collapse
Affiliation(s)
- Z Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
| | | | | | | |
Collapse
|
32
|
Luk'yanchuk IA, Bratkovsky AM. Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field. PHYSICAL REVIEW LETTERS 2008; 100:176404. [PMID: 18518315 DOI: 10.1103/physrevlett.100.176404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2007] [Indexed: 05/26/2023]
Abstract
We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.
Collapse
Affiliation(s)
- Igor A Luk'yanchuk
- University of Picardie Jules Verne, Laboratory of Condensed Matter Physics, Amiens, 80039, France and L. D. Landau Institute for Theoretical Physics, Moscow, Russia
| | | |
Collapse
|
33
|
Gangadharaiah S, Farid AM, Mishchenko EG. Charge response function and a novel plasmon mode in graphene. PHYSICAL REVIEW LETTERS 2008; 100:166802. [PMID: 18518232 DOI: 10.1103/physrevlett.100.166802] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2007] [Indexed: 05/26/2023]
Abstract
Polarizability of noninteracting 2D Dirac electrons has a 1/square root(qv-omega) singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N-->infinity, where N is the "color" degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the nth order ladder term to the same order random phase approximation contribution is ln(n)|qv-omega|/N(n). We perform an analytical summation of the infinite series of ladder diagrams which describe the excitonic effect. Beyond the threshold, qv>omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.
Collapse
Affiliation(s)
- S Gangadharaiah
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
| | | | | |
Collapse
|
34
|
Honerkamp C. Density waves and cooper pairing on the honeycomb lattice. PHYSICAL REVIEW LETTERS 2008; 100:146404. [PMID: 18518058 DOI: 10.1103/physrevlett.100.146404] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2007] [Indexed: 05/26/2023]
Abstract
Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density-wave order. Away from half-filling, f-wave triplet-pairing and d + id singlet-pairing instabilities are found to emerge out of density-wave regimes.
Collapse
Affiliation(s)
- Carsten Honerkamp
- Theoretical Physics, Universität Würzburg, D-97074 Würzburg, Germany
| |
Collapse
|
35
|
Huang YC, Chang CP, Lin MF. Magnetic and quantum confinement effects on electronic and optical properties of graphene ribbons. NANOTECHNOLOGY 2007; 18:495401. [PMID: 20442470 DOI: 10.1088/0957-4484/18/49/495401] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Through the tight-binding calculation, we demonstrate that magnetic and quantum confinements have a great influence on the low-energy band structures of one-dimensional (1D) armchair graphene ribbons. The magnetic field first changes 1D parabolic bands into the Hall-edge states which originate in the Landau wavefunctions deformed by one or two ribbon edges. The quantum confinement dominates the characteristics of the Hall-edge states only when the Landau wavefunctions touch two ribbon edges. Then, some of the Hall-edge states evolve as the Landau states when the field strength grows. The partial flat bands (Landau levels), related to the Landau states, appear. The magnetic field dramatically modifies the energy dispersions and it changes the size of the bandgap, shifts the band-edge states, destroys the degeneracy of the energy bands, induces the semiconductor-metal transition and generates the partial flat bands. The above-mentioned magneto-electronic properties are completely reflected in the low-frequency absorption spectra--the shift of peak position, the change of peak symmetry, the alteration of peak height, the generation of new peaks and the change of absorption edges. As a result, there are magnetic-field-dependent absorption frequencies. The findings show that the magnetic field could be used to modulate the electronic properties and the absorption spectra.
Collapse
Affiliation(s)
- Y C Huang
- Department of Physics, National Cheng Kung University, 701 Tainan, Taiwan
| | | | | |
Collapse
|
36
|
Herbut IF. Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice. PHYSICAL REVIEW LETTERS 2007; 99:206404. [PMID: 18233168 DOI: 10.1103/physrevlett.99.206404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2007] [Indexed: 05/25/2023]
Abstract
The core of the vortex in the Néel order parameter for an easy-plane antiferromagnet on a honeycomb lattice is demonstrated to bind two zero-energy states. Remarkably, a single electron occupying this midgap band has its spin fragmented between the two sublattices: Whereas it yields a vanishing total magnetization, it shows a finite Néel order, orthogonal to the one of the assumed background. The requisite easy-plane anisotropy may be introduced by a magnetic field parallel to the graphene layer, for example. The results are relevant for spin-1/2 fermions on the graphene's or optical honeycomb lattice, in the strongly interacting regime.
Collapse
Affiliation(s)
- Igor F Herbut
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| |
Collapse
|
37
|
Jiang Z, Zhang Y, Stormer HL, Kim P. Quantum Hall states near the charge-neutral Dirac point in graphene. PHYSICAL REVIEW LETTERS 2007; 99:106802. [PMID: 17930402 DOI: 10.1103/physrevlett.99.106802] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2007] [Indexed: 05/25/2023]
Abstract
We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.
Collapse
Affiliation(s)
- Z Jiang
- Department of Physics, Columbia University, New York, New York 10027, USA.
| | | | | | | |
Collapse
|
38
|
Zhang Y, Talapatra S, Kar S, Vajtai R, Nayak SK, Ajayan PM. First-principles study of defect-induced magnetism in carbon. PHYSICAL REVIEW LETTERS 2007; 99:107201. [PMID: 17930406 DOI: 10.1103/physrevlett.99.107201] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2005] [Revised: 02/25/2007] [Indexed: 05/25/2023]
Abstract
We have studied the role of defects on the magnetic properties of carbon materials using first-principles density functional methods. We show that, while the total magnetization decreases both for diamond and graphite with increase in vacancy density, the magnetization decreases more rapidly for graphitic structures. The presence of nitrogen nearby a vacancy is shown to produce larger macroscopic magnetic signals as compared to a standalone carbon vacancy. The results indicate the possibility of tuning magnetization in carbon by controlled defect generation and doping.
Collapse
Affiliation(s)
- Y Zhang
- Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180-3590, USA
| | | | | | | | | | | |
Collapse
|
39
|
Abanin DA, Novoselov KS, Zeitler U, Lee PA, Geim AK, Levitov LS. Dissipative quantum hall effect in graphene near the Dirac point. PHYSICAL REVIEW LETTERS 2007; 98:196806. [PMID: 17677649 DOI: 10.1103/physrevlett.98.196806] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2007] [Indexed: 05/16/2023]
Abstract
We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.
Collapse
Affiliation(s)
- Dmitry A Abanin
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
| | | | | | | | | | | |
Collapse
|
40
|
Gusynin VP, Sharapov SG, Carbotte JP. Anomalous absorption line in the magneto-optical response of graphene. PHYSICAL REVIEW LETTERS 2007; 98:157402. [PMID: 17501382 DOI: 10.1103/physrevlett.98.157402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2006] [Indexed: 05/15/2023]
Abstract
The intensity as well as position in energy of the absorption lines in the infrared conductivity of graphene, both exhibit features that are directly related to the Dirac nature of its quasiparticles. We show that the evolution of the pattern of absorption lines as the chemical potential is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to this level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.
Collapse
Affiliation(s)
- V P Gusynin
- Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
| | | | | |
Collapse
|
41
|
Abstract
Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
Collapse
Affiliation(s)
- A K Geim
- Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | | |
Collapse
|
42
|
Luk'yanchuk IA, Kopelevich Y. Dirac and normal fermions in graphite and graphene: implications of the quantum Hall effect. PHYSICAL REVIEW LETTERS 2006; 97:256801. [PMID: 17280377 DOI: 10.1103/physrevlett.97.256801] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2006] [Indexed: 05/13/2023]
Abstract
Spectral analysis of the Shubnikov-de Haas magnetoresistance oscillations and the quantum Hall effect (QHE) measured in quasi-2D highly oriented pyrolytic graphite (HOPG) [Phys. Rev. Lett. 90, 156402 (2003)] reveals two types of carriers: normal (massive) electrons with Berry phase 0 and Dirac-like (massless) holes with Berry phase pi. We demonstrate that recently reported integer- and semi-integer QHEs for bilayer and single-layer graphenes take place simultaneously in HOPG samples.
Collapse
Affiliation(s)
- Igor A Luk'yanchuk
- Laboratory of Condensed Matter Physics, University of Picardie Jules Verne, Amiens 80039, France
| | | |
Collapse
|
43
|
Herbut IF. Interactions and phase transitions on graphene's honeycomb lattice. PHYSICAL REVIEW LETTERS 2006; 97:146401. [PMID: 17155272 DOI: 10.1103/physrevlett.97.146401] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2006] [Indexed: 05/12/2023]
Abstract
The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semimetal-antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and the magnetic field are discussed.
Collapse
Affiliation(s)
- Igor F Herbut
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| |
Collapse
|
44
|
Khveshchenko DV. Electron localization properties in graphene. PHYSICAL REVIEW LETTERS 2006; 97:036802. [PMID: 16907527 DOI: 10.1103/physrevlett.97.036802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2006] [Indexed: 05/11/2023]
Abstract
We study localization properties of the Dirac-like electronic states in monolayers of graphite. In the framework of a general disorder model, we discuss the conditions under which such standard localization effects as the logarithmic temperature-dependent conductivity correction appear to be strongly suppressed, as compared to the case of a two-dimensional electron gas with parabolic dispersion, in agreement with recent experimental observations.
Collapse
Affiliation(s)
- D V Khveshchenko
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| |
Collapse
|
45
|
Gusynin VP, Sharapov SG, Carbotte JP. Unusual microwave response of dirac quasiparticles in graphene. PHYSICAL REVIEW LETTERS 2006; 96:256802. [PMID: 16907333 DOI: 10.1103/physrevlett.96.256802] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2006] [Indexed: 05/06/2023]
Abstract
Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small, the intraband response can exhibit a cusp around zero frequency Omega and this unusual line shape changes to Drude-like by increasing the chemical potential |mu|, with width linear in mu. The interband contribution at T=0 is a constant independent of Omega with a lower cutoff at 2mu. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap Delta. At a large magnetic field B, the diagonal and Hall conductivities at small Omega become independent of B but remain nonzero and show a structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, E0 = +/-Delta, is field independent in sharp contrast to the conventional case.
Collapse
Affiliation(s)
- V P Gusynin
- Bogolyubov Institute for Theoretical Physics, Metrologicheskaya Street 14-b, Kiev, 03143, Ukraine
| | | | | |
Collapse
|
46
|
Gusynin VP, Sharapov SG. Unconventional integer quantum Hall effect in graphene. PHYSICAL REVIEW LETTERS 2005; 95:146801. [PMID: 16241680 DOI: 10.1103/physrevlett.95.146801] [Citation(s) in RCA: 242] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2005] [Indexed: 05/05/2023]
Abstract
Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.
Collapse
Affiliation(s)
- V P Gusynin
- Bogolyubov Institute for Theoretical Physics, Metrologicheskaya Street 14-b, Kiev, 03143, Ukraine.
| | | |
Collapse
|
47
|
Gorbar EV, Homayouni S, Miransky VA. Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories. Int J Clin Exp Med 2005. [DOI: 10.1103/physrevd.72.065014] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
48
|
Matsui T, Kambara H, Niimi Y, Tagami K, Tsukada M, Fukuyama H. STS observations of Landau levels at graphite surfaces. PHYSICAL REVIEW LETTERS 2005; 94:226403. [PMID: 16090417 DOI: 10.1103/physrevlett.94.226403] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2004] [Indexed: 05/03/2023]
Abstract
Scanning tunneling spectroscopy (STS) measurements were made on surfaces of two different kinds of graphite samples, Kish graphite and highly oriented pyrolytic graphite (HOPG), at very low temperatures and in high magnetic fields. We observed a series of peaks in the tunnel spectra associated with Landau quantization of the quasi-two-dimensional electrons and holes. A comparison with the calculated local density of states at the surface layers allows us to identify Kish graphite as bulk graphite and HOPG as graphite with a finite thickness of 40 layers. This explains the qualitative difference between the two graphites reported in the recent transport measurements which suggested the quantum-Hall effect in HOPG. This work demonstrates how powerful the combined approach between the high quality STS measurement and the first-principles calculation is in material science.
Collapse
Affiliation(s)
- T Matsui
- Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | | | | | | | | | | |
Collapse
|
49
|
Rontani M, Sham LJ. Coherent transport in a homojunction between an excitonic insulator and semimetal. PHYSICAL REVIEW LETTERS 2005; 94:186404. [PMID: 15904388 DOI: 10.1103/physrevlett.94.186404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2004] [Indexed: 05/02/2023]
Abstract
From the solution of a two-band model, we predict that the thermal and electrical transport across the junction of a semimetal and an excitonic insulator will exhibit high resistance behavior and low entropy production at low temperatures, distinct from a junction of a semimetal and a normal semiconductor. This phenomenon, ascribed to the dissipationless exciton flow which dominates over the charge transport, is based on the much longer length scale of the change of the effective interface potential for electron scattering due to the coherence of the condensate than in the normal state.
Collapse
Affiliation(s)
- Massimo Rontani
- INFM National Research Center on NanoStructures and BioSystems at Surfaces (S3), Via Campi 213/A, 41100 Modena, Italy
| | | |
Collapse
|
50
|
Zhang Y, Small JP, Amori MES, Kim P. Electric field modulation of galvanomagnetic properties of mesoscopic graphite. PHYSICAL REVIEW LETTERS 2005; 94:176803. [PMID: 15904325 DOI: 10.1103/physrevlett.94.176803] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2004] [Indexed: 05/02/2023]
Abstract
Electric field effect devices based on mesoscopic graphite are fabricated for galvanomagnetic measurements. Strong modulation of magnetoresistance and Hall resistance as a function of the gate voltage is observed as the sample thickness approaches the screening length. Electric field dependent Landau level formation is detected from Shubnikov-de Haas oscillations. The effective mass of electron and hole carriers has been measured from the temperature dependent behavior of these oscillations.
Collapse
Affiliation(s)
- Yuanbo Zhang
- Department of Physics and the Columbia Nanoscale Science and Engineering Center, Columbia University, New York, New York 10027, USA
| | | | | | | |
Collapse
|