DOCSLIB.ORG

Magic of High-Order Van Hove Singularity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Magic of High-Order Van Hove Singularity Magic of high-order van Hove singularity The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Yuan, Noah F. Q. et al. "Magic of high-order van Hove singularity." Nature Communications 10, 1 (December 2019): 5769 © 2019 The Author(s) As Published http://dx.doi.org/10.1038/s41467-019-13670-9 Publisher Springer Science and Business Media Version Final published version Citable link https://hdl.handle.net/1721.1/126294 Terms of Use Creative Commons Attribution 4.0 International license Detailed Terms https://creativecommons.org/licenses/by/4.0/ ARTICLE https://doi.org/10.1038/s41467-019-13670-9 OPEN Magic of high-order van Hove singularity Noah F.Q. Yuan 1, Hiroki Isobe1 & Liang Fu1* The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove sin- gularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed. 1 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. *email: [email protected] NATURE COMMUNICATIONS | (2019) 10:5769 | https://doi.org/10.1038/s41467-019-13670-9 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13670-9 he recent discovery of unconventional insulating states and shifts to the Fermi level under gating (the corresponding density superconductivity in twisted bilayer graphene (TBG)1,2 has is within 10% of half filling), the VHS peak in tunneling density of T 45 fi attracted enormous interest. At ambient pressure, these states splits into two new peaks (see also ref. ). These ndings intriguing phenomena of correlated electrons only occur near a clearly demonstrate the prominent role of VHS in magic-angle specific twist angle θ 1:1, widely referred to as the magic TBG. However, it is also known from general consideration and angle. The existence of such a magic angle was first predicted previous STS measurements46–48 that VHS are present at all twist from band structure calculations. Based on a continuum model3,4, angles. It is therefore unclear whether VHS at magic angle is Bistritzer and MacDonald showed5 that the lowest moiré bands in anything special. TBG become exceptionally flat at this magic angle, and are hence In this work, we propose a new perspective that relates magic expected to exhibit strong electron correlation. This pioneering angle to a new type of VHS in the single-particle energy spectrum work inspired a large body of experimental works in recent years, of TBG. We show that as the twist angle decreases below a critical 1,2 θ — which culminated in the discovery reported in refs. The origin value c, the van Hove saddle point which marks the change of of magic-angle phenomena, i.e., the emergence of super- topology in Fermi surface (Lifshitz transition)—undergoes a conductivity and correlated insulator, is now under intensive topological transition whereby a single saddle point splits into 6–25 θ study . two new ones. Right at c, the saddle point changes from second- While the reduction of bandwidth is undoubtedly important, it order to higher-order; the DOS at VHS is significantly enhanced is evident that the phenomenology of magic-angle TBG cannot be from logarithmic to power-law divergence, which promises ascribed to a completely flat band. Quantum oscillation at low stronger electron correlation. We propose that proximity to such magnetic fields reveals doping-dependent Fermi surfaces within “high-order van Hove singularity”, which requires tuning to the the narrow moiré band. Detailed scanning tunneling spectroscopy critical twist angle or pressure, is an important factor responsible (STS) studies26–28 and compressibility measurements29 show that for correlated electron phenomena in TBG near half filling. the moiré bandwidth at a magic angle is a few tens of meV, larger We demonstrate by topological argument that high-order VHS than what previous calculations found5,30–35. Moreover, there is can be generally achieved by tuning the band structure with just a no direct evidence from existing STS measurements at various single control parameter. For TBG, besides twist angle, pressure fl can also induce superconductivity at a twist angle larger than twist angles that the moiré band is exceptionally at right at the magic angle (see also ref. 28). These experimental results moti- 1:1 49. By tracking the evolution of the moiré band with twist vated us to consider additional feature of electronic structure angle and pressure, we locate the high-order VHS in experi- which may create favorable condition for correlated electron mentally relevant parameter regime and predict its key feature, a phenomena in magic-angle TBG. distinctive asymmetric peak in DOS. This feature compares well One such feature is the van Hove singularity (VHS) in moiré with the experimentally observed VHS peak in magic-angle TBG, bands. The importance of VHS has already been recognized in as shown in Fig. 1. We also discuss the splitting of VHS peak by our theory of correlated TBG36,37 and related studies38–44 using nematic or density wave order. the weak coupling approach. Generally speaking, VHS with divergent density of states (DOS) in two-dimensional systems are Results associated with saddle points of energy dispersion in k space. Ordinary and high-order VHS. In two-dimensional (2D) elec- When a VHS is close to Fermi energy, the increased DOS tron systems with energy dispersion EðkÞ, an ordinary VHS with fi ampli es electron correlation, resulting in various ordering logarithmically diverging DOS occurs at a saddle point ks, instabilities, such as density wave and superconductivity at low determined by temperature36. Indeed, the two recent STS measurements on gate- 26,27 fi tunable TBG around magic angle nd that when the VHS ∇ ¼ ; ð Þ kE 0 and det D<0 1 a 50 b 45 95 40 90 35 85 30 80 × (nS) 25 c G (nS) 75 20 G+G 15 70 10 = 1.32≈√2 65 5 0 –60 –40 –20 0 20 40 60 1 2 4 6 8 10 E (meV) |E–Ev | (meV) Fig. 1 Theoretical fit to the tunneling conductance measurement26.aOpen circles are tunneling conductance G of twisted bilayer graphene at twist angle 1:10, and solid lines are fitting according to Eq. (5) with details given in the Supplementary Material Sec. I. Dashed lines denote singularity energies, ¼ : indicating the asymmetry of conductance peaks. b The peak at Ev 16 72 meVp plottedffiffiffi in logarithmic scales. Electron and hole sides of the peak fall into À = η ¼ : ¼ : two parallel lines with the same slope 1 4 and asymmetry ratio 1 32 2. The only parameter in b is the background offset Gc 57 6 nS. 2 NATURE COMMUNICATIONS | (2019) 10:5769 | https://doi.org/10.1038/s41467-019-13670-9 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13670-9 ARTICLE where D 1 ∂ ∂ E is the 2 ´ 2 Hessian matrix of E at k . Since D these VHS points in the vicinity of this transition is solely ij 2 i j s Λ is symmetric by definition, we can rotate the axes to diagonalize D governed by the local energy dispersion near 0. We now expand EðkÞ near Λ to higher orders: and Taylor expand the energy dispersion near ks as 0 E À E ¼Àαp2 þ βp2, where E is the VHS energy, the À ¼Àα 2 þ β 2 þ γ 2 þ κ 4 þ ¼ ; ð Þ v x y v E Ev p p p p p 3 ¼ À x y x y y momentum p k ks is measured from the saddle point, and Γ the coefficients Àα, β are the two eigenvalues of D with where px (py) is parallel (perpendicular) to M line. In the fi Λ Àαβ ¼ det D<0. This dispersion describes two pieces of Fermi expansion (3), rst-order terms vanish because 0 has by definition zero Fermi velocity. Moreover, only even power terms contours that intersect at the saddle point ks. It is known from a topological consideration that due to the periodicity of EðkÞ on of py are allowed because of the two-fold rotation symmetry of ð ; Þ the Brillouin zone (a torus), van Hove saddle points appear quite TBG, which acts within each valley and maps px py to generally in energy bands of two-dimensional materials50. ð ; À Þ γ κ px py . The third-order term and fourth-order term are We now introduce the concept of high-order VHS associated fi essential to describe the splitting of VHS across the transition, with a high-order saddle point de ned by the following condition: which we shall show below along with the relation to scaling properties. ∇ ¼ ¼ ; ð Þ kE 0 and det D 0 2 The behavior of VHS and Fermi contour of the energy dispersion (3) depends crucially on the sign of β. For β > 0, p ¼ 0 which imply αβ ¼ 0. There exist two types of high-order VHS. (i.e., Λ ) is an ordinary van Hove saddle point with logarithmic fi α ¼ β ¼ ¼ 0 The rst type corresponds to 0, i.e., D 0.
Load more

Recommended publications
  • Aluminene As Highly Hole Doped Graphene
    Aluminene as Highly Hole Doped Graphene C. Kamal,1 Aparna Chakrabarti,1 and Motohiko Ezawa2 1Indus Synchrotrons Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India 2Department of Applied Physics, University of Tokyo, Hongo 7-3-1, 113-8656, Japan Monolayer structures made up of purely one kind of atoms are fascinating. Many kinds of honeycomb systems including carbon, silicon, germanium, tin, phosphorus and arsenic have been shown to be stable. However, so far the structures are restricted to group IV and V elements. In this letter, we systematically investigate the stability of monolayer structures made up of aluminium, in four different geometric configurations (planar, buckled, puckered and triangular), by employing density functional theory based electronic structure calculation. Our results on cohesive energy and phonon dispersion predict that only planar honeycomb structure made up of aluminium is stable. We call it ”aluminene” according to the standard naming convention. It is a metal. Results of electronic band structure suggest that it may be regarded as a highly hole doped graphene. We also present the tight-binding model and the Dirac theory to discuss the electronic properties of aluminene. PACS numbers: 68.65.-k, 61.46.-w, 81.07.-b, 31.15.E-, 71.15.Mb Monolayer structures made up of purely one kind of atoms graphene. We also report the geometric and electronic prop- possess many novel properties different from their bulk coun- erties of aluminene with alkali metal (M = Li and Na) adsorp- terparts. The best example is graphene, which is a hon- tion. Further, we construct an 8-band tight-binding model and eycomb monolayer of carbon[1, 2].
    [Show full text]
  • Controlling a Van Hove Singularity and Fermi Surface Topology at a Complex Oxide Heterostructure Interface
    Lawrence Berkeley National Laboratory Recent Work Title Controlling a Van Hove singularity and Fermi surface topology at a complex oxide heterostructure interface. Permalink https://escholarship.org/uc/item/8gh642n7 Journal Nature communications, 10(1) ISSN 2041-1723 Authors Mori, Ryo Marshall, Patrick B Ahadi, Kaveh et al. Publication Date 2019-12-04 DOI 10.1038/s41467-019-13046-z Peer reviewed eScholarship.org Powered by the California Digital Library University of California ARTICLE https://doi.org/10.1038/s41467-019-13046-z OPEN Controlling a Van Hove singularity and Fermi surface topology at a complex oxide heterostructure interface Ryo Mori 1,2, Patrick B. Marshall3, Kaveh Ahadi3, Jonathan D. Denlinger4, Susanne Stemmer3 & Alessandra Lanzara1,5* 1234567890():,; The emergence of saddle-point Van Hove singularities (VHSs) in the density of states, accompanied by a change in Fermi surface topology, Lifshitz transition, constitutes an ideal ground for the emergence of different electronic phenomena, such as superconductivity, pseudo-gap, magnetism, and density waves. However, in most materials the Fermi level, EF,is too far from the VHS where the change of electronic topology takes place, making it difficult to reach with standard chemical doping or gating techniques. Here, we demonstrate that this scenario can be realized at the interface between a Mott insulator and a band insulator as a result of quantum confinement and correlation enhancement, and easily tuned by fine control of layer thickness and orbital occupancy. These results provide a tunable pathway for Fermi surface topology and VHS engineering of electronic phases. 1 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
    [Show full text]
  • Controlling a Van Hove Singularity and Fermi Surface Topology at a Complex Oxide Heterostructure Interface
    ARTICLE https://doi.org/10.1038/s41467-019-13046-z OPEN Controlling a Van Hove singularity and Fermi surface topology at a complex oxide heterostructure interface Ryo Mori 1,2, Patrick B. Marshall3, Kaveh Ahadi3, Jonathan D. Denlinger4, Susanne Stemmer3 & Alessandra Lanzara1,5* 1234567890():,; The emergence of saddle-point Van Hove singularities (VHSs) in the density of states, accompanied by a change in Fermi surface topology, Lifshitz transition, constitutes an ideal ground for the emergence of different electronic phenomena, such as superconductivity, pseudo-gap, magnetism, and density waves. However, in most materials the Fermi level, EF,is too far from the VHS where the change of electronic topology takes place, making it difficult to reach with standard chemical doping or gating techniques. Here, we demonstrate that this scenario can be realized at the interface between a Mott insulator and a band insulator as a result of quantum confinement and correlation enhancement, and easily tuned by fine control of layer thickness and orbital occupancy. These results provide a tunable pathway for Fermi surface topology and VHS engineering of electronic phases. 1 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 2 Applied Science & Technology, University of California, Berkeley, CA 94720, USA. 3 Materials Department, University of California, Santa Barbara, CA 93106-5050, USA. 4 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 5 Department of Physics, University of California, Berkeley, CA 94720, USA. *email: [email protected] NATURE COMMUNICATIONS | (2019) 10:5534 | https://doi.org/10.1038/s41467-019-13046-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13046-z uantum interactions at the interfaces between strongly The additional circular pockets at the BZ corner are present in 19,23 correlated materials trigger new emergent phenomena neither bulk SrTiO3 nor SmTiO3 .
    [Show full text]
  • Excitonic Density Wave and Spin-Valley Superfluid in Bilayer
    ARTICLE https://doi.org/10.1038/s41467-020-20802-z OPEN Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide ✉ ✉ Zhen Bi 1,2 & Liang Fu1 Artificial moiré superlattices in 2d van der Waals heterostructures are a new venue for realizing and controlling correlated electronic phenomena. Recently, twisted bilayer WSe2 emerged as a new robust moiré system hosting a correlated insulator at moiré half-filling over 1234567890():,; a range of twist angle. In this work, we present a theory of this insulating state as an excitonic density wave due to intervalley electron–hole pairing. We show that exciton condensation is strongly enhanced by a van Hove singularity near the Fermi level. Our theory explains the remarkable sensitivity of the insulating gap to the vertical electric field. In contrast, the gap is weakly reduced by a perpendicular magnetic field, with quadratic dependence at low field. The different responses to electric and magnetic field can be understood in terms of pair- breaking versus non-pair-breaking effects in a BCS analog of the system. We further predict superfluid spin transport in this electrical insulator, which can be detected by optical spin injection and spatial-temporal imaging. 1 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA. 2 Department of Physics, the Pennsylvania State University, ✉ University Park, PA, USA. email: [email protected]; [email protected] NATURE COMMUNICATIONS | (2021) 12:642 | https://doi.org/10.1038/s41467-020-20802-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-20802-z new era of band engineering and novel electronic phase of moiré bands in bilayer TMD originating from K and K0 valleys Adesign is promised by the discovery of moiré superlattices are decoupled at the single-particle level and treated separately in 2d van der Waals heterostructures.
    [Show full text]
  • The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove
    The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities Thesis by Tristan McKinney In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 Defended May 29, 2018 ii © 2018 Tristan McKinney ORCID: 0000-0003-2365-1810 All rights reserved except where otherwise noted To Mom iv ACKNOWLEDGEMENTS The limitations of my memory and stamina make it impossible to list here all who have guided, cajoled, and comforted me on the way to completing this work. I apologize to everyone I wrongfully forget. I would like to begin by thanking the generations of individuals who built and fought for a world where I can live and think freely. Without liberty, life is a hollow exercise in futility; with it, there is a chance for meaning. More personally, I deeply and sincerely thank my advisor, Anton Kapustin. His mentorship and insight has helped me understand a small part of the universe in a way no one else has, and that is an incomparable gift. I also owe a debt of gratitude to our collaborator Ira Rothstein for teaching me to question all assumptions and drill down to the bedrock of truth. I thank the members of my committee: Maria Spiropulu, for always looking out for me as if I were her own student; Mark Wise, for his open door and willingness to answer any question; and Olexei Motrunich, for his flexibility and helpful input. I was blessed with the opportunity to teach a number of delightfully intelligent students and to work with dedicated professors in our common goal of sharing knowledge.
    [Show full text]
  • Dutch Contributions to the Sixth International Congress of Slavicists Gratis Epub, Ebook
    DUTCH CONTRIBUTIONS TO THE SIXTH INTERNATIONAL CONGRESS OF SLAVICISTS GRATIS Auteur: none Aantal pagina's: none pagina's Verschijningsdatum: 1968-04-01 Uitgever: Walter De Gruyter EAN: 9783111031439 Taal: nl Link: Download hier Phonological characteristics of the Čakavian dialect of Kali on the island of Ugljan (1994) Van Hove singularities revisited. Beginning with the work of Hirsch and Scalapino the importance of ln 2 - Van Hove singularity in T c - enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle- particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit one bare charge is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel attraction and SDW repulsion and CDW attraction in the ph-channel. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. Leon Van Hove Léon Van Hove , eminent Belgian theoretical physicist and Research Director General of CERN from , died on 2 September, only eighteen months after a special symposium at CERN marked his 65th birthday and his formal retirement from the Organization to which he had contributed so much.
    [Show full text]
  • Overdoping Graphene Beyond the Van Hove Singularity
    PHYSICAL REVIEW LETTERS 125, 176403 (2020) Editors' Suggestion Featured in Physics Overdoping Graphene beyond the van Hove Singularity Philipp Rosenzweig ,1,* Hrag Karakachian ,1 Dmitry Marchenko ,2 Kathrin Küster ,1 and Ulrich Starke 1 1Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany 2Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, 12489 Berlin, Germany (Received 14 July 2020; accepted 9 September 2020; published 19 October 2020) At very high doping levels the van Hove singularity in the πà band of graphene becomes occupied and exotic ground states possibly emerge, driven by many-body interactions. Employing a combination of ytterbium intercalation and potassium adsorption, we n dope epitaxial graphene on silicon carbide past the πà van Hove singularity, up to a charge carrier density of 5.5 × 1014 cm−2. This regime marks the unambiguous completion of a Lifshitz transition in which the Fermi surface topology has evolved from two electron pockets into a giant hole pocket. Angle-resolved photoelectron spectroscopy confirms these changes to be driven by electronic structure renormalizations rather than a rigid band shift. Our results open up the previously unreachable beyond-van-Hove regime in the phase diagram of epitaxial graphene, thereby accessing an unexplored landscape of potential exotic phases in this prototype two-dimensional material. DOI: 10.1103/PhysRevLett.125.176403 Graphene, a honeycomb monolayer of carbon atoms, has complicated by the severe band structure renormalizations been extensively studied in view of its two-dimensional which have not been taken into account until recently [15]. (2D) massless Dirac fermions [1–5].
    [Show full text]
  • Arxiv:1901.05432V3 [Cond-Mat.Str-El] 11 May 2019
    Magic of high-order van Hove singularity Noah F. Q. Yuan, Hiroki Isobe, and Liang Fu Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA We introduce a new type of van Hove singularity in two dimensions, where a saddle point in momentum space is changed from second-order to high-order. Correspondingly, the density of states near such \high-order van Hove singularity" is significantly enhanced from logarithmic to power-law divergence, which promises stronger electron correlation effects. High-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moir´esuperlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. The recent discovery of unconventional insulating (a) 50 states and superconductivity in twisted bilayer graphene (b) 45 95 (TBG) [1, 2] has attracted enormous interest. At am- bient pressure, these intriguing phenomena of correlated 40 90 electrons only occur near a specific twist angle θ ≈ 1:1◦, 35 85 30 widely referred to as the magic angle. The existence of 80 (nS) such a magic angle was first predicted from band struc- 25 c G(nS) 75 ture calculations. Based on a continuum model [3, 4], 20 G+G Bistritzer and MacDonald showed [5] that the lowest 15 70 moir´ebands in TBG become exceptionally flat at this 10 =1.32 2 65 magic angle, and are hence expected to exhibit strong 5 electron correlation. This pioneering work inspired a 0 -60 -40 -20 0 20 40 60 1 2 4 6 8 10 large body of experimental works in recent years, which E(meV) |E-E |(meV) v culminated in the discovery reported in Ref.
    [Show full text]
  • Optical Spectroscopy of Graphene and Gold Nanostructures
    OPTICALSPECTROSCOPYOF GRAPHENEANDGOLDNANOSTRUCTURES Von der Fakultät für Mathematik, Physik und Informatik der Universität Bayreuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von daniela christiane wolf geb. Ullrich aus Nürtingen Universität Bayreuth 2016 prüfungsausschuss: Prof. Dr. Markus Lippitz (Erstgutachter) Prof. Dr. Jürgen Köhler (Zweitgutachter) Prof. Dr. Stephan Kümmel (Prüfungsvorsitz) Apl. Prof. Dr. Lothar Kador tag der einreichung: 02. März 2016 tag des kolloquiums: 29. Juni 2016 ABSTRACT This thesis covers two prominent material systems in the still emerging field of nano-optics. On the one hand, we study the optical properties of graphene, from a general point of view as well as under symmetry breaking induced by strain. On the other hand, we make use of the plasmonic properties of gold nanostructures and investigate the generated nonlinear signals on a local scale. With both systems being promising candidates for nanophotonic applications, a spectroscopic investigation is of utmost importance to gain a deeper under- standing of the interaction of these systems with light. Graphene’s band structure exhibits a saddle point, which gives rise to a unique optical response in the visible and ultraviolet wavelength regime. Assuming a discrete excitonic state in the vicinity of the saddle point, a classical Fano model based on interference between a continuum of states and the discrete state can be applied. It reproduces very well both lineshape and position of the measured spectrum even down to infrared wavelengths. After a discussion of the general optical properties, we study the influence of strain on graphene. Unlike most other modifications, strain breaks the symmetry of the lattice and the band structure and is hence predicted to induce profound changes in the optical spectrum.
    [Show full text]
  • Van Hove Singularities and Resonant Tunneling in Carbon Nanotubes
    Van Hove Singularities and Resonant Tunneling in Carbon Nanotubes I n a u g u r a l - D i s s e r t a t i o n zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakult¨at der Heinrich-Heine-Universit¨at Dusseldorf¨ vorgelegt von Sascha Hugle¨ aus Freiburg i. Br. April 2003 Referent: Prof. Dr. R. Egger Koreferent: Prof. Dr. H.-K. Janssen Tag der mundlic¨ hen Prufung:¨ 21.05.2003 Gedruckt mit der Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult¨at der Heinrich-Heine-Universit¨at Dusseldorf¨ \Im Lichte bereits erlangter Erkenntnis erscheint das glucklich¨ Erreichte fast wie selbstverst¨andlich, : : :. Aber das ahnungsvolle, Jahre w¨ahrende Suchen im Dunkeln mit seiner Abwechslung von Zuversicht und Ermattung und seinem endlichen Durchbrechen zur Wahrheit, das kennt nur, wer es selber erlebt hat." A. Einstein Contents Introduction 1 1 Carbon nanotubes 5 1.1 Growth and purification . 5 1.2 Crystallographic structure . 7 1.3 Electronic properties . 8 1.4 Differences between single- and multi-wall nanotubes . 13 1.5 Scanning tunneling microscopy/spectroscopy . 15 1.6 Applications . 17 2 Disordered multi-wall nanotubes 19 2.1 Disorder and dimensionality . 19 2.2 Low-energy theory for multi-wall nanotubes . 20 2.3 Disorder mechanisms . 22 2.3.1 General remarks . 22 2.3.2 Topological disorder and random vector potential . 23 2.3.3 Random chemical potential . 24 2.4 Diagrammatic perturbation theory . 24 2.4.1 Perturbation expansion for the Greens function . 25 2.4.2 Ensemble-averaging . 25 2.4.3 Self energy . 27 3 Van Hove singularities in disordered multi-wall nanotubes 29 3.1 Introduction .
    [Show full text]
  • Discovery of a Weak Topological Insulating State and Van Hove Singularity in Triclinic Rhbi2
    Physics and Astronomy Publications Physics and Astronomy 2020 Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2 Kyungchan Lee Iowa State University and Ames Laboratory, [email protected] Gunnar F. Lange TCM Group Lin-Lin Wang Iowa State University and Ames Laboratory, [email protected] Brinda Kuthanazhi Iowa State University and Ames Laboratory, [email protected] Thais V. Trevisan Iowa State University and Ames Laboratory, [email protected] See next page for additional authors Follow this and additional works at: https://lib.dr.iastate.edu/physastro_pubs Part of the Condensed Matter Physics Commons The complete bibliographic information for this item can be found at https://lib.dr.iastate.edu/physastro_pubs/715. For information on how to cite this item, please visit http://lib.dr.iastate.edu/howtocite.html. This Article is brought to you for free and open access by the Physics and Astronomy at Iowa State University Digital Repository. It has been accepted for inclusion in Physics and Astronomy Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2 Abstract Time reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected 'strong' TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficulto t match the experimental success of strong TIs.
    [Show full text]
  • Designing Singularities in Electronic Dispersions
    Designing singularities in electronic dispersions The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:39947204 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Designing singularities in electronic dispersions A dissertation presented by Oleksandr Shtyk to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts June 2018 © 2018 Oleksandr Shtyk All rights reserved. Dissertation Advisor: Author: Claudio Chamon Oleksandr Shtyk Designing singularities in electronic dispersions Abstract This dissertation is devoted to the study of singularities in electronic dispersions and their implications for electronic systems. First, we consider two-dimensional interacting electrons at a monkey saddle with ∝ 3 − 2 dispersion px 3px py. Such dispersion naturally arises as a singularity when three van Hove saddles merge in an elliptical umbilic elementary catastrophe and can be interpreted as a multicritical Lifshitz point. It can be realized in biased bilayer graphene and can be 3~2 identified by its signature Landau level behavior Em ∝ (Bm) and related oscillations in thermodynamic and transport properties, such as Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features.
    [Show full text]