DOCSLIB.ORG

Topological Insulators: Electronic Structure, Material Systems and Its Applications

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Topological Insulators: Electronic Structure, Material Systems and Its Applications Network for Computational Nanotechnology UC Berkeley, Univ. of Illinois, Norfolk(NCN) State, Northwestern, Purdue, UTEP Topological Insulators: Electronic structure, material systems and its applications Parijat Sengupta Network for Computational Nanotechnology Electrical and Computer Engineering Purdue University Complete set of slides from my final PhD defense Advisor : Prof. Gerhard Klimeck A new addition to the metal-insulator classification Nature, Vol. 464, 11 March, 2010 Surface states Metal Trivial Insulator Topological Insulator 2 2 Tracing the roots of topological insulator The Hall effect of 1869 is a start point How does the Hall resistance behave for a 2D set-up under low temperature and high magnetic field (The Quantum Hall Effect) ? 3 The Quantum Hall Plateau ne2 = σ xy h h = 26kΩ e2 Hall Conductance is quantized B Cyclotron motion Landau Levels eB E = ω (n + 1 ), ω = , n = 0,1,2,... n c 2 c mc 4 Plateau and the edge states Ext. B field Landau Levels Skipping orbits along the edge Skipping orbits induce a gapless edge mode along the sample boundary Question: Are edge states possible without external B field ? 5 Is there a crystal attribute that can substitute an external B field Spin orbit Interaction : Internal B field 1. Momentum dependent force, analogous to B field 2. Opposite force for opposite spins 3. Energy ± µ B depends on electronic spin 4. Spin-orbit strongly enhanced for atoms of large atomic number Fundamental difference lies under a Time Reversal Symmetric Operation Time Reversal Symmetry Violation 1. Quantum Hall 2. Intrinsic B field 6 Quantum Hall effect with spin-dependent B field Two copies of the Quantum Hall Effect The Quantum Hall effect had skipping orbits induced edge states What is the counterpart in the case of a spin dependent B field ? 7 The edge/surface states… We need to produce this Normal Insulator Robust if they are bound to the surface Every material possesses these surface states but they are fragile to perturbation and disorder Key question : How to generate a bound surface state ? 8 Step 1) for bound surface states – A zero gap material Zero gap semiconductor Positive gap semiconductor * 9 *These notations are valid only for ZB crystals Step 2) Inversion of the zero gap material If HgTe is confined – the band gap splits from its zero value to a negative band gap semiconductor Normal ordered material Inverted ordered material Bands of opposite parity (p like band and s like band) interchange their relative positions. 10 Step 3) Contact with a “normal” band-gap ordered material Interface Region II Region I Band-gap is > 0 Band-gap is < 0 E E k k Normal ordered material Inverted ordered material There must be a state that closes the band-gap (band-gap = 0) for a continuous transition from region I to region II 11 Experimental observations: Surface states of Bi2Se3 * Surface state are usually probed using ARPES -1 k (A ) Bi2Se3 has inverted band order at Γ and is in contact with normal-ordered vacuum 12 * Angle Resolved Photoemission spectroscopy The TRIM points Before we proceed, some basic facts about band structure theory If both space inversion and time reversal symmetry are simultaneously fulfilled, then the following holds There are certain special points on the Brillouin zone where equation (3) is always true Such points are known as Time Reversal Invariant Momenta Points (TRIM) 13 TRIM points 14 How does the band structure appear at the TRIM points ? Trivial Insulator Topological Insulator 15 Topology The key concept is of smooth deformation : But a sphere cannot be transformed in to a donut without scooping Sphere can be transformed in to an cuboid material out of it! A coffee mug in to a donut Sphere and donut belong to two different classes Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything. 16 Topology and electron bands Cond band Valence band Band-gap > 0 is preserved Band-gap changes from + to - Smooth deformation Not a smooth deformation Positive band-gap and negative band-gap material belong to two different topological classes! 17 Topology and electron bands Cond band Valence band Must proceed as A B A Band-gap closing B Two topologically inequivalent classes A and B cannot be continuously deformed in to one another. A connection state must be present. Which compounds exhibit topological insulator behaviour? 18 Naturally available topological insulators Bi2Te3 , Bi2Se3 , Sb2Te3 are topological insulators: Robust states on the surface under room temperature conditions Bi2Te 3 Quintuple layer ordered as Te(1) - Bi(1) -Te(2) - Bi(1) - Te(1) Te Bi Inequivalent Te atom serves as Te centre of inversion Bi Te quintuple layer quintuple These belong to the class of 3D topological insulators 19 Engineered topological insulators Topological insulators with protected states on the edge of a quantum well CdTe/HgTe/CdTe quantum well heterostructure (zinc-blende) GaSb/InAs quantum well heterostructure (zinc-blende) These are known as 2D topological insulators 20 Numerical modeling of 3D topological insulators Dispersion obtained through ARPES* sp3d5s* tight binding calculation Surf. states Six quintuple layer (~6.0 nm) Bi2Te 3 quantum well Stable surface states (SS) in the mid-gap region 21 *Rev of Mod. Phys, Vol 82, Oct-Dec 2010 Validation: Reproducing experimental Fermi surface warping Fermi surface Energy [eV] Energy [eV] k [nm-1] Similar warping of iso-energetic Bi2Te 3 surfaces has been observed in ARPES measurements. Numerical calculations performed with 20-band tight binding model 22 Surface states in a six quintuple layered quantum well (6.0 nm) Bi2Te 3 Bi2Se3 Sb2Te 3 Band structure of 3D topological insulators with 4-band k.p model* How do k.p calculations compare to tight binding? 23 Hamiltonian for the surface state The surface states are characterized by a linear Hamiltonian given as vpf()σσ xy− yx p 3 The next higher order term that satisfies C3v symmetry must be k 33 vf(σσ xy p− yx p )( ++ λ kk+− ) σz What this means is that as we move away from the Γ point, higher order terms dominate Experimentally proven through ARPES* *Physical Review Letters, 104(1):016401, Jan 2010 24 Comparing k.p to tight binding for 3D TIs Energy contour with modified k.p 3 Energy contour with 20-band tight binding that includes higher order k terms Fermi surface [eV] sp3d5s* tight binding gives correct Fermi- k.p can correctly predict energies close to surface warping Full symmetry the Γ point. Full crystal symmetry absent! (including higher order terms) included in the Hamiltonian 25 Common electronic structure trait in 2D and 3D TIs Both 2D and 3D TIs are narrow band-gap compounds with high spin-orbit coupling Spin-orbit coupling induces band inversion necessary for a TI Question : Any other intrinsic mechanism like so-coupling that can invert bands? Broken gap devices yield inverted band order 26 Is there any other crystal attribute that can invert bands? Spin-orbit coupling which inverts bands is effectively an internal magnetic field Question: Can electric field similarly invert bands? Commonly used wurtzite-based nitride crystals are moderate ferroelectrics Possesses an internal polarization (electric) field : A crystal property Wurtzite belongs to hexagonal crystal lattice system with two inter-penetrating hcp lattices c/a = (8/3)1/2 This ratio has curious properties 27 Spontaneous polarization in Wurtzite crystal • In ideal wurtzite crystal the c/a ratio = (8/3)1/2 • In real wurtzite crystal this ratio is altered - The X-N (X = Al, Ga, In) bond along c-axis is deformed leading to a net dipole moment • The dipoles cancel in bulk but remain at the surface Unit Cell of Wurtzite XN Purple = X (Al, Ga, In) Green = N Spontaneous Polarization due to crystal asymmetry in wurtzite 28 Schematic showing operation of internal E-field in nitrides* 1. To invert the band order internal electric field must be maximized 2. Piezoelectric field is stronger than spontaneous polarization 3. A strong piezo field needs a large strain 4. InN grown on GaN has large strain (~11 % lattice mismatch) 5. InN is a narrow band-gap material 29 *Journal of Applied Phys. Vol.85, 3222 (1999) The GaN-InN-GaN system Ec = 3.4 eV GaN and InN are lattice mismatched by ~11 % 2.2 eV Large piezoelectric constants result in strong internal electric field GaN InN 0.7 eV Spontaneous polarization is closely matched Less 0.5 eV significant Ga-faced Ev = 0 Straddling : Type-I heterojunction GaN Psp Fixed charge potential GaN is relaxed. InN is biaxially strained (compressive) InN Psp Ppz GaN Psp Spontaneous and piezoelectric polarization field GaN/InN/GaN produces large built-in fields Potential drop in InN well = 3.827 V 30 What can this large electric field do? The large electric field alters the position of the band edges For instance: Gradient of band edges due to built-in electric field of a p-n junction E Similar trend for the band-edge position of c Vbi the InN region Ef p-type E n-type Potential drop v Ec1 in InN well Ev1 The conduction Ec 1 band edge has fallen below the Ev1 valence band Coordinate position of InN well edge Creation of a broken-gap heterostructure 31 8-band k.p electronic structure calculations σ Geometry 1 Construction HH=++(88x ) Vsp+ pz H strain E1 GaN σ H = Eff. Hamiltonian Structure 2 Relaxation E2 InN Strain is computed with the Bir- σ 3 Strain E3 GaN Pikus def. potentials σ Electrostatics 4 σσ= (GaN ) εσ11E = 1 1 sp Hamiltonian Construction σσ=−++GaN σ InN σ ε2EE 2−= εσ 11 2 2 sp ( ) sp ( ) pz Eigen Solver εε13EE−= 22 σ 3 σσ32= − = Interface charge σ i Single Particle Electric field outside the Energies σσ41= − structure is set to zero and ε are dielectric const.
Load more

Recommended publications
  • Edge States in Topological Magnon Insulators
    PHYSICAL REVIEW B 90, 024412 (2014) Edge states in topological magnon insulators Alexander Mook,1 Jurgen¨ Henk,2 and Ingrid Mertig1,2 1Max-Planck-Institut fur¨ Mikrostrukturphysik, D-06120 Halle (Saale), Germany 2Institut fur¨ Physik, Martin-Luther-Universitat¨ Halle-Wittenberg, D-06099 Halle (Saale), Germany (Received 15 May 2014; revised manuscript received 27 June 2014; published 18 July 2014) For magnons, the Dzyaloshinskii-Moriya interaction accounts for spin-orbit interaction and causes a nontrivial topology that allows for topological magnon insulators. In this theoretical investigation we present the bulk- boundary correspondence for magnonic kagome lattices by studying the edge magnons calculated by a Green function renormalization technique. Our analysis explains the sign of the transverse thermal conductivity of the magnon Hall effect in terms of topological edge modes and their propagation direction. The hybridization of topologically trivial with nontrivial edge modes enlarges the period in reciprocal space of the latter, which is explained by the topology of the involved modes. DOI: 10.1103/PhysRevB.90.024412 PACS number(s): 66.70.−f, 75.30.−m, 75.47.−m, 85.75.−d I. INTRODUCTION modes causes a doubling of the period of the latter in reciprocal space. Understanding the physics of electronic topological in- The paper is organized as follows. In Sec. II we sketch the sulators has developed enormously over the past 30 years: quantum-mechanical description of magnons in kagome lat- spin-orbit interaction induces band inversions and, thus, yields tices (Sec. II A), Berry curvature and Chern number (Sec. II B), nonzero topological invariants as well as edge states that are and the Green function renormalization method for calculating protected by symmetry [1–3].
    [Show full text]
  • Topological Insulators Physicsworld.Com Topological Insulators This Newly Discovered Phase of Matter Has Become One of the Hottest Topics in Condensed-Matter Physics
    Feature: Topological insulators physicsworld.com Topological insulators This newly discovered phase of matter has become one of the hottest topics in condensed-matter physics. It is hard to understand – there is no denying it – but take a deep breath, as Charles Kane and Joel Moore are here to explain what all the fuss is about Charles Kane is a As anyone with a healthy fear of sticking their fingers celebrated by the 2010 Nobel prize – that inspired these professor of physics into a plug socket will know, the behaviour of electrons new ideas about topology. at the University of in different materials varies dramatically. The first But only when topological insulators were discov- Pennsylvania. “electronic phases” of matter to be defined were the ered experimentally in 2007 did the attention of the Joel Moore is an electrical conductor and insulator, and then came the condensed-matter-physics community become firmly associate professor semiconductor, the magnet and more exotic phases focused on this new class of materials. A related topo- of physics at University of such as the superconductor. Recent work has, how- logical property known as the quantum Hall effect had California, Berkeley ever, now uncovered a new electronic phase called a already been found in 2D ribbons in the early 1980s, and a faculty scientist topological insulator. Putting the name to one side for but the discovery of the first example of a 3D topologi- at the Lawrence now, the meaning of which will become clear later, cal phase reignited that earlier interest. Given that the Berkeley National what is really getting everyone excited is the behaviour 3D topological insulators are fairly standard bulk semi- Laboratory, of materials in this phase.
    [Show full text]
  • On the Topological Immunity of Corner States in Two-Dimensional Crystalline Insulators ✉ Guido Van Miert1 and Carmine Ortix 1,2
    www.nature.com/npjquantmats ARTICLE OPEN On the topological immunity of corner states in two-dimensional crystalline insulators ✉ Guido van Miert1 and Carmine Ortix 1,2 A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero- dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragile: the kagome lattice does not realize a higher-order topological insulator. We support this finding by introducing a criterion based on a corner charge-mode correspondence for the presence of topological midgap corner modes in n-fold rotational symmetric chiral insulators that explicitly precludes the existence of a HOTI protected by a threefold rotational symmetry. npj Quantum Materials (2020) 5:63 ; https://doi.org/10.1038/s41535-020-00265-7 INTRODUCTION a manifestation of the crystalline topology of the D − 1 edge 1234567890():,; Topology and geometry find many applications in contemporary rather than of the bulk: the corresponding insulating phases have physics, ranging from anomalies in gauge theories to string been recently dubbed as boundary-obstructed topological 38 theory. In condensed matter physics, topology is used to classify phases and do not represent genuine (higher-order) topological defects in nematic crystals, characterize magnetic skyrmions, and phases.
    [Show full text]
  • A Topological Insulator Surface Under Strong Coulomb, Magnetic and Disorder Perturbations
    LETTERS PUBLISHED ONLINE: 12 DECEMBER 2010 | DOI: 10.1038/NPHYS1838 A topological insulator surface under strong Coulomb, magnetic and disorder perturbations L. Andrew Wray1,2,3, Su-Yang Xu1, Yuqi Xia1, David Hsieh1, Alexei V. Fedorov3, Yew San Hor4, Robert J. Cava4, Arun Bansil5, Hsin Lin5 and M. Zahid Hasan1,2,6* Topological insulators embody a state of bulk matter contact with large-moment ferromagnets and superconductors for characterized by spin-momentum-locked surface states that device applications11–17. The focus of this letter is the exploration span the bulk bandgap1–7. This highly unusual surface spin of topological insulator surface electron dynamics in the presence environment provides a rich ground for uncovering new of magnetic, charge and disorder perturbations from deposited phenomena4–24. Understanding the response of a topological iron on the surface. surface to strong Coulomb perturbations represents a frontier Bismuth selenide cleaves on the (111) selenium surface plane, in discovering the interacting and emergent many-body physics providing a homogeneous environment for deposited atoms. Iron of topological surfaces. Here we present the first controlled deposited on a Se2− surface is expected to form a mild chemical study of topological insulator surfaces under Coulomb and bond, occupying a large ionization state between 2C and 3C 25 magnetic perturbations. We have used time-resolved depo- with roughly 4 µB magnetic moment . As seen in Fig. 1d the sition of iron, with a large Coulomb charge and significant surface electronic structure after heavy iron deposition is greatly magnetic moment, to systematically modify the topological altered, showing that a significant change in the surface electronic spin structure of the Bi2Se3 surface.
    [Show full text]
  • Topological Insulator Interfaced with Ferromagnetic Insulators: ${\Rm{B}}
    PHYSICAL REVIEW MATERIALS 4, 064202 (2020) Topological insulator interfaced with ferromagnetic insulators: Bi2Te3 thin films on magnetite and iron garnets V. M. Pereira ,1 S. G. Altendorf,1 C. E. Liu,1 S. C. Liao,1 A. C. Komarek,1 M. Guo,2 H.-J. Lin,3 C. T. Chen,3 M. Hong,4 J. Kwo ,2 L. H. Tjeng ,1 and C. N. Wu 1,2,* 1Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany 2Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan 3National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan 4Graduate Institute of Applied Physics and Department of Physics, National Taiwan University, Taipei 10617, Taiwan (Received 28 November 2019; revised manuscript received 17 March 2020; accepted 22 April 2020; published 3 June 2020) We report our study about the growth and characterization of Bi2Te3 thin films on top of Y3Fe5O12(111), Tm3Fe5O12(111), Fe3O4(111), and Fe3O4(100) single-crystal substrates. Using molecular-beam epitaxy, we were able to prepare the topological insulator/ferromagnetic insulator heterostructures with no or minimal chemical reaction at the interface. We observed the anomalous Hall effect on these heterostructures and also a suppression of the weak antilocalization in the magnetoresistance, indicating a topological surface-state gap opening induced by the magnetic proximity effect. However, we did not observe any obvious x-ray magnetic circular dichroism (XMCD) on the Te M45 edges. The results suggest that the ferromagnetism induced by the magnetic proximity effect via van der Waals bonding in Bi2Te3 is too weak to be detected by XMCD, but still can be observed by electrical transport measurements.
    [Show full text]
  • Topological Insulator Materials for Advanced Optoelectronic Devices
    Book Chapter for <<Advanced Topological Insulators>> Topological insulator materials for advanced optoelectronic devices Zengji Yue1,2*, Xiaolin Wang1,2 and Min Gu3 1Institute for Superconducting and Electronic Materials, University of Wollongong, North Wollongong, New South Wales 2500, Australia 2ARC Centre for Future Low-Energy Electronics Technologies, Australia 3Laboratory of Artificial-Intelligence Nanophotonics, School of Science, RMIT University, Melbourne, Victoria 3001, Australia *Corresponding email: [email protected] Abstract Topological insulators are quantum materials that have an insulating bulk state and a topologically protected metallic surface state with spin and momentum helical locking and a Dirac-like band structure.(1-3) Unique and fascinating electronic properties, such as the quantum spin Hall effect, topological magnetoelectric effects, magnetic monopole image, and Majorana fermions, are expected from topological insulator materials.(4, 5) Thus topological insulator materials have great potential applications in spintronics and quantum information processing, as well as magnetoelectric devices with higher efficiency.(6, 7) Three-dimensional (3D) topological insulators are associated with gapless surface states, and two-dimensional (2D) topological insulators with gapless edge states.(8) The topological surface (edge) states have been mainly investigated by first-principle theoretical calculation, electronic transport, angle- resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM).(9) A variety of compounds have been identified as 2D or 3D topological insulators, including HgTe/CdTe, Bi2Se3, Bi2Te3, Sb2Te3, SmB6, BiTeCl, Bi1.5Sb0.5Te1.8Se1.2, and so on.(9-12) On the other hand, topological insulator materials also exhibit a number of excellent optical properties, including Kerr and Faraday rotation, ultrahigh bulk refractive index, near-infrared frequency transparency, unusual electromagnetic scattering and ultra-broadband surface plasmon resonances.
    [Show full text]
  • Room Temperature Magnetization Switching in Topological Insulator
    Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques Yi Wang1*, Dapeng Zhu1*, Yang Wu1, Yumeng Yang1, Jiawei Yu1, Rajagopalan Ramaswamy1, Rahul Mishra1, Shuyuan Shi1,2, Mehrdad Elyasi1, Kie-Leong Teo1, Yihong Wu1, and Hyunsoo Yang1,2 1Department of Electrical and Computer Engineering, National University of Singapore, 117576, Singapore 2Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546 Singapore *These authors contributed equally to this work. Correspondence and requests for materials should be addressed to H.Y. (email: [email protected]). Topological insulators (TIs) with spin momentum locked topological surface states (TSS) are expected to exhibit a giant spin-orbit torque (SOT) in the TI/ferromagnet systems. To date, the TI SOT driven magnetization switching is solely reported in a Cr doped TI at 1.9 K. Here, we directly show giant SOT driven magnetization switching in a Bi2Se3/NiFe heterostructure at room temperature captured using a magneto-optic Kerr effect microscope. We identify a large charge-to-spin conversion efficiency of ~1–1.75 in the thin TI films, where the TSS is dominant. In addition, we find the current density required for the magnetization switching is extremely low, ~6×105 A cm–2, which is one to two orders of magnitude smaller than that with heavy metals. Our demonstration of room temperature magnetization switching of a conventional 3d ferromagnet using Bi2Se3 may lead to potential innovations in TI based spintronic applications. 1 The spin currents generated by charge currents via the spin Hall effect1-4 and/or Rashba-Edelstein effect5,6 can exert spin-orbit torques (SOTs) on the adjacent FM layer and result in the current induced magnetization switching.
    [Show full text]
  • Topological Materials∗ New Quantum Phases of Matter
    GENERAL ARTICLE Topological Materials∗ New Quantum Phases of Matter Vishal Bhardwaj and Ratnamala Chatterjee In this article, we provide an overview of the basic concepts of novel topological materials. This new class of materials developed by combining the Weyl/Dirac fermionic electron states and magnetism, provide a materials-science platform to test predictions of the laws of topological physics. Owing to their dissipationless transport, these materials hold high promises for technological applications in quantum comput- Vishal Bhardwaj is a PhD ing and spintronics devices. student in Department of physics IIT Delhi. He works on thin film growth and experimental Introduction characterization of half Heusler alloys based In condensed matter physics, phase transitions in materials are topologically non-trivial generally understood using Landau’s theory of symmetry break- semi-metals. ing. For example, phase transformation from gas (high symmet- Prof. Ratnamala Chatterjee ric) to solid (less symmetric) involves breaking of translational is currently a Professor and symmetry. Another example is ferromagnetic materials that spon- Head, Physics Department at I.I.T Delhi. Areas of her taneously break the spin rotation symmetry during a phase change research interests are: novel from paramagnetic state to ferromagnetic state below its Curie magnetic & functional temperature. materials including topological insulators, However, with the discovery of quantum Hall effect in 2D sys- Heusler alloys for shape tems, it was realized that the conducting to insulating phase tran- memory, magnetocaloric & spintronics applications, sitions observed in Hall conductivity (σxy) do not follow the time- magnetoelectric multiferroic reversal symmetry breaking condition. Thus it was realized that a materials, shape memory in new classification of matter based on the topology of materials is ceramics, and microwave required to understand quantum phase transitions in quantum Hall absorbing materials.
    [Show full text]
  • Quantum Hall Effect on Top and Bottom Surface States of Topological
    Quantum Hall Effect on Top and Bottom Surface States of Topological Insulator (Bi1−xSbx)2Te 3 Films R. Yoshimi1*, A. Tsukazaki2,3, Y. Kozuka1, J. Falson1, K. S. Takahashi4, J. G. Checkelsky1, N. Nagaosa1,4, M. Kawasaki1,4 and Y. Tokura1,4 1 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan 2 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 3 PRESTO, Japan Science and Technology Agency (JST), Chiyoda-ku, Tokyo 102-0075, Japan ４ RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. * Corresponding author: [email protected] 1 The three-dimensional (3D) topological insulator (TI) is a novel state of matter as characterized by two-dimensional (2D) metallic Dirac states on its surface1-4. Bi-based chalcogenides such as Bi2Se3, Bi2Te 3, Sb2Te 3 and their combined/mixed compounds like Bi2Se2Te and (Bi1−xSbx)2Te 3 are typical members of 3D-TIs which have been intensively studied in forms of bulk single crystals and thin films to verify the topological nature of the surface states5-12. Here, we report the realization of the Quantum Hall effect (QHE) on the surface Dirac states in (Bi1−xSbx)2Te 3 films (x = 0.84 and 0.88). With electrostatic gate-tuning of the Fermi level in the bulk band gap under magnetic fields, the quantum Hall states with filling factor ν = ± 1 are resolved with 2 quantized Hall resistance of Ryx = ± h/e and zero longitudinal resistance, owing to chiral edge modes at top/bottom surface Dirac states.
    [Show full text]
  • Topological Electronic Structure and Intrinsic Magnetization in Mnbi4te7: a Bi2te3 Derivative with a Periodic Mn Sublattice
    PHYSICAL REVIEW X 9, 041065 (2019) Topological Electronic Structure and Intrinsic Magnetization in MnBi4Te7: A Bi2Te3 Derivative with a Periodic Mn Sublattice Raphael C. Vidal,1,2,* Alexander Zeugner,3,* Jorge I. Facio,4,* Rajyavardhan Ray,4 M. Hossein Haghighi,4 Anja U. B. Wolter,4,2 Laura T. Corredor Bohorquez,4 Federico Caglieris,4 Simon Moser,2,5,6 Tim Figgemeier,1,2 Thiago R. F. Peixoto ,1,2 Hari Babu Vasili,7 Manuel Valvidares,7 Sungwon Jung,8 Cephise Cacho,8 Alexey Alfonsov,4 Kavita Mehlawat,4,2 Vladislav Kataev ,4 Christian Hess ,4,2 Manuel Richter,4,9 Bernd Büchner,4,2,10 † ‡ Jeroen van den Brink,4,2,10 Michael Ruck,3,2,11 Friedrich Reinert,1,2 Hendrik Bentmann,1,2, and Anna Isaeva 4,2,10, 1Experimental Physics VII, Universität Würzburg, D-97074 Würzburg, Germany 2Würzburg-Dresden Cluster of Excellence ct.qmat, Germany 3Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, D-01062 Dresden, Germany 4Leibniz IFW Dresden, Helmholtzstraße 20, D-01069 Dresden, Germany 5Experimental Physics IV, Universität Würzburg, D-97074 Würzburg, Germany 6Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 7ALBA Synchrotron Light Source, E-08290 Cerdanyola del Valles, Spain 8Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom 9Dresden Center for Computational Materials Science (DCMS), Technische Universität Dresden, D-01062 Dresden, Germany 10Faculty of Physics, Technische Universität Dresden, D-01062 Dresden, Germany 11Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany (Received 19 June 2019; published 31 December 2019) Combinations of nontrivial band topology and long-range magnetic order hold promise for realizations of novel spintronic phenomena, such as the quantum anomalous Hall effect and the topological magnetoelectric effect.
    [Show full text]
  • (2020) Time-Crystalline Phases and Period-Doubling Oscillations in One-Dimensional Floquet Topological Insulators
    PHYSICAL REVIEW RESEARCH 2, 043239 (2020) Time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators Yiming Pan 1,* and Bing Wang2 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel 2National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China (Received 12 October 2019; accepted 9 September 2020; published 16 November 2020) In this work, we report a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically driven systems. The rigidity and realization of spontaneous discrete time-translation symmetry (DTS) breaking in our TFTC model require necessarily coexistence of anomalous topological invariants (0 modes and π modes), instead of the presence of disorders or many-body localization. We found that in a particular frequency range of the underlying drive, the anomalous Floquet phase coexistence between 0 and π modes can produce the period doubling (2T , two cycles of the drive) that breaks the DTS spontaneously, leading to the subharmonic response (ω/2, half the drive frequency). The rigid period-2T oscillation is topologically protected against perturbations due to both nontrivially opening of 0 and π gaps in the quasienergy spectrum, thus, as a result, can be viewed as a specific “Rabi oscillation” between two Floquet eigenstates with certain quasienergy splitting π/T . Our modeling of the time-crystalline “ground state” can be easily realized in experimental platforms such as topological photonics and ultracold fields. Also, our work can bring significant interest to explore topological phase transition in Floquet systems and to bridge the gap between Floquet topological insulators and photonics, and period-doubled time crystals.
    [Show full text]
  • Photoinduced Floquet Topological Magnons in a Ferromagnetic
    Photoinduced Floquet topological magnons in a ferromagnetic checkerboard lattice Zhiqin Zhang1,a, Wenhui Feng1,a, Yingbo Yao3, Bing Tang1,2* 1 Department of Physics, Jishou University, Jishou 416000, China 2The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology, Jishou University, Jishou 416000, China 3 College of Information and Electronic Engineering, Hunan City University, Yiyang 413000,China Keywords: Floquet topological magnons; Topological phase transitions; The Floquet-Bloch theory; Irradiated checkerboard ferromagnets ABSTRACT This theoretical work is devoted to investigating laser-irradiated Floquet topological magnon insulators on a two-dimensional checkerboard ferromagnet and corresponding topological phase transitions. It is shown that the checkerboard Floquet topological magnon insulator is able to be transformed from a topological magnon insulator into another one possessing various Berry curvatures and Chern numbers by changing the light intensity. Especially, we also show that both Tamm-like and topologically protected Floquet magnon edge states can exist when a nontrivial gap opens. In addition, our results display that the sign of the Floquet thermal Hall conductivity is also tunable via varying the light intensity of the laser field. * Corresponding author. E-mail addresses: [email protected] a These authors contributed equally to this work. 1. Introduction Up to now, topological insulators have received more and more attention from both theoretical and experimental researchers[1]. Such nontrivial insulators have been realized in a lot of electronic systems, which possess a bulk energy band gap like a common insulator but possess the topologically protected edge (or surface) states because of the bulk-boundary correspondence[2]. Theoretically, the idea of the topological band structure does not depend on the statistical characteristic of the quasiparticle (boson or fermion ) excitations.
    [Show full text]