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Controlling the Surface Band Gap in Topological States of Matter

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Controlling the Surface Band Gap in Topological States of Matter Controlling the Surface Band Gap in Topological States of Matter Partha Sarathi Mandal Dissertation zur Erlangung des akademischen Grades "doctor rerum naturalium" (Dr. rer. nat.) in der Wissenschaftsdisziplin Physik kondensierter Materie eingereicht an der Mathematisch-Naturwissenschaftlichen Fakultät Institut für Physik und Astronomie der Universität Potsdam und Helmholtz Zentrum Berlin Potsdam, 29.10.2020 Hauptbetreuer: apl. Prof. Dr. Oliver Rader Gutachter: Prof. Dr. Hans-Joachim Elmers Prof. Dr. Martin Weinelt Contents Abstract 2 1 Motivation 4 2 Topological Phases of Matter 7 2.1 Distinction of Topological Phases of Matter . .8 2.2 Integer Quantum Hall State . .8 2.3 Quantum Spin Hall State and Topological Insulators . 15 2.3.1 3D Z2 Topological Insulator . 19 2.3.2 Symmetry-Protected Topological Phases . 21 2.4 Topological Crystalline Insulators . 21 2.4.1 Topological State with Rotational Symmetry . 22 2.4.2 Topological State with Mirror Symmetry . 25 2.5 Quantum Anomalous Hall State . 27 2.6 Spin Orbit Coupling and Rashba Effect . 30 3 Experimental Techniques 35 3.1 Photoelectron Spectroscopy . 35 3.1.1 Single Electron Picture . 35 3.1.2 Three Step Model . 37 3.2 Many Body Aspects . 41 3.3 Symmetry and Selection Rules . 43 3.4 Dimensionality: Bulk and Surface States . 43 3.5 Instrumentation . 45 3.5.1 Experimental Setup . 45 3.5.2 Light Source: Synchrotron radiation . 46 3.5.3 Sample Preparation for ARPES . 48 4 Topological Crystalline Insulator Phase in Pb1−xSnxSe 50 4.1 Observation of TCI Phase in Pb1−xSnxSe .................... 52 4.1.1 Sample Growth and Structural Characterization . 52 4.1.2 Temperature and Sn Concentration Dependent Band Inversion of Un- doped Pb1−xSnxSe............................. 53 4.2 Gapped Surface State in the Topological Phase: Influence of Bi Doping . 56 4.2.1 TCI to Z2 Phase Transition . 65 5 Topological Crystalline Insulator Phase in Pb1−xSnxTe 73 5.1 Basic Properties of Pb1−xSnxTe.......................... 74 5.2 Topological Phase Transition of Pb1−xSnxTe .................. 77 5.3 Giant Rashba Splitting in Pb1−xSnxTe Controlled by Bi Doping in Bulk . 82 6 Gapped Surface State in Mn-induced Bi2Te3 Heterostructures 93 6.1 Magnetic or Non-Magnetic Band Gap? . 94 6.1.1 ARPES on Bi2Te3 ............................. 96 6.1.2 ARPES on Bi2Se3 ............................. 100 6.2 Ferromagnetic Origin of the Gapped Surface State . 100 Summary 105 Kurzfassung 108 Appendix 110 A Pb1−xSnxSe 110 B Pb1−xSnxTe 113 List of Publication 115 Acknowledgements 118 Bibliography 120 To my parents who taught me the value of education Abstract In the present study, we employ the angle-resolved photoemission spectroscopy (ARPES) technique to study the electronic structure of topological states of matter. In particular, the so-called topological crystalline insulators (TCIs) Pb1−xSnxSe and Pb1−xSnxTe, and the Mn- doped Z2 topological insulators (TIs) Bi2Te3 and Bi2Se3. The Z2 class of strong topological insulators is protected by time-reversal symmetry and is characterized by an odd number of metallic Dirac type surface states in the surface Brillouin zone. The topological crystalline insulators on the other hand are protected by the individual crystal symmetries and exhibit an even number of Dirac cones. The topological properties of the lead tin chalcogenides topological crystalline insulators can be tuned by temperature and composition. Here, we demonstrate that Bi-doping of the Pb1−xSnxSe(111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z2 topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy in the bulk. As a consequence a gap appears at Γ, while the three Dirac cones at the M points of the surface Brillouin zone remain intact. We interpret this new phase transition is caused by lattice distortion. Our findings extend the topological phase diagram enormously and make strong topological insulators switchable by distortions or electric field. In contrast, the bulk Bi doping of epitaxial Pb1−xSnxTe(111) films induces a giant Rashba splitting at the surface that can be tuned by the doping level. Tight binding calculations identify their origin as Fermi level pinning by trap states at the surface. Magnetically doped topological insulators enable the quantum anomalous Hall effect (QAHE) which provide quantized edge states for lossless charge transport applications. The edge states are hosted by a magnetic energy gap at the Dirac point which has not been ex- perimentally observed to date. Our low temperature ARPES studies unambiguously reveal the magnetic gap of Mn-doped Bi2Te3. Our analysis shows a five times larger gap size below the Tc than theoretically predicted. We assign this enhancement to a remarkable structure modification induced by Mn doping. Instead of a disordered impurity system, a self-organized alternating sequence of MnBi2Te4 septuple and Bi2Te3quintuple layers is formed. This en- hances the wave-function overlap and gives rise to a large magnetic gap. Mn-doped Bi2Se3 forms similar heterostructure, but only a nonmagnetic gap is observed in this system. This 2 3 correlates with the difference in magnetic anisotropy due to the much larger spin-orbit in- teraction in Bi2Te3 compared to Bi2Se3. These findings provide crucial insights for pushing lossless transport in topological insulators towards room-temperature applications. Chapter 1 Motivation \If you shut the door to all errors, truth will be shut out." | Rabindranath Tagore; Nobel laureate in Literature (1913) The topological classification of materials is one of the most critical developments in condensed-matter physics in the last decades. Recently a new type of topological phase termed topological crystalline insulator (TCI) has been theoretically predicted and experi- mentally observed in three dimensional materials such as SnTe, Pb1−xSnxSe, and Pb1−xSnxTe class of narrow gap IV-VI semiconductors. These newly discovered TCIs have a complex sur- face band structure involving an even number of Dirac cones in contrast to the established Z2 topological insulators. In TCIs, the metallic surface states are protected by point group symmetry of the crystalline lattice rather than time reversal symmetry. In comparison to Z2 topological insulators, TCIs feature enhanced tunability of topological surface states (TSSs) by external perturbations such as temperature, composition, strain as well as electric and magnetic fields. Opening a gap in the surface state can be used for a wide range of tech- nological applications and is of fundamental interest in condensed matter physics. In the majority of previous works, bulk TCI crystals cleaved along the (001) natural cleavage planes of the lead tin chalcogenides were studied, while TSSs of other planes such as (110) or (111) have remained relatively unexplored. Due to the polar nature of (111) plane, one would expect different properties of the TSSs in comparison to the non-polar (001) plane which contains both cations and anions. We concentrate on the (111) surface where the surface state at Γ is additionally protected by time-reversal symmetry. The temperature is well known to tune the lattice constant and drive the bulk band inversion in a simple way. Chapter 4 of this thesis focuses on temperature and Sn concentration dependence of the TCI phase transition in Pb1−xSnxSe. The Pb1−xSnxSe epilayers were grown by molecular beam epitaxy and studied using angle resolved photoemission spectroscopy (ARPES). Inter- estingly, the Pb1−xSnxSe samples doped with 1{2% of Bi shows a gapped surface state at the Γ in the TCI phase. We demonstrate that Bi-doping in this system induces a quantum phase 4 5 transition from a topological crystalline insulator to a Z2 topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy and induces a gap at Γ, while the three Dirac cones at the M points of the surface Brillouin zone remain intact. Our interpretation of this new phase transition is due to rhombohedral lattice distortion. These findings extend the topological phase diagram enormously, and the potential applications could arise through ferroelectric phases - ones that have not been thought of before in this system. Lossless con- duction of electricity in topological materials can be switched on and off at will, by electrical pulses or by mechanical strain. In chapter 5, we have systematically studied the (111) TSSs of Pb1−xSnxTe:Bi epilayers grown by molecular beam epitaxy and using temperature dependent ARPES measurements with different Sn concentration. The high intrinsic p-type carrier concentration due to Pb/Sn vacancies in Pb1−xSnxTe were compensated by Bi doping that allowed us to obtain n-type samples and thus, to observe the conduction and the valence bands. We find a gap closing for Sn concentration larger than 40% at low temperature. Moreover, a giant Rashba splitting was observed for the valence band while conduction band did not show such behavior. In particular, we found that the Rashba splitting increases with increasing Bi concentration, and it was absent for undoped epilayers. The value of kR-splitting and Rashba parameter for −1 the samples doped with Bi were as large as kR = 0.017A˚ and αR = 3.5 eVA,˚ comparable to the values reported for other giant Rashba split systems. Bismuth Telluride (Bi2Te3) is a prototypical example for a three-dimensional (3D) Z2 topological insulator with a gapped bulk band structure and a two-dimensional (2D) topolog- ical surface state with Dirac-like energy-momentum dispersion and spin-momentum locking. The surface state is protected by time-reversal symmetry and is immune to surface impurities and backscattering. When 3d transition metals such as Mn, Fe, Cr or V are incorporated as magnetic dopants, their local exchange fields can break time reversal symmetry and thus may lift the degeneracy of the Dirac points with a gap opening of the topological surface state. This is the main topic of chapter 6. Band gap opening in the surface state of Z2 topological insulator by breaking time re- versal symmetry in the presence of magnetic moment has a long standing controversy in the community.
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