Room temperature topological insulators
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1 Room temperature topological insulators Ronny Thomale Julius-Maximilians Universität Würzburg ERC Topolectrics SFB Tocotronics Synquant Workshop, KITP, UC Santa Barbara, Nov
2 Correlated electron systems Frustrated Magnetism Superconductivity Spin-orbit Phenomena Quantum Hall Effect
3 Correlated electron systems Frustrated Magnetism Superconductivity Spin-orbit Phenomena Quantum Hall Effect
4 Correlated electron systems Frustrated Magnetism Superconductivity Topological Quantum Phases Spin-orbit Phenomena Quantum Hall Effect
5 Outline
6 Outline Topological phases a elevated temperature - paradigm: quantum Hall effect
7 Outline Topological phases a elevated temperature - paradigm: quantum Hall effect Room temperature QSHE: Bi/SiC(0001) - low-energy model: substrate renormalization - experiment: tentative QSHE with 650 mev band gap
8 Outline Topological phases a elevated temperature - paradigm: quantum Hall effect Room temperature QSHE: Bi/SiC(0001) - low-energy model: substrate renormalization - experiment: tentative QSHE with 650 mev band gap Edge state hierarchy of TCIs: (Pb,Sn)Se - toy-model: midgap states in a staggered flux lattice - experiment: 1D non-dispersive DOS along odd-step terraces
9 Topological phases at elevated temperature
10 Integer Quantum Hall effect (IQHE) Chiral mode at the edge of the sample Von Klitzing 1980; Laughlin 1981; Thouless 1982; Haldane 1988 E Localized levels r xy edge momentum s xy = C e2 h Chern number C 2 Z : topological invariant B
11
12
13 Quantum spin Hall effect
14 Quantum spin Hall effect in HgTe König et al. (Molenkamp group), Science 2007 Time-reversed counterpropagating edge modes
15 Mechanisms of QSHE Band inversion Bernevig, Hughes, Zhang, Science 2006 Dirac electron mass due to SOC Kane & Mele PRL 2005
16 Room temperature QSHE: Bi/SiC(0001)
17 Bi/SiC(0001) monolayer-substrate compound
18 Bi/SiC(0001) monolayer-substrate compound
19 Theoretical compound modelling
20 Electronic structure indication from DFT: SOC opens large gap at the K point
21 Edge states
22 Band structure analysis w/o spin-orbit coupling Orbital filtering at low energies: px and py orbital content dominates substrate removes pz from Fermi level propagation of local L z S z atomic SOC Effective σ band model: p A x" i, pa y" i, pb x" i, pb y" i; pa x# i, pa y# i, pb x# i, pb y# i.
23 Effective model for the Bi monolayer p A x" i, pa y" i, pb x" i, pb y" i; pa x# i, pa y# i, pb x# i, pb y# i. H ss eff = H ss H ss ""/## = Hss 0,""/## ± l SOC H ss "# =(Hss #" ) = l R H "" "# ss H#" ss H## ss i 0 0 Bi i 0 0 i 0 1 C A m 1 m 2 C A 0 0 m 2 m 3 m 4 m m 5 m 6 0 0
24 Effective model with SOC H ss eff = H0 ss + l SOC HSOC ss + l RHR ss
25 Theory vs. ARPES
26 Theory vs. ARPES band gap: 0.67 ev!
27 Local edge state spectroscopy
28 Midgap states at 1D TCI step edges: (Pb,Sn)Se
29 0 Step edges on topological crystalline insulators < ; D 3E 6Q 6H E * F ( 0 ; < * F pick a (0,1) step edge orientation and distinguish even from odd steps QP +HLJKW QP employ STM to analyze step edges on (Pb,Sn)Se surfaces QP H G HYHQ VWHS 'LVWDQFH QP RGG VWHS
30 Large 1D DoS only at odd step widths! D E F / / (',QWHQVLW\ D X QP,QWHQVLW\ D X +HLJKW QP 'LVWDQFH QP 'LVWDQFH QP ( () H9
31 Merging step edges
![I I I I I >@ Atomistic approach: DFT T S S T[ I I LI S F [ FRPSRQHQW T S D (QHUJ\ H9 (QHUJ\ H9 (QHUJ\ H9 S 'LUDF FRQHV H H z W x ] FRPSRQHQW S (1) (4) (2) (5) (3) (6) W W T W T S D](/docs-images/78/77973114/images/32-0.jpg "VWHS VWHS VWHS T S D VWHS empirical confirmation: 1D DoS only at odd step edges remainder dispersive features are likely to stem from finite size and equal sublattice hybridization")
32 I I I I I >@ Atomistic approach: DFT T S S T[ I I LI S F [ FRPSRQHQW T S D (QHUJ\ H9 (QHUJ\ H9 (QHUJ\ H9 S 'LUDF FRQHV H H z W x ] FRPSRQHQW S (1) (4) (2) (5) (3) (6) W W T W T S D VWHS VWHS VWHS T S D VWHS empirical confirmation: 1D DoS only at odd step edges remainder dispersive features are likely to stem from finite size and equal sublattice hybridization
33 Microscopic explanation: toy model The phenomenon is related to a generalization of the Su-Schrieffer-Heeger model to two spatial bulk dimensions Minimal 2D toy model: staggered flux lattice features 1D SSH midgap states Details matter: Chirality of dirac cones, edge projection etc. ODWWLFH XQLW FHOO D I I T\ E ( G S >@ I I I T S S I I LI S F (QHUJ\ H9 (QHUJ\ H9 S S T 'LUDF FRQHV H H T[ W W W W
34 Research team and references F. Reis et al., Bismuthene on an SiC Substrate: A Candidate for a New High-Temperature Quantum SpinHall Paradigm, arxiv: , under review. P. Sessi et al., Robust spin-polarized midgap states at step edges of topological crystalline insulators, to appear in Science.
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