Chiral Anomaly Ky Kx
Total Page:16
File Type:pdf, Size:1020Kb
Topological Materials Claudia Felser the revolution • Non-trivial Phenomena captured by Single-Particle Picture → predictive design of novel materials and functionalities • Novel Transport Phenomena determined by Global Properties • quantized transport from topological protection • giant responses … • Vision: • Quantum effects at room temperature, spintronics • Catalysis, energy conversion • … How does a materials scientist find topological materials? outline • Introduction • Topological insulators • Weyl semimetals – broken symmetry • Magnetic Weyl semimetals • New Fermions • Outlook – axion insultors and beyond outline • Introduction • Topological insulators • Weyl semimetals – broken symmetry • Magnetic Weyl semimetals • New Fermions • Outlook – axion insultors and beyond the predictions © Nature http://topologicalquantumchemistry.org/ the concept predictive materials Topological quantum chemistry design Bradlyn, et al., Nature 2017 1807.10271, 1807.08756 © Nature new concepts control/ for topological Lian, et al., PNAS 2018 synthesis functionality classes: magnetic correlated higher order … verification of emergent electronic phenomena structure Qi et al. Nat. Com. (2016) Liu et al. Nat. Mat. (2016) the materials •explorative search for new materials & predictive design •high quality single crystal growth •epitaxial growth of ultrathin films and heterostructures •2D materials and micro/nano structures Co2MnGa MgO the materials •explorative search for new materials & predictive design •high quality single crystal growth •epitaxial growth of ultrathin films and heterostructures •2D materials and micro/nano structures Co2MnGa MgO the measurements Giant Responses family of quantum Hall effects 1985 Klaus von Klitzing 1998 S Oh Science 340 (2013) 153 Horst Ludwig Störmer and Daniel Tsui 2016 2010 David Thouless, Duncan Haldane und Michael Kosterlitz Andre Geim and Konstantin Novoselov topology in the electronic structure topology in the electronic structure Magic electron numbers Hückel: Möbius: 4n+2 aromatic 4n aromatic 4n antiaromatic 4n+2 antiaromatic topology in the electronic structure outline • Introduction • Topological insulators • Weyl semimetals – broken symmetry • Magnetic Weyl semimetals • New Fermions • Outlook – axion insultors and beyond topological insulators – quantum spin Hall Heavy insulating elements? Strained a-Sn and Bi-bilayer First prediction in graphene by Kane 2 λSOC~ Z for valence shells Kane and Mele, PRL 95, 146802 (2005) topological insulators – quantum spin Hall - - - + Inert pair effect Kane and Mele, PRL 95, 146802 (2005) Bernevig, et al., Science 314, 1757 (2006) Bernevig, S.C. Zhang, PRL 96, 106802 (2006) König, et al. Science 318, 766 (2007) CO08CH 11-Yan-Felser ARI 31 December 2016 13:25 topological insulators – quantum spin Hall a TI - - . SOC y - l n + o e s Weyl points u l a n o s r g WSM r e o p . r s Band inversion DSM o w F e i Inert pair effect . v 7 e b 1 r / l Dirac point 9 a 2 u / n Kane and Mele, PRL 95, 146802 (2005) 3 n 0 Bernevig, et al., Science 314, 1757 (2006) a n C = 0 C = 1 o Bernevig, S.C. Zhang, PRL 96, 106802 (2006) m o z König, et al. Science 318, 766 (2007) r n f i a d e M d a f c d o o l y n t i w s o r e D v Hole . i Electron 8 n . 7 U 1 g 0 r 2 e . b s n y e t h u P Type-I WSM Type-II WSM G r e s t t e a n n Figure 1 M a . h s o n T he topological insulator (T I) and W eyl semimetal (W SM) or Dirac semimetal (DSM). T he topology of J e - d both a TI and a W SM/DSM originates from similar inverted band structure. (a) T he spin-orbit coupling n 7 o 9 0 (SOC) opens a full gap after the band inversion in a TI, giving rise to metallic surface states on the surface. C 6 . v B (b)In aWSM /DSM,the bulk bandsare gappedbythe SOCin the 3Dmomentumspaceexcept at some I e R W isolating linearly crossing points, namely W eyl points/Dirac points, as a 3D analog of graphene. Due to the . y u b n topology of the bulk bands, T SSs appear on the surface and form exotic Fermi arcs. In a DSM all bandsare n d e A doubly degenerated, whereas in a W SM the degeneracy islifted owing to the breaking of the inversion d i v symmetry or time-reversal symmetry or both. (c)The type-I W SM.The Fermi surface(FS) shrinks tozero o r p at the W eyl points when the Fermi energy issufficiently close to the W eyl points. (d)The type-II W SM. s s Due to the strong tilting of the W eyl cone, the W eyl point acts as the touching point between electron and e c c hole pockets in the FS. A which iscalled aFermi arc. T he Fermi arc isapparently different from the FSof aTI, an ordinary insulator, or a normal metal, which is commonly a closed loop. T herefore, the Fermi arc offers strong evidence for identifying a W SM by a surface-sensitive technique such as angle-resolved photoemission spectroscopy (ARPES). If T RS exists in a W SM, at least two pairs of W eyl points may exist, where T RS transforms one pair to the other by reversing the chirality. T he Fermi arc still appears, as we discussin thisreview. H owever, the AH E diminishesbecause the Berry phases contributed from two W eyl pairscancel each other. Instead, an intrinsic spin H all effect arises(34) that can be considered as the spin-dependent Berry phase and remains invariant under the T RS. www.annualreviews.org • Topological Materials 11.3 Changes may still occur before final publication online and in print topological insulators Starting with Bismuth Bi-Sb Legierungen Bi2Se3 und verwandte Strukturen Moore and Balents, PRB 75, 121306(R) (2007) Fu and Kane, PRB 76, 045302 (2007) Murakami, New J. Phys. 9, 356 (2007) Hsieh, et al., Science 323, 919 (2009) Xia, et al., Nature Phys. 5, 398 (2009); Zhang, et al., Nature Phys. 5, 438 (2009) CO08CH 11-Yan-Felser ARI 31 December 2016 13:25 topological insulators a TI . SOC y l n o e s Weyl points u l a n o s r g WSM r e o p . r s Band inversion DSM o w F e i . v 7 e b 1 r / l Dirac point 9 a 2 u / n 3 n 0 a n C = 0 C = 1 o m o z r n f i a d e M d a f c d o o l y n t i w s o r e D v Hole . i Electron 8 n . 7 U 1 g 0 r 2 e . b s n y e t h u P Type-I WSM Type-II WSM G r e s t t e a n n Figure 1 M a . h s o n T he topological insulator (T I) and W eyl semimetal (W SM) or Dirac semimetal (DSM). T he topology of J e - d both a TI and a W SM/DSM originates from similar inverted band structure. (a) T he spin-orbit coupling n 7 o 9 0 (SOC) opens a full gap after the band inversion in a TI, giving rise to metallic surface states on the surface. C 6 . v B (b)In aWSM /DSM,the bulk bandsare gappedbythe SOCin the 3Dmomentumspaceexcept at some I e R W isolating linearly crossing points, namely W eyl points/Dirac points, as a 3D analog of graphene. Due to the . y u b n topology of the bulk bands, T SSs appear on the surface and form exotic Fermi arcs. In a DSM all bandsare n d e A doubly degenerated, whereas in a W SM the degeneracy islifted owing to the breaking of the inversion d i v symmetry or time-reversal symmetry or both. (c)The type-I W SM.The Fermi surface(FS) shrinks tozero o r p at the W eyl points when the Fermi energy issufficiently close to the W eyl points. (d)The type-II W SM. s s Due to the strong tilting of the W eyl cone, the W eyl point acts as the touching point between electron and e c c hole pockets in the FS. A which iscalled aFermi arc. T he Fermi arc isapparently different from the FSof aTI, an ordinary insulator, or a normal metal, which is commonly a closed loop. T herefore, the Fermi arc offers strong evidence for identifying a W SM by a surface-sensitive technique such as angle-resolved photoemission spectroscopy (ARPES). If T RS exists in a W SM, at least two pairs of W eyl points may exist, where T RS transforms one pair to the other by reversing the chirality. T he Fermi arc still appears, as we discussin thisreview. H owever, the AH E diminishesbecause the Berry phases contributed from two W eyl pairscancel each other. Instead, an intrinsic spin H all effect arises(34) that can be considered as the spin-dependent Berry phase and remains invariant under the T RS. www.annualreviews.org • Topological Materials 11.3 Changes may still occur before final publication online and in print chemistry Claudia Felser and Xiao-Liang Qi , Guest Editors, MRS Bull. 39 (2014) 843. Tl+1 Sn2+ Bi+3 inert pair effect predicting topological insulators Hg Te Bernevig et al., Science 314, 1757 (2006), König et al., Science 318 (2007) 766. 1, 2, 3, … ZnS Heusler XYZ C1b Zr Ni Sn 4 + 10 + 4 = 18 2s +6p electrons 2s +6p+10d electrons Ga As 33 ++ 55 == 88 Li Mg As 1 + 2 + 5 = 8 Graf, Felser, Parkin, IEEE TRANSACTIONS ON MAGNETICS 47 (2011) 367 Graf, Felser, Parkin, Progress in Solid State Chemistry Chemistry 39 (2011) 1 predicting topological insulators ScNiSb CO08CH 11-Yan-Felser ARI 31 December 2016 13:25 LaPtBi a TI Chadov, et al., Nature Mat.