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Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK Topological Kondo Insulators:Happy Birthday Gil! Magnetism meets Topology Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Piers Coleman, Rutgers CMT. Topological Kondo Insulators: Magnetism meets Topology Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Topological Kondo Insulators: Magnetism meets Topology Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Collaborators Maxim Dzero Kent State Kai Sun Michigan Victor Galitski Maryland " 4"% ",'* Vic Onur Vic Alexandrov, IAS Onur Erten, Rutgers Joel Moore, Berkeley Phil Anderson, Princeton Suchitra Sebastian Cambridge Gil Lonzarich Cambridge Topological Kondo Insulators: Magnetism meets Topology Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Collaborators Maxim Dzero Kent State Kai Sun Michigan Victor Galitski Maryland " 4"% ",'* Vic Onur Vic Alexandrov, IAS Onur Erten, Rutgers Joel Moore, Berkeley Phil Anderson, Princeton Suchitra Sebastian Cambridge Gil Lonzarich Cambridge M. Dzero, K. Sun, V. Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) T. Takimoto, J. Phys. Soc. Jpn. 80, 123710 (2011). V. Alexandrov, P. Coleman, O. Erten, Phys. Rev. Lett. 114:177202 (2015). Maxim Dzero, Jing Xia, Victor Galitski, Piers Coleman, Annual Reviews CMP (2016), ArXiv 1506.05635 Topological Kondo Insulators: Magnetism meets Topology Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Outline • SmB6 and the rise of topology • TKIs: a link with superfluid He-3 • Is SmB6 topological? • The Magnetic Connection. Kondo insulators: History &,!91!$*&$$A HH9HOK9GOLOB (($"&"+#A'%%&,+ GL9GKK9GOOHB B6 2.7+ Sm SmB6 K Kondo insulators: History &,!91!$*&$$A HH9HOK9GOLOB (($"&"+#A'%%&,+ GL9GKK9GOOHB "%($+, '&' / B6 2.7+ Sm SmB6 K Kondo insulators: History Hybridization picture. &,!91!$*&$$A HH9HOK9GOLOB Maple + Wohlleben, 1972 (($"&"+#A'%%&,+ GL9GKK9GOOHB Mott Phil Mag, 30,403,1974 Allen and Martin, 1979 "%($+, '&' / H =(|kσVσα(k)α| +H.c) E(k) k Ef L Kondo insulators: History Hybridization picture. &,!91!$*&$$A HH9HOK9GOLOB Maple + Wohlleben, 1972 (($"&"+#A'%%&,+ GL9GKK9GOOHB Mott Phil Mag, 30,403,1974 Allen and Martin, 1979 "%($+, '&' / H =(|kσVσα(k)α| +H.c) E(k) k Ef “In SmB6 and high-pressure SmS a very small gap separates occupied from unoccupied states, this in our view being due to hybridization of 4f and 4d bands.” Mott 1974 L Kondo insulators: History Hybridization picture. &,!91!$*&$$A HH9HOK9GOLOB Maple + Wohlleben, 1972 (($"&"+#A'%%&,+ GL9GKK9GOOHB Mott Phil Mag, 30,403,1974 Allen and Martin, 1979 Cooley, Aronson, et al. 1995 H =(|kσVσα(k)α| +H.c) E(k) k Ef In SmB6 and high-pressure SmS a very small gap separates occupied from unoccupied states, this in our view being due to hybridization of 4f and 4d bands. M !*"+''('$' 5; N !*"+''('$' 5; g=1 g=3 g=genus g=0 g=2 N !*"+''('$' 5; "*&-$'%,*5'('$' 5 g=1 g=3 g=genus g=0 g=2 N !*"+''('$' 5; <1++?'&&,!'*%=1++A1&(1$"+!B9'&&,AGNJNB "*&-$'%,*5'('$' 5 1 Ω κdA = =(1− g) 4π 4π g=1 g=3 g=genus g=0 g=2 N !*"+''('$' 5; "*&-$'%,*5 ',!321&-'&'** O Berry v. Klitzing Laughlin Thouless Haldane !*"+''('$' 5; "*&-$'%,*5 ',!321&-'&'** Integer Quantum Hall von Klitzing, Dorda & Pepper (1980) O Berry v. Klitzing Laughlin Thouless Haldane !*"+''('$' 5; "*&-$'%,*5 ',!321&-'&'** Integer Quantum Hall ak = i un,k|∇k|un,k ,$9AGONHB n=1,2N von Klitzing, Dorda & Pepper (1980) O Berry v. Klitzing Laughlin Thouless Haldane ak = i un,k|∇k|un,k ,$9AGONHB n=1,2N !*"+''('$' 5; Kane Mele Zhang Molencamp Hasan Balents Moore Roy Fu "*&-$'%,*5 ',!321&-'&'** Z2 Topological Insulators Integer Quantum Hall "&!& 92; '!5+AHFGFB; von Klitzing, Dorda & Pepper (1980) O ? P 11% GF '&2&-'&$& "&+1$,'* ? P 11% GF Conventional band insulator: adiabatic continuation of the vacuum. '&2&-'&$& "&+1$,'* ? ! P 11% GF Topological insulator '('$' "$<"&+1$,'*= A**5'&&-'&<,3"+,=B ? ! P 11% GG Topological insulator : adiabatically disconnected from the vacuum. Gap must close at interface between '('$' "$<"&+1$,'*= two different vacua A**5'&&-'&<,3"+,=B ? ! P 11% Metallic surfaces.GG 1D Topological Insulator Igor William Tamm Shockley Tamm 1932, Shockley, Phys Rev, 56, 317 (1939): 1D TI 1D Topological Insulator Igor William Tamm Shockley P=-1 tp p + + - V - -t P=+1 + + Tamm 1932, Shockley, Phys Rev, 56, 317 (1939): 1D TI 1D Topological Insulator Igor William Tamm Shockley P=-1 tp p + + - V - -t P=+1 + + Tamm 1932, Shockley, Phys Rev, 56, 317 (1939): 1D TI Open BCs- broken translation symmetry odd/even states mix to form edge states. Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007) Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007) Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007) Topological Texture of Berry Connection Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007) Z2= 1 Z2= -1 Topological Texture of Berry Connection Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007) Z2 = δ(Γi) i 1& & AHFFNB:*",5)1-'&; Z2= 1 Z2= -1 Topological Texture of Berry Connection FIG. 27 ARPES data for Bi2Se3 thin films of thickness (a) 1QL (b) 2QL (c) 3QL (d) 5QL (e) 6QL, measured at room temperature (QL stands for quintuple layer). From Zhang et al., 2009. H >1&,1%$$+ @ FIG. 25 ARPES data for the dispersion of the surface states of ¯ ¯ ¯ ¯ Bi2Se3, along directions (a) Γ − M and (b) Γ − K in the surface ¯ ¯ A '&" ,$9FM>NB Brillioun zone. Spin-resolved ARPES data is shown along Γ−M for a fixed energy in (d), from which the spin polarization in momentum space (c) can be extracted. From Xia et al., 2009 and Hsieh et al., @I Bi2Se3 ,Bi2Te 3, Sb2Te 3 2009. (Zhang et al ,Xia et al ,Chen et al, Hsieh et al (09)) GK FIG. 27 ARPES data for Bi2Se3 thin films of thickness (a) 1QL (b) 2QL (c) 3QL (d) 5QL (e) 6QL, measured at room temperature (QL stands for quintuple layer). From Zhang et al., 2009. H >1&,1%$$+ @ FIG. 25 ARPES data for the dispersion of the surface states of ¯ ¯ ¯ ¯ Bi2Se3, along directions (a) Γ − M and (b) Γ − K in the surface ¯ ¯ A '&" ,$9FM>NB Brillioun zone. Spin-resolved ARPES data is shown along Γ−M for a fixed energy in (d), from which the spin polarization in momentum space (c) can be extracted. From Xia et al., 2009 and Hsieh et al., @I Bi2Se3 ,Bi2Te 3, Sb2Te 3 2009. (Zhang et al ,Xia et al ,Chen et al, Hsieh et al (09)) *,!*+,*'& $5'**$,'1&,*(*,+8 $,*'&+8 ,*'& $5"&,*-& 9"&&",("&'*",9'(*",5; GK Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) Many Body Localized Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) Many Body Many Body Localized Delocalization Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) Many Body Many Body Localized Delocalization Are Kondo insulators topological? R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979) Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010) Many Body Many Body Localized Delocalization Band Theory SmB6: T. Takimoto, J. Phys. Soc. Jpn. 80, 123710 (2011). Maxim Dzero, Kai Sun, Piers Coleman and Victor Galitski, Phys. Rev. B 85 , 045130-045140 (2012). Gutzwiller + Band Theory F. Lu, J. Zhao, H. Weng, Z. Fang and X. Dai, Phys. Rev. Lett. 110, 096401 (2013). Victor Alexandrov, Maxim Dzero and Piers Coleman PRL (2013). ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 GM ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 GM ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 Three crossings: THREE DIRAC CONES ON SURFACE. GM ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 Three crossings: THREE DIRAC CONES ON SURFACE. GN ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 sˆdˆ((kk))== kkˆˆ Vαβ(k) = Vsk · σ αβ X ˆ sk = (sin kx, sin ky, sin kz) ∼ k Three crossings: THREE DIRAC CONES ON SURFACE. GN ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 sˆdˆ((kk))== kkˆˆ Vαβ(k) = Vsk · σ αβ X ˆ sk = (sin kx, sin ky, sin kz) ∼ k Three crossings: THREE DIRAC CONES Hybridization of f (P=+) and d (P=-) vanishes at X point. ON SURFACE. GN ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 =3 V s · σ H(k) = k k V sk · σ f k sˆdˆ((kk))== kkˆˆ Vαβ(k) = Vsk · σ αβ X ˆ sk = (sin kx, sin ky, sin kz) ∼ k Three crossings: THREE DIRAC CONES Hybridization of f (P=+) and d (P=-) vanishes at X point. ON SURFACE. GN ,1*+',!&3%'$ Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635 =3Like He-3B: an adaptive insulator. V s · σ H(k) = k k V sk · σ f k sˆdˆ((kk))== kkˆˆ Vαβ(k) = Vsk · σ αβ X ˆ sk = (sin kx, sin ky, sin kz) ∼ k Three crossings: THREE DIRAC CONES Hybridization of f (P=+) and d (P=-) vanishes at X point.
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