Psychology

Model for a Quantum Hall Effect without Landau Levels

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Model for Quntum Hll Effect without Lndu Levels F.D.M. Hldne Physicl Review Letters, Volume 61, Numer 18, Oct 31, 1988 Presented y group 12: Luke Yeo, Jimmy Yun, Lizhong Zhng, Xioyu Zhng, Dewen Zhong Deprtment
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Model for Quntum Hll Effect without Lndu Levels F.D.M. Hldne Physicl Review Letters, Volume 61, Numer 18, Oct 31, 1988 Presented y group 12: Luke Yeo, Jimmy Yun, Lizhong Zhng, Xioyu Zhng, Dewen Zhong Deprtment of Physics University of Illinois t Urn-Chmpign Phys 596, Dec 2,2016 Bckground out this pper Author: F. Duncn M. Hldne Eugene Higgins Professor in Princeton University Noel Lurete of 2016 This pper hs een cited 1500 times Impct on lter study of topologicl physics nd 2D mteril such s grphene Model for Clssicl Hll Effect Hll effect mesurement setup. Apply E field in x-direction nd B field in z-direction. Mesure Hll voltge in y-direction Hll Resistnce Hll Resistnce Model of Quntum Hll Effect Quntum Hll Effect (QHE): quntiztion of conductnce in strong mgnetic fields nd low temperture Integer Quntum Hll Effect ν = 1,2,3 σ xy = e2 ν h Frctionl Quntum Hll Effect ν = 1 3, 2 5, 3 7 Hll conductnce quntum of conductnce Mgnetic Field (von Klitzing) Mgnetic Field (Tsui nd Störmer) Interpreting the Integer nd Frctionl Quntum Hll Effects Integer QHE: Free electrons moving in mgnetic field defined in terms of cnonicl moment (momentum nd vector potentil) H = Π x 2 + Π y 2 Π = p + ea Similr mthemticlly to quntum hrmonic oscilltor E = ħω B n ω B = eb m These energies re known s Lndu levels. Frctionl QHE involves interctions nd is much more complicted Hldne s Toy Model for Quntum Hll Effect Pictoril representtion of Hldne model Energy +M on red sites nd M on Q lue sites Nonuniform B in regions (+) nd ( ) B tot = 0 so no Lndu Levels Lines indicte hopping etween nerest neighors (solid) nd next-nerest neighors (dshed) On-site Energy Hldne Model Genertes Quntum Hll Effect Conductnce Phse Digrm σ xy = νe2 h ν = 0 ν = 1 ν = +1 Sme result s cnonicl quntum Hll effect ν = 0 π Berry s Phse 0 π Hldne Model nd Topology B fields nd hopping produce Berry s phse This prticulr Berry s phse gives rise to Berry s curvture Integrte this Berry s curvture over ll spce gives sme quntized σ xy s QHE Pictoril representtion of Hldne model Quntized in terms of topologicl Chern numer Critique Cler New perspective on QHE Prity nomly not well motivted Hrd to implement experimentlly Current Relted Reserch Experimentl Oservtion of Quntum Hll Effect nd Berry's Phse in Grphene (By Yuno Zhng 2005) Experimentl Oservtion of the Quntum Anomlous Hll Effect in Mgnetic Topologicl Insultor (By Qi-Kun Xue, Shou-Cheng Zhng 2013) Attempts to extend Hldne model to explin frctionl Quntum Hll Effect Quntum Spin Hll Effect QHE in Grphene Result (2005) Quntized Mgnetoresistnce (Red) nd Hll Resistnce(lck) of grphene device t T = 30 mk nd Vg = 15 V QHE in Grphene Result (2005) Quntized Mgnetoresistnce (Red) nd Hll Resistnce(lck) of grphene device t T = 30 mk nd Vg = 15 V QHE in Grphene Result (2005) A schemtic digrm of the Lndu level density of sttes (DOS) nd corresponding quntum Hll conductnce (σ_xy) s function of energy. Room-temperture quntum Hll effect in grphene(2007) Quntum Anomlous Hll Effect Oservtion (2013) Quntum Anomlous Hll Effect for different Temperture Effect Frctionl Quntum Hll Nonelions in the frctionl quntum Hll effect(moore/red 1991) Oservtion of the frctionl quntum Hll effect in grphene (2009) Quntum Spin Hll Effect Quntum spin Hll effect (BA Bernevig, SC Zhng 2005) Quntum spin Hll effect in grphene(cl Kne, EJ Mele, 2005) Quntum spin Hll effect nd topologicl phse trnsition in HgTe quntum wells( BA Bernevig, TL Hughes, SC Zhng,2006) Summry Integer QHE cn occur in the sence of B fields Simple model llows for computtion of Hll conductnce Quntiztion due to ccumultion of phse hints t underlying topologicl structure
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