Correlations of Electrons in Magnetic Fields 전건상 이화여자대학교 2018. 4. 4., POSTECH 물리학과 Colloquium

Hall effect

Classical & quantum Hall effect (Classical) Hall effect Quantized Hall effect ?

2D electron gas – GaAs heterostructure

Landau levels

Integral quantum Hall effect von Klitzing, Dorda, Popper (1980)

Explanation of IQHE

Berry phase and Chern number Berry curvature of energy bands Hall conductivity : topologically protected, rather insensitive to details Thouless, Kohmoto, Nightingale, den Nijs (1982)

Fractional quantum Hall effect Tsui, Stormer, Gossard (1982)

Fractional quantum Hall effect [Du,Stormer,Tsui,Pfeiffer,West (1993)]

Trial wave function at 1/3-filling

Hierarchy scenario Quasiholes and quasiparticles condense to new FQHE states Relative intensity is inconsistent with experiments. Haldane(1983), Halperin(1984)

Composite fermions IQHE of composite fermions → FQHE of electrons Jain(PRL,1989)

Fractions observed Consistent with composite fermions in fractions and stability

New fractions observed FQHE of composite fermions? Pan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2003)

FQHE : n=1 Landau Level Xia,Pan,Vicente,Adams,Sullivan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2004) Fogler, Koulakov, Shklovskii (PRL,1996)

Even Denominator: ν=1/2

Even denominator: higher LL Cooper pairing for p-wave bound state of composite fermions at n=1 LL Scarola, Park, Jain (Nat,2000) Xia,Pan,Vicente,Adams,Sullivan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2004) Eisenstein, Cooper, Pfeiffer, West (PRL,2002)

Composite fermions at zero effective magnetic field Scarola, Park, Jain (Nat,2000)

Topological quantum computations Use topological properties of non-abelian FQHE at ν=5/2 LL “qubit” = non-local entity composed of several well-separated quasiparticles Advantage: more stable against decoherence das Sarma, Freedman, Nayak (PRL,2005);(PT,2006) Read (PT,2012)

Quantum Hall effect in graphene Novoselov,Geim,Morozov,Jiang,Katsnelson,Grigorieva,Dubonos,Firsov (Nat,2005) Zhang,Tan,Stormer,Kim (Nat,2005)

FQHE in graphene Bolotin,Ghahari,Shulman,Stormer,Kim (Nat,2009) Du,Skachko,Duerr,Luican,Andrei (Nat,2009)

Black Phosphorous Li,Yang,Ye,Zhang,Zhu,Lou,Zhou,Li,Watanabe,Taniguchi,Chang,Wang,Chen,Zhang (NN,2016) Li,Yu,Ye,Ge,Ou,Wu,Feng,Chen,Zhang (NN,2014)

MgZnO/ZnO 2DES Tsukazaki,Akasaka,Nakahara,Ohno,Ohno,Maryenko,Ohtomo,Kawasaki (NM,2010) Falson,Maryenko,Friess,Zhang,Kozuka,Tsukazaki,Smet,Kawasaki (NP,2015)

Anisotropy of electronic band Band mass anisotropy Reflected in Fermi surface at zero field Reflected in Landau states with finite magnetic fields Composite fermions under high fields induced by isotropic interactions

Role of anisotropy of electronic band Jo,Rosales,Mueed,Pfeiffer,West,Baldwin,Winkler,Padmanabhan,Shayegan (PRL,2017)

Role of anisotropy of electronic band DMRG calculation variational CF wave function Coulomb interaction Interplay of correlations and band anisotropy Ippoliti,Geraedts,Bhatt (PRB,2017); Jeon,Balram,Jain (in prep.)

International System of Units Newell (PT,2014); Knotts,Mohr,Phillips (2017)

New SI base quantities Effective May 20, 2019 Newell (PT,2014); Knotts,Mohr,Phillips (2017)

Josephson and von Klitzing constants Newell (PT,2014)

Von Klitzing constant: GaAs/AlGaAs vs. Graphene Janssen,Fletcher,Goebel,Williams,Tzalenchuk,Yakimova,Kubatkin,Lara-Avilla,Falko (NJP,2011)

Watt Balance and the kilogram 𝑎 𝐵𝐼𝐿=𝑚𝑔 𝑏 𝐵𝐿𝑣= 𝑉 2 𝑎 & 𝑏 𝑚= 𝐼 𝑉 2 𝑔𝑣 4th generation Watt balance, NIST-4: absolute uncertainty less than 20μg for 1kg Newell (PT,2014)

ADDITIONAL HALL EFFECTS?

Quantum spin Hall effects Finite band gap in the bulk Two bands localized at the edges traverse the gap Strong spin-orbit coupling Spin-filtered nonchiral edge states: electrons with opposite spin propagate in opposite directions topological insulator with Z2 topological order Kane, Mele (PRL,2005)

QSHE: HgTe quantum well König,Wiedmann,Brüne,Roth,Buhmann,Molenkamp,Qi,Zhang (Sci,2007)

Bismuthen: Room-temperature QSHE? Reis,Li,Dudy,Bauernfeind,Glass,Hanke,Thomale,Schäfer,Claessen (Sci,2017)

Quantum anomalous Hall effect quantized Hall transport without magnetic field ferromagnetic insulating material + topologically nontrivial band structure V-doped (Bi,Sb)2Te3 Chang,Zhao,Kim,Zhang,Assaf,Heiman,Zhang,Liu,Chan,Moodera (PRL,2015) Chang,Zhang,Feng,Shen,Zhang,Guo,Li,Ou,Wei,Wang,Ji,Feng,Ji,Chen,Jia,Dai,Fang,Zhang,He,Wang,Lu,Ma,Xue (Sci,2013)

Quantum valley Hall effect AB-BA domain walls with external electric fields Topologically protected valley polarized chiral modes Maximum conductance ~ two quantum conductance Decrease of conductance with mean free path 420nm Vaezi,Liang,Ngai,Yang,Kim(PRX,2013) Ju,Shi,Nair,Lv,Jin,Velasco,Ojeda-Aristizabal,Bechtel,Martin,Zettl,Analytis,Wang (Nat,2015)

Concluding… QHE, FQHE, composite fermions in semiconductor, graphene, vdw material, oxide … Topological computation, new SI, anisotropy,… Quantum (spin, anomalous, valley,…) Hall effects …

Concluding … 2D Library “Lego” on atomic scale Geim, Grigorieva (Nat,2013)