Non-equilibrium Non-equilibrium Fluctuations in Strongly - PowerPoint PPT Presentation

International Symposium in Honor of Professor Nambu for the 10th Anniversary of his Nobel Prize in Physics Osaka City University, December 12-13, 2018 Non-equilibrium Non-equilibrium Fluctuations in Strongly Fluctuations in Strongly Correlated Quantum Liquids Correlated Quantum Liquids Kensuke Kobayashi Graduate School of Science, Osaka University Center for Spintronics Research Network, Osaka University Quantum Information and Quantum Biology Division, Institute for Open and Transdisciplinary Research Initiatives, Osaka University 1

Outline 1. Mesoscopic systems 2. Fluctuation = Noise 3. Kondo effect & Fluctuation Quantum Liquid  Symmetry crossover  On-chip collision experiment to On-chip collision experiment to probe non-equilibrium quantum liquids probe non-equilibrium quantum liquids 2

Mesoscopic Systems 3

Solid-state device where quantum Mesoscopic System mechanics manifests itself. Quantum computing 1980ʼs- Stage for fundamental physics Exotic materials Charge nanotube, graphene, topological… Example Spin  Electron interference MEMS Phase  Single electron control micro-electro mechanical systems etc. Coherence Spintronics Interaction ~ 0.8μm … etc. Webb et al. PRL 54, 2696 (1985) Strongly-correlated  Degree of freedom in the design physics / Quantum liquid  Controllability this talk 4

“Conductance is Transmission.” � � electron electron Rolf Landauer (1927–1999) Mesoscopic Mesoscopic lead lead lead lead � � system system transmit � � Landauer formula � �� � � � ∼ ��. � �� �� � Conductance gives you information on the electronic properties of single site quantum systems (interference, single-level transport, Kondo physics…). 5

Quantum Point Contact (QPC) Constriction width ~ Fermi wave length of electrons (~50 nm) → Conductance quantized due to formation of perfect quantum channel. n -AlGaAs i -AlGaAs electron gas Width increases. plateau i -GaAs 2 nd channel � � plateau 0 → 100 % � � 1 st channel 0 → 100 % Landauer Formula � � 2� � � � � � � 6 van Wees et al., PRL 60, 848 (1988).

Quantum Dot (Artificial Atom) Electrons in a small box ↓ Charging effect & Confinement ↓ QD Lead Lead Discrete energy levels in QD. Electron Gate # of electrons in QD is fixed. Electron can pass QD only when the level coincides with those of the leads. QD Lead Lead Current Gate voltage (V) Gate Voltage 7

Mesoscopic Systems (from our work) Mesoscopic Systems (from our work) Quantum Dot Atom in Interferometer (artificial atom) Wave-particle duality Particle nature Phys. Rev. Lett. 106 , 176601 (2011); J. Phys. Soc. Jpn 73, L3235 (2004) Electron Interferometer  Wave nature Phys. Rev. Lett. 88, 256806 (2002); 92, 176802 Phys. Rev. Lett 104, 080602 (2010); Phys. Rev. B 79, (2004); 95, 066801 (2005); Phys. Rev. B 68, 161306 (R) (2009); 83, 155431 (2011); J. Phys. Soc. 235304 (2003); 70, 035319 (2004); 73, 195329 Jpn 71, L2094 (2002); Physica E 42, 1091 (2010). (2006). 8

Fluctuation = Noise 9

Some electrons cannot transmit transmit lead lead lead lead Mesoscopic Mesoscopic electron electron system system Reflected You can’t avoid this. Noise = Current fluctuation 10

Noise = Variance of # of electrons Review: Blanter-Büttiker, Phys. Rep. 336 , 1 (2000). I I Resistor V R = 1/ G t FFT Current noise power spectral density � � ��� [ � � /�� ] � � ≡ � Different Unit = New Info. Different Unit = New Info. �� � � � ����� �� Current: Current: � � � � � � � � � � Noise: Noise: 11

Shot Noise = Noneq. Current Fluctuation inject transmit barrier A reflected Not so simple! Not so simple! Noise � � Schottky (1918) Electrons are Poisson process: indep. event Ave. = Var. → � � 〈 �� � 〉 correlated. ∝ 〈�〉 � � 〈�〉 � � �〈�〉 � : time Current 〈�〉 � � � Fano factor � � ��〈�〉 � � � 2〈 �� � 〉 � 2� � 〈 �� � 〉 � 2� � 〈�〉 Effective charge � � � 2� ∗ 〈�〉 � 2�〈�〉 � � � 12

Shot noise in QPC transmitted reflected → shot noise Exp. �� � Nakamura, et al. PRB 79, Current 201308(R) (2009). � � � Noise � � � ∑ � �1 � � � � � � Fano factor ∑ � � � Blanter and Büttiker, Phys. Rep. 336 , 1 (2000). 13

Fractional quantum Hall Cooper pair in SN junction ∗ effect ∗ Shot noise Shot noise current （mA） current （pA） Saminadayar et al ., PRL 79 , 2526 (1997); Normal Super. de-Picciotto et al ., Nature 389 , 162 (1997). Jehl et al ., Nature 405 , 50 (2000). Nobel Prize in Physics (1998) 14

“The noise is the signal.” Nature 392, 658 (1998) Rolf Landauer (1927–1999) Fluctuation Theorem Fluctuation Theorem Spin polarization Spin polarization Mesoscopic Stern–Gerlach on chip nonequilibrium Reservoir System statistical physics. Nakamura et al., PRL 104, 080602 (2010); Kohda et al. Nature Comm. 3, 1082 (2012). PR B 83, 155431 (2011) Nishihara et al. APL 100, 203111 (2012). Spin shot noise Spin shot noise Edge dynamics Edge dynamics Edge mixing in graphene pn junction in QH regime Arakawa et al., PRL 114, 016601 (2015); Matsuo et al. Sci. Rep. 5, 11723 (2015). Iwakiri, Niimi, Kobayashi, APEX 10, 053001 (2017). Matsuo et al. et al. Nature Comm. 6, 8066 (2015). 15

Kondo effect & Fluctuation Ferrier et al. , Nature Physics 12 , 230 (2016). Teratani et al., J. Phys. Soc. Jpn. 85, 094718 (2016). Ferrier et al., Phys. Rev. Lett. 118 , 196803 (2017). Hata et al., Phys. Rev. Lett. (in press): Noise of Andreev-Kondo effect 16

Collaborators Experiment: T. Arakawa, T. Hata, S. –H. Lee, R. Fujiwara (Osaka University) M. Ferrier, R. Delagrange, R. Weil, R. Deblock, H. Bouchiat (CNRS, Université Paris sud) Theory: R. Sakano (University of Tokyo) Y. Teratani, A. Oguri (Osaka City University) Financial support: Financial support: Grant-in-Aid for Scientific Research (S) (26220711) Grant-in-Aid for Scientific Research (S) (26220711) JSPS KAKENHI (26400319, 16K17723, 15K17680, 25103003, JSPS KAKENHI (26400319, 16K17723, 15K17680, 25103003, 15H05854) 15H05854) Yazaki Memorial Foundation for Science and Technology Yazaki Memorial Foundation for Science and Technology 17

Quantum liquid Single particle Many particles electron, neutron, atom, molecule… Quantum liquid Particle flow Particle flow ~de Broglie length interaction  Quantum liquid: Essentially different from a single particle ex. liquid He, BEC, supercondutivity….  Non-equilibrium quantum liquid: strongly-correlated systems, cold-atom physics, spintronics … 18

Kondo effect 1964 Kondo effect 1964 Magnetic impurity in metals Magnetic impurity in metals Quantum dot Quantum dot J. Kondo 1930- J. Kondo 1930- High T High T Kondo state = Quantum liquid Kondo state = Quantum liquid A localized spin screened by many electrons A localized spin screened by many electrons Low T Low T R G T T Kondo effect in QD: Gordhaber-Gordon et al. Nature 391, 156 (1998); Cronenwett et al., Science 281, 540 (1998); Schmid et al. Physica B 256-258, 182 (1998). van der Wiel et al., Science 289, 2105 (2000). 19

Why Kondo effect in QD? Impact of Kondo effect (1964) Impact of Kondo effect (1964) (1) Single (2) External control Kondo state  A monument in solid state physics  A monument in solid state physics  Typical quantum many body effect  Typical quantum many body effect  Extensively studied & understood  Extensively studied & understood (but limited within equilibrium to (but limited within equilibrium to linear response regime) linear response regime) (3) Eq. ↔ Non-eq. tunable Realization of Kondo effect in a QD (1998-) Realization of Kondo effect in a QD (1998-) → Ideal test bed to explore nonequibilirium → Ideal test bed to explore nonequibilirium quantum many-body systems quantum many-body systems Gordhaber-Gordon et al. Nature 391, 156 (1998); Cronenwett et al., Science 281, 540 (1998); Schmid et al. Physica B 256-258, 182 (1998). van der Wiel et al., Science 289, 2105 (2000). 20

Kondo shot noise Kondo state Theory predicts enhanced shot noise due to Kondo correlation. Theory：Sela, Oreg, von Oppen, and Koch, PRL 97, 086601 (2006); Golub, PRB 73, 233310 (2006); Gogolin and Komnik, PRL 97, 016602 (2006); Mora, Leyronas, and Regnault PRL 100, 036604 (2008); Vitushinsky, Clerk, and Le Hur, PRL 100, 036603 (2008). Fujii, JPSJ 79, 044714 (2010); Sela and Malecki, PRB 80, 233103 (2010); Sakano, Fujii, and Oguri, PRB 83, 075440 (2011)… Only a few experiments : Zarchin et al., PRB 77, 241303 (2008); Delattre et al., Nat. Phys. 5, 208 (2009); Yamauchi, KK et al., PRL 106, 176601 (2011) 21

Device & Measurements Dilution fridge: 15 ~ 800 mK Dilution fridge: 15 ~ 800 mK Carbon nanotube Carbon nanotube quantum dot quantum dot Pd/Al Pd/Al Source Source Drain Drain Magnetic field Magnetic field Gate electrode Gate electrode � � � � 1 M٠1 M٠Measure � �� Measure � �� � � Mixer Mixer �� �� V V Measure G Measure G 22