Quantum Dots – Past, Present and Open Questions Yigal Meir Department of Physics & The Ilse Katz Center for Meso- and Nano-scale Science and Technology.

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Presentation transcript:

Quantum Dots – Past, Present and Open Questions Yigal Meir Department of Physics & The Ilse Katz Center for Meso- and Nano-scale Science and Technology Beer Sheva, ISRAEL

Quantum dot – an artificial device, small enough so that quantization of energy levels and electron charge are important

vertical quantum dots Single molecules

Tarucha et al.

VgVg LL RR Transmission resonance when

Example: 2d harmonic oscillator

Coulomb Blockade charging of a capacitor

Coulomb blockade peaks Single electron transistor Kastner et al.

Now include quantum effects: energies wavefunctions The peak amplitude depends on the wavefunction the electron tunnels into

n=1 n=0 Example - Quantum Hall effect: All states within a landau level are degenerate, except edge states, E n =(n+1/2)h  c The radii are quantized  r 2 =n  0 (n – Landau level index)

McEuen et al.

Spin flips Kouwenhoven et al.

Level statistics and random matrix theory

Artificial molecules Dynamics

RR LL Probes the excited states Nonlinear transport

Foxman et al.

Correlation between excited state of N electrons and the ground states of N+1 electrons Marcus et al.

B

Is transport through a quantum dot coherent ? Yacoby, Heiblum

Checking quantum measurement theory Aleiner, Wingreen, Meir

Buks et al.

The Kondo effect

Relevant to transport through quantum dots Ng and Lee Glazman and Raikh

chemical potential Conductance (2e 2 /h)

Goldhaber-Gordon, Kastner (1998) Cronenwett et al. (1998)

Kouwenhoven et al.

Temperature [K] Kondo scaling Goldhaber-Gordon et al.

The Kondo effect out of equilibrium Meir, Wingreen, Lee

The two-impurity Anderson model Georges & Meir chang

Kondo vs. RKKY Marcus et al.

The two-channel Kondo effect Non- Fermi liquid ground state

Oreg & Goldhaber-Gordon

More open questions Phase of transmission amplitude Heiblum

eV=  E Inelastic process ? Ensslin

Noise measurements and electron bunching Heiblum

Thomas et al. (1996,1998,2000) The “0.7 anomaly”

Rejec and Meir

conclusions Quantum dots are controllable miniaturized devices, which can be instrumental in our understanding of mesoscopic and strongly correlated systems. May be the basic ingredient in applications of quantum computing. In spite of their apparent simplicity, still many open questions.

P. A. LeeP. NordlanderM. Kastner N. S. WingreenM. PustilnikU. Meirav J. KinaretA. GolubP. McEuen B. L. AltshulerY. AvishaiE. Foxman X.-G. WenA. AuerbachD. Goldhaber-Gordon A.-P. JauhoP. RojtL. Kouwenhoven A. L. AleinerO. Entin-WohlmanR. Ashoori E. ShopenA. AharonyM. Heiblum A. GeorgesT. AonoA. Yacoby D. C. LangrethY. DubiC. Marcus K. HiroseT. RejecK. Ensslin Y. GefenT. Ihn Theory:Experiment: