Electronic States and Transport in Quantum dot Ryosuke Yoshii YITP Hayakawa Laboratory

Mesoscopic system In recent years, we can fabricate nano scale semiconductors. Macroscopic system My research field: mesoscopic systems Microscopic system (Meson,Mesopotamia, etc) Intermediate ~100nm Various tunable parameters We can design quantum device Why mesoscopic?

Nano-fabrication of semiconductors (1) Two-dimensional electron gas in semiconductor hetero-structures: Epitaxial growth, layer by layer InGaAs 2DEG 1.1 Small box for electron (Quantum dot) You can make the sheet of electron gas (2) Small metallic electrodes: Electron-beam lithography

Quantum dot quantum-mechanical boxes Energy levels are discretized (Nanoscale semiconductor device) Quantum dots are Gate We can control electro-statical potential with gate voltage. Tunable by Electron gas First layerSecond layer

Quantum dot quantum-mechanical boxes Energy levels are discretized (Nanoscale semiconductor device) Quantum dots are Gate We can control electro-statical potential with gate voltage. Tunable by First layerSecond layer Electron gas Negative voltage

Quantum dot quantum-mechanical boxes Energy levels are discretized (Nanoscale semiconductor device) Quantum dots are Gate We can control electro-statical potential with gate voltage. Tunable by First layer Negative voltage Second layer Quantum dot Negative voltage

Tunnel effect Large potential for electrons Energy of conduction electron < potential sourcedrainsourcedrain Gate voltage

lead This process is forbidden. When energy level in the quantum dot does not lie between Fermi energy of two leads. This process is allowed. When energy level in the quantum dot lies between Fermi energy of two leads. lead Transport

Number of electrons in Quantum dot is fixed Coulomb oscilation In the region between two peaks sourcedrain source drain source # of electrons is 2 “Tunable one by one”by “tunnel” Spin of electron Small magnet

Quantum point contact The electron number in QD is countable as resistance We can detect the dynamics of # of electrons Gustavsson et al, PRL Full counting statistics

2.Our research topics Coulomb valley Energy does not conserve 2.1 Kondo effect 2nd order perturbation for tunnel process “Cotunneling”: more than one electron participates.

spin in quantum dot is screened by conduction electrons: Kondo singlet state (Many-body state) Result in screening effect Effective Hamiltonian Spin flip process Antiferromagnetic

Kondo temperature T K : binding energy of the Kondo singlet state T<<T K : Kondo singlet state is formed. Resonant tunneling through the singlet state. Conductance increases with lowering the temperature spin

Quamtum master equation with couting field eigen vector for largest eigenvalue left right Total derivative with : parameter of system Can we make adiabatic pump with changing the observer’s parameters? With localized spin? With many body effect? Cumulant generating function This geometrical representation “adiabatic pump for physical quantity.?” Impossible for lead+dot in case of spinless fermion T. Yuge, T. Sagawa, H. Hayakawa, unpublished 2.2 Quamtum pumping T. Sagawa and H. Hayakawa, PRE 84, ‘11

Quantum master equation for Kondo model 3.Results in second order

Eigen vectors RemarksF is independent of J F depend on b, but a

Case of

If we add the potential scattering term In general, is independent of In progress

4.Summary We have examined the master equation for Kondo model We have shown the quantum pumping is independent of J We have shown that the geometric term of the cumulant generating function only depends on the off diagonal part of QME We have shown that the Kondo model without potential scattering term doesn’t produce the quantum pumping