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Schwerpunkt Project SPINTRONICS-- 1285 (with J. von Delft LMU Munich QD 2010 Chernogolovka Russia-Israel Schwerpunkt Project SPINTRONICS-- 1285 (with J. von Delft LMU Munich QD 2010 Chernogolovka Russia-Israel cooperation IMOST (YG-I. Burmistrov) CHARGE – SPIN INTERPLAY IN QUANTUM DOTS I. Burmistrov, YG, M. Kiselev see also… B. Nissan, YG, M. Kiselev, I. Lerner in progress. . I. Burmistrov, YG, M. Kiselev, L. Medvedovsky – numerics A. Saha, A. Shnirman, A. Altland, YG – geometric phases

what the problem is why is it non-trivial what can we do about it what the problem is why is it non-trivial what can we do about it …

QUANTUM DOT : ENERGY SCALES QUANTUM DOT : ENERGY SCALES

Universal Hamiltonian Zero-mode interaction charging spin Kurland, Aleiner, Altshuler (2000) Aleiner, Brouwer, Glazman (2002) Universal Hamiltonian Zero-mode interaction charging spin Kurland, Aleiner, Altshuler (2000) Aleiner, Brouwer, Glazman (2002) superconducting

Mesoscopic Stoner Instability Mesoscopic Stoner Instability

0 0 1 2 1 0. 5 paramagnetism mesoscopic Stoner instability macroscopic Andreev and 0 0 1 2 1 0. 5 paramagnetism mesoscopic Stoner instability macroscopic Andreev and Kamenev 1997 Kurland, Aleiner, Altshuler 2000 Aleiner, Brouwer, Glazman 2002 Stoner instability

MOTIVATION: conductance vs. gate voltage MOTIVATION: conductance vs. gate voltage

MOTIVATION CALCULATE…. TUNNELING DENSITY OF STATES (GF) MAGNETIC SUSCEPTIBILITY (dc, ac) TRANSPORT THROUGH QD MOTIVATION CALCULATE…. TUNNELING DENSITY OF STATES (GF) MAGNETIC SUSCEPTIBILITY (dc, ac) TRANSPORT THROUGH QD …… Alhassid and Rupp, PRL 91, 056801 (2003); Usaj, Baranger, PRB 67, 121308 (2003) Alhassid, Rupp, Kaminski and Glazman PRB 69, 115331(2004); Tureci and Alhassid, PRB 74, 165333 (2006); some aspects --analyzed exactly

MOTIVATION: conductance vs. gate voltage other quantities: J> 0. 5 near (& below) Stoner MOTIVATION: conductance vs. gate voltage other quantities: J> 0. 5 near (& below) Stoner instability: Pd ~ 0. 8 Co impurities in Pd; Pnictides -- >0. 94

what the problem is why is it non-trivial what can we do about it what the problem is why is it non-trivial what can we do about it …

detour… charging (Coulomb blockade) derivation of the Coulomb blockade employing functional bosonization Kamenev +YG detour… charging (Coulomb blockade) derivation of the Coulomb blockade employing functional bosonization Kamenev +YG 1996 Efetov + Tschersich 2003 Sedlmayr, Yurkevich, Lerner 2006

to calculate tunneling density of states needs GF. in imaginary time: Kamenev, YG 1996 to calculate tunneling density of states needs GF. in imaginary time: Kamenev, YG 1996

interaction term decouple by Hubbard-Stratonovich transformation: interaction term decouple by Hubbard-Stratonovich transformation:

gauge transformation: winding number gauge transformation: winding number

Fermionic action Hubbard-Stratonovich Gauge Abelian action U(1) symmewtry functional bosonization Fermionic action Hubbard-Stratonovich Gauge Abelian action U(1) symmewtry functional bosonization

END OF detour… charging (Coulomb blockade) now do the same with spin exchange: END OF detour… charging (Coulomb blockade) now do the same with spin exchange:

Hubbard-Stratonovich Hubbard-Stratonovich

charge+ spin Non-Abelian action ( SU(2) symmetry) various attempts: perturbation in spin anisotropy (Kiselev, charge+ spin Non-Abelian action ( SU(2) symmetry) various attempts: perturbation in spin anisotropy (Kiselev, YG, 2006) mapping into coupled stochastic eqs. (Kiselev, YG) ? ? ? Ising spin (Nissan, YG, Kiselev, Lerner) Geometric phase (Saha, Shnirman, Altland, Gefen)

what the problem is why is it non-trivial what can we do about it what the problem is why is it non-trivial what can we do about it …

EXACT SOLUTION: action non-Abelian trick: Kolokolov (1990); Wei-Norman (1963) EXACT SOLUTION: action non-Abelian trick: Kolokolov (1990); Wei-Norman (1963)

time ordering time ordering

EXACT RESULTS Static susceptibility Pauli Curie Stoner inst. EXACT RESULTS Static susceptibility Pauli Curie Stoner inst.

EXACT RESULTS canonical partition function without EXACT RESULTS canonical partition function without

NON-TRIVIAL CHECKS : NON-TRIVIAL CHECKS :

New energy scale emerges : For for crucial dependence on specific realizations; may calculate New energy scale emerges : For for crucial dependence on specific realizations; may calculate

TDOS high T TDOS high T

Coulomb peak: dot degenerate between 4 e & 5 e e e 4 e Coulomb peak: dot degenerate between 4 e & 5 e e e 4 e 5 e

TDOS intermediate T exponentially suppressed osc. precession physics TDOS intermediate T exponentially suppressed osc. precession physics

with anisotropy– stronger effect with anisotropy– stronger effect

TDOS low T TDOS low T

SUMMARY: exact solution (non-monotonic TDOS; susceptibility; ) Possible Generalizations / Extensions • • anisotropic SUMMARY: exact solution (non-monotonic TDOS; susceptibility; ) Possible Generalizations / Extensions • • anisotropic spin interactions ; finite B; susceptibility (d. c. + a. c. ) include superconductivity channel conductance: sequential tunneling; cotunneling. • disorder