Capri spring school, April 2009 With collaborators: P. Mehta - Princeton C. Bolech - Rice A. Jerez -...
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Transcript of Capri spring school, April 2009 With collaborators: P. Mehta - Princeton C. Bolech - Rice A. Jerez -...
Capri spring school, April 2009
With collaborators:
P. Mehta - Princeton C. Bolech - Rice A. Jerez - NJIT, Rutgers G. Palacios - Rutgers N. Andrei - RutgersSpecial Thanks: C. Yee -Rutgers
Sung Po Chao
Nonequilibrium transport in the Anderson model of a biased Quantum Dot
Goldhaber-Gordon et al, Cronenwet et al.van der Wiel et al.
Conductance vs gate voltage - Kondo enhancement in odd valleys
Differential conductance vs bias - Nonequilibrium dynamics
T varies in the range 15-800mK
Quantum Dot in and out of Equilibrium
Equilibrium
Nonequilibrium
(Lee & Ng,Glazman & Raikh)
Hamiltonian to describe the system: Single Impurity Anderson model
Scattering Bethe Ansatz approach: (P.Mehta, N.Andrei 06)1. Diagonalize the Hamiltonian out of equilibrium:
2 . Compute expectation value:
Current and Dot Occupation
Current and dot-occupation operators:
Expectation value expressed in terms of Bethe Ansatz density :
with and given by
Conductance in equilibrium: Numerical results
• Conductance vs. gate voltage
- Direct calculation from current. - Verifies Friedel SR - TBA vs SBA
Von Delft, notes
Conductance out of equilibrium: Numerical results..2 cases
Case 1:
Case 2: From Kondo to mixed valence
(0 refers to equilibrium Fermi surface of the leads)
Conductance out of equilibrium: Numerical results case 1
• Obtain Tk from quadratic fit for Kondo peak nearby V=0. Observed universality for small
voltage region.
• Conductance vs. bias voltage V:
• Conductance nearby zero voltage:
• Conductance for voltage larger than Kondo temp:
Conductance out of equilibrium: Numerical results case 2
• Conductance vs. bias voltage :
• Contour plot of conductance vs source-drain voltage and gate voltage:
• The Kondo effect forms as is decreased, destroyed as the bias voltage is increased
(M Grobis et al,PRL 100,246601)