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Probing the Kondo Density of States in Three-Terminal Quantum Rings
The Kondo effect is one of the hallmarks of many-body physics. It was discovered in bulk
metals with magnetic impurities providing localized unpaired spins, and observed later in
semiconductor quantum dots. The Kondo effect is the coherent coupling of a single unpaired
electron spin with a Fermi sea of electrons around this single spin. [1] The spins of the
surrounding electrons screen this single spin effectively forming a singlet.
In quantum dots the electron resides on a conducting island which is coupled through
tunnel contacts with the leads containing Fermi seas. [2] The strength of the coupling
is controlled by appropriate gate voltages applied to gates of the device. In this project
a novel device has been fabricated, namely a three-terminal quantum ring. [3]
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Figure 1: AFM image of the oxide lines defining the three-terminal quantum
ring. The three lateral gates marked LG1-LG3 are used to control the
conductance of the tunnel contacts. Currents are measured through leads 1,2,
and 3. The plunger gates PG control the charge on the quantum ring. |
The yellow lines mark lateral barriers being impenetrable for the electrons. Electrons can
tunnel from contacts 1 through 3 in and out of the quantum ring. Lateral gates LG1 through
LG3 are used to tune the coupling strength, lateral gates named PG are plunger gates which
tune the symmetry of the ring and the number of electrons on the device. Whether the single
spin residing on the quantum ring has Kondo correlations with the electrons in a given lead
depends on the tunneling coupling of the dot to this specific lead. In a three-terminal
configuration, which is unique to this experiment, one can determine, which lead has Kondo
correlation with the dot and which does not.
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Figure 2: Scheme of the DOS in a quantum dot connected to three
leads. One lead with chemical potential μ3 is in the
Kondo regime, the other two leads 1 and 2 are not. In addition, a finite
symmetric bias is applied between the two non-Kondo-correlated
leads. |
By carefully tuning the tunnel couplings different situations can be realized. In the above
case one lead termed μ3 has a large coupling to the dot (thin barrier),
and therefore gives to an additional contribution to the density of states in the dot shown
by the green peak. The two other leads μ1 and μ2
are weakly coupled (thick barrier) and do not provide additional contributions to the
density of states. In another situation two leads μ2 and
μ3 provide Kondo correlations and one lead μ1 does not.
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Figure 3:
Measurement of the Kondo resonances for different configurations of
the biases. The probing lead is number 1, a symmetric bias is applied between leads
2 and 3. For large bias between leads 2 and 3 the main resonance related to the Kondo
effect splits in two, which is a manifestaion of the non-equilibrium Kondo
effect. |
If there is no bias voltage applied between leads 2 and 3 then there is a single additional
contribution to the density of states which results in the blue maximum shown above in the
differential conductance trace through the quantum ring. If a bias is applied to the two
leads 2 and 3 and they provide two out-of-equilibrium contributions to the density of states
which show up as the two maxima of the red curve in the figure above.
This experiment shows several important things:
The spin correlations between a quantum system and its leads can be controlled and probed. The
additional density of states provided by Kondo correlations can by probed experimentally in and
out-of-equilibrium. Three terminal quantum devices allow the determination of intrinsic properties
of quantum devices.
The electrical tunability of many parameters of quantum dots makes them a favorable system to
study the Kondo effect, in particular out-of-equilibrium, which is an important theoretical
issue. Recently, theoretical proposals have shown that quantum dots might be suitable systems
for measuring the local density of states (DOS) in the Kondo regime in and out-of-equilibrium,
a challenge in scanning tunneling experiments.
For a quantum dot at equilibrium connected to two leads, the screening of the local spin by
electrons from both leads gives rise to a peak in the DOS aligned with the chemical potential
of the leads, and with a width of order kTK, TK being the Kondo
temperature. When a bias larger than kTK/e is applied between the leads a splitting
of the enhanced DOS into two peaks aligned with the two chemical potentials of the leads has
been predicted theoretically. These peaks will be reduced relative to the equilibrium peak,
due to incoherent scattering between the two leads.
[1] |
Kondo Effect in a Many-Electron Quantum Ring
A. Fuhrer, T. Ihn, K. Ensslin, W. Wegscheider, and M. Bichler
Phys. Rev. Lett. 93, 176803 (2004)
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[2] |
Multi-terminal transport through a quantum dot in the Coulomb blockade regime
R. Leturcq, D. Graf, T. Ihn, K. Ensslin, D. D. Driscoll, A. C. Gossard
Europhys. Lett., 67 (3), pp. 439-445 (2004)
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[3] |
Probing the Kondo Density of States in a Three-Terminal Quantum Ring
R. Leturcq, L. Schmid, K. Ensslin, Y. Meir, D. C. Driscoll, and A. C. Gossard
Phys. Rev. Lett. 95, 126603 (2005)
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Contact:
Klaus Ensslin |
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Laboratory for Solid State Physic
ETH Zurich
Switzerland
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