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Register a new userMagnetic Field Probing of an SU(4) Kondo Resonance in a Single Atom Transistor
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Added by
Giuseppe Carlo Tettamanzi Dr
Publication date
2011
fields
Physics
and research's language is
English
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Semiconductor nano-devices have been scaled to the level that transport can be dominated by a single dopant atom. In the strong coupling case a Kondo effect is observed when one electron is bound to the atom. Here, we report on the spin as well as orbital Kondo ground state. We experimentally as well than theoretically show how we can tune a symmetry transition from a SU(4) ground state, a many body state that forms a spin as well as orbital singlet by virtual exchange with the leads, to a pure SU(2) orbital ground state, as a function of magnetic field. The small size and the s-like orbital symmetry of the ground state of the dopant, make it a model system in which the magnetic field only couples to the spin degree of freedom and allows for observation of this SU(4) to SU(2) transition.
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Single dopants in semiconductor nanostructures have been studied in great details recently as they are good candidates for quantum bits, provided they are coupled to a detector. Here we report coupling of a single As donor atom to a single-electron transistor (SET) in a silicon nanowire field-effect transistor. Both capacitive and tunnel coupling are achieved, the latter resulting in a dramatic increase of the conductance through the SET, by up to one order of magnitude. The experimental results are well explained by the rate equations theory developed in parallel with the experiment.
We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a $T^{2}$ coefficient of conductance becomes zero at quarter-filling whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU($4$) scaling behavior at $mu_{B}B<k_{B}T_{K}^{mathrm{SU(4)}}$ and it exhibits the SU($2$) universality at $mu_{B}Bgg k_{B}T_{K}^{mathrm{SU(4)}}$, where $T_{K}^{mathrm{SU(4)}}$ is the SU($4$) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for $mu_{B}B gtrsim k_{B}T_{K}^{mathrm{SU(4)}}$.
In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $ u=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.
Using a time-dependent Anderson Hamiltonian, a quantum dot with an ac voltage applied to a nearby gate is investigated. A rich dependence of the linear response conductance on the external frequency and driving amplitude is demonstrated. At low frequencies the ac potential produces sidebands of the Kondo peak in the spectral density of the dot, resulting in a logarithmic decrease in conductance over several decades of frequency. At intermediate frequencies, the conductance of the dot displays an oscillatory behavior due to the appearance of Kondo resonances of the satellites of the dot level. At high frequencies, the conductance of the dot can vary rapidly due to the interplay between photon-assisted tunneling and the Kondo resonance.
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