Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Transport Measurement of Andreev Bound States in a Kondo-Correlated Quantum Dot Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 Rosa López Institute of Interdisciplinary Physics and Complex Systems UIB Experiment: B.-K. Kim, Y.-H. Ahn, J.-J. Kim, M.-H. Bae, N. Kim Theory: R. Lopez, K. Kang, M.-S. Choi Geneva 5th July 2013 Our story is about a Josephson-junction Superconductor Normal metal Insulator Quantum dot ... Superconductor Due to Andreev reflexion the current can flow without any voltage drop! -> Supercurrent One-page summary Usual Josephson phase-current relation 0-junction But, under some conditions pi-junction This phase transition is followed by the crossing of the Andreev bound states! Tunneling spectroscopy of the ABS and the 0-pi transition Outline 1. Kondo effect • Andreev bound states (ABS) • 0-p transition • Nonequilibrium transport measurement of ABS Resistivity vs temperature (residual resistance) nonmagnetic impurity metal http://physics.info/condensed-matter/ Phonon scattering decreases with decreasing temperatures Resistance minimum: due to static impurities, dependent on impurity concentration Resistivity vs temperature: mathematical formula Residual resistance due to nonmagnetic impurities: temperature independent • Fermi liquid contribution (electron-electron scattering) • Lattice vibration (phonon scattering) What happens with magnetic impurities? (Bulk Kondo effect) First observation: Electrical resistivity of Au de Hass et al., 1934 First theoretical explanation: J. Kondo, 1964 Kondo temperature Resistivity vs temperature: mathematical formula high-energy excitations also contribute! Kondo’s explanation for the resistance minimum As T goes to zero, this term diverges. The so-called Kondo temperature TK is defined as the energy scale limiting the validity of Kondo’s perturbation theory. Kondo Hamiltonian and RG flow Spin flip-flop scattering For antiferromagnetic isotropic model ß-function Hewson, The Kondo problem to heavy fermions (1993) Kondo singlet http://en.wikipedia.org/wiki/Kondo_effect At low T, the impurity magnetic moment and one conduction electron moment bind very strongly and make a singlet (nonmagnetic) state. Asymptotic freedom http://www.theory.caltech.edu/~preskill/Nobel2004_JP.pdf Like the quark, at high energies the local moments inside metals are asymptotically free, but at temperatures below TK they strongly interact with the surrounding electrons so that they become confined at low energies. P. Coleman (2006) Mesoscopic Kondo effect lead (contact,terminal) L C R central region L. Kouwenhoven and L. Glazman, Physics Today (2001) In a metal: scattering from impurities mixes electron waves with different momenta. This momentum transfer increases the resistance. In a quantum dot: all electrons have to travel through the device as there is no other path. States belonging to the two opposite electrodes are mixed due to the Kondo effect. Thus, this mixing increases the conductance. In order to observe the Kondo effect, there must be a well-defined local moment! Anderson model Noninteracting single particle Hamiltonian Conduction (lead) Hamiltonian Dot Hamiltonian Tunneling Hamiltonian L C R Formation of a local moment Magnetization vs Coulomb interaccion Spin flip and resonance level Kondo resonance, hallmark of the Kondo effect Many spin-flip events give rise to the Kondo effect, and as a result an extra resonance appears at the Fermi level. Kondo effect in the unitary limit W. G. van der wiel et al., Science (2000) Question: In the presence of (magnetic) impurities, what happens if we replace the normal leads by the superconducting leads? N C N S C S With nonmagnetic impurities? nonmagnetic impurity local (dot) density of state With N leads Superconductor (SC) Proximity induced gap Bound states are induced, but they are located at the gap edges! Density of states (SC) What happens in a SC with magnetic impurities? Yu-Shiba-Rusinov (YSR) bound states: Bound states emerging as a result of the exchange coupling J Pair creation (annihilation) YSR bound state solution YSR states A. V. Balatsky et al., RMP (2006) Andreev reflection and Andreev bound states (ABS) At the NS interface, an electron produces a Cooper pair in the superconductor and a retroreflected hole in the normal region N S S electron and retroreflected hole, and vice versa, make a complete loop so that according to Bohr’s quantization rule we have bound states. Zagoskin, Quantum theory of many-body systems (1998) The 0-p Transition S S QD M.-S. Choi et al., PRB (2004) Two characteristic energy scales: p-junction • Kondo temperature 0-junction • Superconducting gap Ground state: doublet vs singlet Possible explanation for the p-junction In order that electrons be in the canonical order, it is necessary in the indicated step to permute the order of the two electrons. Canonical order This exchange is responsible for the negative sign due to fermion anticommutation rule! B. I. Spivak and S. A. Kivelson, PRB (1991) Phase diagram The energy flow goes to the strong fixed point. The flow is not attracted to the strong fixed point. Andreev bound states J. Bauer et al., JPCM (2007) Importantly The 0-p transition is always followed by the crossing of the ABS! J.S Lim and M-S Choi JPCM (2008) and J. Bauer et al., JPCM (2007) Large gap limit: effective single site Hamiltonian Lead degrees of freedom are integrated out so that only the d-site is considered. Proximity effect Bogoliubov transformation A. Oguri et al., arXiv:1210.3260 (2012) Why the 0-p transition is followed by the crossing of the Andreev bound states? Occupation and corresponding energy Singlet Doublet Singlet Phase boundary: Possible excitations: The excitations correspond to the positions of the ABS. When EA=U/2, the ABS crosses the Fermi level and signal the 0-p transition. Critical current is measured Vg is tuned to show the 0-p transition What’s new in our experiment? Previous experiments: Up to date, ABS has been measured only in equilibrium. Measurements of the ABS in the weak coupling regime. • Either ABS or 0-p transition has been measured separately. Our experiment: First measurements of the ABS in the strong coupling regime. We observe two different prototypes of the Kondo ridges depending on the ratio . In nonequilibrium, simultaneous observation of ABS level crossing and the 0-p transition has been achieved! Physics gets complicated: What happens in a finite bias? Multiple Andreev reflection (MAR) AC Josephson effect Time-dependent Hamiltonian Bloch theory Space periodic H. Sambe, PRA (1973) S.-I Chu and D. A. Telnov, PR (2004) Floquet theory Time periodic MAR in a SNS junction J. C. Cuevas and W. Belzig, PRL (2003) MAR in a S-QD-S subpeaks When we replace the normal region by a resonant level (quantum dot), physics depends on the level position, onsite Coulomb interaction and so on. General condition: The resonant level must align with the energetic path. M. R. Buitelaar et al., PRL (2003) Andreev Transport is probed odd odd even MAR peak questionable ??? Our experiment Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 • Normal State Kondo peaks appear in the odd valleys Normal • Superconducting State Even valleys show peaks due to quasiparticle cotunneling at Vsd=2D,-2D toguether with a weak Andreev reflection at at Vsd=D,-D MAR (X) Superconducting (magnetic field x) Odd valley show a rich subgap structure for -D<Vsd<D Two types of Kondo ridges: D and E Depending on the Tk and D relative strength Our experiment Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 More carefully D valley Kondo dominant D valley Anticrossing E valley 0-p transition E valley Crossing Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 Our experiment Asymmetry Factor • Right barrier much weaker coupled to the CNT • Right barrier works as a probe of the ABS formed by the left barrier and the CNT Andreev Bound States probed by the dI/dVsd are Our experiment Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 Andreev Bound States are probed by the dI/dVsd The observed anticrossing (D) and crossing (E) are indeed an anticrossing and crossing of the Andreev Bound States Remember: an ABS anticrossing signals a 0-p transition Our experiment Phys. Rev. Lett. 110, 076803 arXiv:1209.4738 Now we demonstrate the conection of the crossing of the ABS with the 0-p transition An ABS anticrossing signals a 0-p transition: The critical current signal is high in the 0-junction behavior whereas in the p-junction the critical current is drastically reduced NRG result: J. S. Lim and R. Lopez’s contribution Ridge D Ridge E Actually, the left lead is in equilibrium with the QD so that we can employ the NRG. FYI: How to measure the critical current IC? M. Tinkham, Introduction to superconductivity (1996) Experiment NRG Conclusion Gate tunable ABS are reported in I-V measurement in an Al-CNT-Al Josephson junction. The observed dI/dV shows the two distinct types of the Kondo ridges associated with ABS. ABS displays crossing (anti-crossing) behavior, which is the main characteristics of the 0-p transition (0-junction) tuned by a gate voltage applied to the QD. This feature is also consistent with a measurement of the gatedependent critical current. The experimental results are confirmed by a NRG calculation. Thank you for your attention. 참석해 주셔서 감사합니다.