Broken SU(4) symmetry in a Kondo-correlated carbon nanotube

Schmid, Daniel; Smirnov, Sergey; Margańska, Magdalena; Dirnaichner, Alois; Stiller, P. L.; Grifoni, Milena; Hüttel, A. K.; Strunk, Christoph

doi:10.1103/physrevb.91.155435

Cited by 51 publications

(108 citation statements)

References 52 publications

(143 reference statements)

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“…The signature of a valley mixing has been seen in several transport experiments on ultraclean CNT quantum dots in magnetic field [5,[18][19][20] and attributed to the presence of weak disorder. We studied the impact of an on-site disorder on the CNT spectra and show the results in Appendix C. The disorder introduces a level splitting in all CNTs.…”

Section: Inclusion Of the Spin-orbit Interaction (Soi)mentioning

confidence: 91%

“…Nevertheless, the valley mixing observed in the experiments [5,18,20] is small, and therefore unlikely to be caused by such strong perturbations. The modeling of the disorder through the variation of the on-site energies should therefore be applicable to describe the experimental situation.…”

Section: Appendix C: Disordermentioning

confidence: 99%

“…In Sec. IV, we include in our discussion the electron spin and show the results of numerical calculations of transmission through both CNT classes in parallel magnetic field, yielding transmission spectra similar to those observed in the experiments [5,[18][19][20]. The paper concludes with a brief summary and a short discussion of the role which the class of the CNTs may play in their applications.…”

Section: Introductionmentioning

confidence: 99%

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The two classes of low-energy spectra in finite carbon nanotubes

2015

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We study the spectra of finite-length carbon nanotubes (CNTs) of arbitrary chirality. They divide into two classes, which arise because of different rotational symmetries of the low-energy eigenstates. In one of them (the zigzag class), the spinless spectrum is doubly degenerate and the two states can be assigned to different values of the valley degree of freedom. In the other (armchair class), the valley degeneracy is removed and the eigenstates are combinations of both valley states. Recent experimental observation of the valley mixing in ultraclean CNT quantum dots is consistent with our theory for armchair-class CNTs.

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Section: Inclusion Of the Spin-orbit Interaction (Soi)mentioning

confidence: 91%

Section: Appendix C: Disordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The two classes of low-energy spectra in finite carbon nanotubes

2015

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“…4a and a cross-section is shown in the middle panel. Because spin and orbital degrees of freedom are degenerated, two channels contribute to transport, and Kondo resonance emerges at every filling factor, N = 1, 2 and 3 electrons [4][5][6][7] . At odd filling, the channels are half transmitted (T 1 = T 2 = 0.5), yielding the same conductance G Q as in the SU(2) symmetry.…”

Section: The Kondo Effectmentioning

confidence: 99%

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

et al. 2015

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Interacting quantum many-body systems constitute a fascinating research field because they form quantum liquids with remarkable properties and universal behaviour The idea is that they behave as an ensemble of non-interacting 'quasi-particles'. However, non-equilibrium properties have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi liquid theory extended to the non-equilibrium regime in a zero-dimensional system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) (ref. The Kondo effect19 is a typical example of a quantum manybody effect, where a localized spin is screened by the surrounding conduction electrons at low temperature to form a unique correlated ground state. The Kondo state is described well by the Fermi liquid theory at equilibrium 1,9 , which makes it an ideal testbed to go beyond equilibrium. To unveil the universal behaviour of nonequilibrium Fermi liquid 11 , we have used the current fluctuations or shot noise in a Kondo-correlated nanotube quantum dot 18 . When electrons are transmitted through this system, the scattering induces the shot noise, which sensitively reflects the nature of the quasi-particles 20 , as shown in the upper panel of Fig. 1a. A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,12-15 . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge). This value, closely related to the Wilson ratio, is universal for the Fermi liquid in the Kondo regime as it depends only on the symmetry group of the system [13][14][15] . Although some aspects of Kondo-associated noise have been reported 8,16,17 , a rigorous, selfconsistent treatment in a regime where universal results apply is at the core of the present work. Actually, by investigating the same nanotube quantum dot in the spin degenerate SU(2) Kondo regime and in the spin-orbit degenerate SU(4) regime, the noise is proved to contain distinct signatures of these two symmetries, confirming theoretical developments of Fermi liquid theory out of equilibrium.In our experiment, we measured the conductance and current noise through a carbon nanotube quantum dot grown by chemical vapour deposition 21 . Iron catalyst was deposited on an oxidized undoped silicon wafer and exposed to 10 mbar of acetylene for 9 s at 900• C. The nanotube was connected with a Pd(6 nm)/Al(70 nm) bilayer deposited by e-gun evaporation. The distance between the contacts is 400 nm and a side gate electrode is deposited to tune the potential of the quantum dot (see Fig. 1b). A magnetic field of 0.08 T is applied to suppress superconductivity of the contacts. To measure accurately the shot noise, our sample is connected to a resonant (2.58 MHz) LC circuit thermalized at the mixing chambe...

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“…The energy of SO coupling is comparable with the energy scale of Kondo effect and therefore the two effects interplay or compete. Several interesting articles have been published taking up this topic [30,41,51,[55][56][57]. The first theoretical analysis showing how SO interaction significantly changes the low-energy Kondo physics in CNTQDs was the paper of Fang et al [56], where the multipeak structure of manybody resonance resulting from the interplay of spin-orbit and Zeeman effect has been analyzed.…”

Section: Introductionmentioning

confidence: 99%

Intra- and inter-shell Kondo effects in carbon nanotube quantum dots

Krychowski¹,

Lipiński²

2018

Eur. Phys. J. B

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Abstract. The linear response transport properties of carbon nanotube quantum dot in the strongly correlated regime are discussed. The finite-U mean field slave boson approach is used to study many-body effects. Magnetic field can rebuilt Kondo correlations, which are destroyed by the effect of spin-orbit interaction or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects of different types: spin, valley or spin-valley, also more exotic phenomena appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the effective intervalley exchange induced by short-range part of Coulomb interaction or due to the intershell mixing. In narrow gap nanotubes the full spin-orbital degeneracy might be recovered in the absence of magnetic field opening the condition for a formation of SU(4) Kondo resonance.

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Broken SU(4) symmetry in a Kondo-correlated carbon nanotube

Cited by 51 publications

References 52 publications

The two classes of low-energy spectra in finite carbon nanotubes

The two classes of low-energy spectra in finite carbon nanotubes

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

Intra- and inter-shell Kondo effects in carbon nanotube quantum dots

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