Field-induced SU(4) to SU(2) Kondo crossover in a half-filling nanotube dot: Spectral and finite-temperature properties

Abstract

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 μ B B < k B T SU(4) K and it exhibits the SU(2) universality at μ B B k B T SU(4) K, where T SU(4) K 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 μ B B k B T SU(4) K .

Three-body correlations in nonlinear response of correlated quantum liquid

“…In this work, using a carbon nanotube QD in the SU (2) Kondo regime, we experimentally prove that the three-body correlations χ σ1σ2σ3 indeed contribute to the nonlinear conductance. Thanks to the quality of our sample, where the Kondo effect in the unitary limit is achieved, we quantitatively measure the three-body correlations, in perfect agreement with recent results of the Fermi liquid theory [18][19][20][21][22][23], and verify their role in the non-equilibrium regime. In particular, we demonstrate their importance when TRS is broken, and solve a longstanding puzzle of the Kondo system under the magnetic field [19].…”

“…Thus, the experimental observation of the deviation from the U = 0 case, which we refer as the free particle (FP) model later, directly tells us the relevance of those correlations in the nonlinear Kondo regime. In addition, recently, the expression of the coefficient α V in the interacting case was theoretically obtained by expanding the Fermi liquid theory to the non-equilibrium regime [18][19][20][21][22][23]. Our present work, relying on a precise experiment, aims to perform an accurate test of this theory.…”

Low-energy physics for an iron phthalocyanine molecule on Au(111)

“…The corresponding peaks are shifted from the Fermi energy (below it in the electron representation as opposed to the hole one used here) by λ a = 6.89 meV, λ b = 6.98 meV. The fact that the position and the half width of the peaks are of the same order is also expected, for example from the SU(4) Anderson model [29][30][31] . The increase of the Kondo energy scale for the π channels has the effect of decreasing the corresponding scale for the z 2 channel.…”

“…The weight of these channels in the ground state configuration of doubly occupied states is very similar (d 2 a = 0.156, d 2 b = 0.152). This fact has an effect of increasing markedly the Kondo temperature of these channels, as expected for example when the symmetry of the SU(2) Kondo model is increased to SU(4) [29][30][31] . We obtain ∆a = 6.53 meV, ∆a = 6.36 meV.…”

Real-space numerical renormalization-group computation of transport properties in the side-coupled geometry

“…These developments and subsequent advances have converted the method into an apt instrument in the rapidly growing area of nano-device development [5]. Numerous examples constitute recent literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”