SU(2)–SU(4) Kondo Crossover and Emergent Electric Polarization in a Triangular Triple Quantum Dot

Abstract

We study an orbitally degenerate Kondo effect in a triangular triple quantum dot (TTQD), where the three dots are connected vertically with a single metallic lead through electron tunneling. Both spin and orbital degrees of freedom play an important role in the SU(4) Kondo effect. This is demonstrated by an equilateral TTQD Kondo system at half-filling, by Wilson's numerical renormalization group method. We show how an emergent electric polarization of the TTQD is associated with a crossover from SU(4) to SU(2) symmetry in the low-temperature state. A marked sign reversal of the electric polarization is generated by the fine-tuning of Kondo coupling with degenerate orbitals, which can be utilized to reveal orbital dynamics in the SU(4) Kondo effect.Since Kondo's pioneering work, 1 quantum impurities coupled to conduction electrons have been one of the major issues of strongly correlated electron systems for over half a century. 2-4 Nowadays, the accumulation of knowledge about the Kondo effect in bulk systems is applied to nanoscale or mesoscopic devices such as quantum dots (QDs) and molecular junctions, which extends the frontiers of quantum phenomena. 5-10 Indeed, typical Kondo behavior is observed in the conductance between metallic leads through a single QD, whose quantized energy levels are highly tuned by the gate voltage. 11-15 Recent nanofabrication techniques have facilitated various geometric configurations of multiple QDs. [16][17][18][19] Multicoupled QDs are considered as variants of a molecule in which spin and charge degrees of freedom play a crucial role through strong electron correlation.Such innovation of the Kondo physics motivates us to study a triangular triple quantum dot (TTQD) as the simplest multiple QD system with a closed loop. 16,18 When the three equivalent QDs form an equilateral triangle, doubly degenerate molecular orbitals of TTQD play the same role as a spin. At half-filling, the TTQD ground state is fourfold-degenerate with respect to both spin and orbital degrees of freedom, namely, SU(4)-symmetric. It is expected that the orbital dynamics leads to a highly symmetric SU(4) Kondo effect as a theoretical extension of a conventional spin SU(2) Kondo effect. 2, 3 Previous theoretical studies of TTQD systems have so far paid much attention to a lateral metallic contact that brings about rich Kondo physics related to three-site spin configurations of TTQD. [20][21][22][23][24][25][26][27][28] In such a lateral geometry, it is not practical to search for the SU(4) Kondo effect since the molecular orbital is not classified as a good quantum number. On the other hand, it is more appropriate to investigate a different TTQD system in which each QD is point-contacted vertically with a single lead. In this case, the SU(4) Kondo effect is realized by the C 3 symmetry of TTQD.In a related context, the SU(4) Kondo physics has been frequently studied using carbon nanotube devices whose dynamical properties come from valley degrees of freedom as well as spins, which correspond to the clockwis...

Spin-isospin Kondo effects for Σc and Σc* baryons and D¯Yasui1, Miyamoto2 2019Phys. Rev. C19070View full textAdd to dashboardCite

“…Simulations of the Kondo effect with SU(3) symmetry in cold atomic gases are also important [122]. It remains unclear as to how the Kondo effect with SU(4) symmetry for a c ( * c ) baryon is related to the Kondo effect with SU(4) symmetry in condensed matter systems, such as quantum dots, which has been studied theoretically [123][124][125][126][127][128][129][130] and experimentally [131][132][133][134]. Those issues need to be addressed in future work.…”

Spin-isospin Kondo effects for $Σ_{c}$ and $Σ_{c}^{\ast}$ baryons and $\bar{D}$ and $\bar{D}^{\ast}$ mesons

“…Simulations of the Kondo effect with SU(3) symmetry in cold atomic gases are also important [121]. It remains unclear as to how the Kondo effect with SU(4) symmetry for a Σ c (Σ * c ) baryon is related to the Kondo effect with SU(4) symmetry in condensed matter systems, such as quantum dots, which has been studied theoretically [122][123][124][125][126][127][128][129] and experimentally [130][131][132][133]. Those issues need to be addressed in future work.…”

Chiral splitting of Kondo peak in triangular triple quantum dot

“…Especially the triple quantumdot system, which present various Kondo effects depending on magnetic field, [13,14] electron filling N tot , [15,16] quantum phase transition, [17][18][19] and low-energy electronic transport properties. [20][21][22][23][24][25][26][27][28] In a ring-like TTQD structure, spin chirality is induced by the noncoplanar spin configuration. Existing studies show spin chirality has been applied to quantum computation by spin cluster qubits [29,30] in TTQD system.…”