Magnetically tunable Kondo-Aharonov-Bohm effect in a triangular quantum dot

Fast creation and transfer of coherence in triple quantum dots by using shortcuts to adiabaticity

Motivated by the progress on shortcuts to adiabaticity, we propose three schemes for speeding up (fractional) stimulated Raman adiabatic passage, and achieving rapid and non-adiabatic creation and transfer of maximal coherence in a triple-quantum-dot system. These different but relevant protocols, designed from counter-diabatic driving, dress-state method, and resonant technique, require their own pumping fields, applied gate voltages and varying tunneling couplings between two spatially separated dots. Such fast and reliable shortcuts not only allow for feasibly experimental realization in solid-state architectures but also may have potential applications in quantum information processing and quantum control.

Suppressed Kondo effect and Kosterlitz-Thouless-type phase transition induced by level difference in a triple dot device

Quantum dot system provides an ideal platform for quantum information processing, within which to demonstrate the quantum states is one of the most important issue for quantum simulation and quantum computation. In this paper, we report a peculiar electron state in a parallel triple dot device where the Ruderman-Kittel-Kasuya-Yosida interaction is invalid when the level differences of the dots sweep into appropriate regime. This extraordinary tendency then results in an antiferromagnetic spin coupling between two of the dots and may lead to zero or full conductance, relying deeply on the relation of the two level spacings. e.g. when the level differences are kept equal, the Kondo effect is totally suppressed although the dots are triply occupied, since in this case a local inter-dot transport loop is found to play an important role in the transmission coefficient. By contrast, when the differences are retained symmetric, the Kondo peak reaches nearly to its unitary limit, owing to that the inter-dot transport process is significantly suppressed. To approach these problems, voltage controllable quantum phase transitions of Kosterlitz-Thouless type and first order are shown, and possible pictures related to the many-body effect and the effective Kondo model are given.

Coherent and incoherent charge transport in linear triple quantum dots

One of the fundamental questions in quantum transport is how charge transfer through complex nanostructures is influenced by quantum coherence. We address this issue for linear triple quantum dots by comparing a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics of charge transfer. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of large coupling to the drain reservoir, can be used to unambiguously evidence coherent processes involved in charge transport across triple quantum dots. Our analytical results are obtained by using the characteristic polynomial approach to full counting statistics.

Transport in serial spinful multiple-dot systems: The role of electron-electron interactions and coherences

Quantum dots are nanoscopic systems, where carriers are confined in all three spatial directions. Such nanoscopic systems are suitable for fundamental studies of quantum mechanics and are candidates for applications such as quantum information processing. It was also proposed that linear arrangements of quantum dots could be used as quantum cascade laser. In this work we study the impact of electron-electron interactions on transport in a spinful serial triple quantum dot system weakly coupled to two leads. We find that due to electron-electron scattering processes the transport is enabled beyond the common single-particle transmission channels. This shows that the scenario in the serial quantum dots intrinsically deviates from layered structures such as quantum cascade lasers, where the presence of well-defined single-particle resonances between neighboring levels are crucial for device operation. Additionally, we check the validity of the Pauli master equation by comparing it with the first-order von Neumann approach. Here we demonstrate that coherences are of relevance if the energy spacing of the eigenstates is smaller than the lead transition rate multiplied by ħ.

Heavy-Fermion Valence-Bond Liquids in Ultracold Atoms: Cooperation of the Kondo Effect and Geometric Frustration

We analyze a microscopic mechanism behind the coexistence of a heavy Fermi liquid and geometric frustration in Kondo lattices. We consider a geometrically frustrated periodic Anderson model and demonstrate how orbital fluctuations lead to a Kondo-screened phase in the limit of extreme strong frustration when only local singlet states participate in the low-energy physics. We also propose a setup to realize and study this exotic state with SU(3)-symmetric alkaline-earth cold atoms.

Gate-controlled transitions in triple dots with interdot repulsion and magnetic field

We study the quantum phase transition (QPT) and electronic transport in triple quantum dots for a wide range of the gate voltage ϵ. We focus on the effect of the interdot repulsion V and the magnetic field B. In the case of particle-hole (p-h) symmetry and B = 0, we find the local quadruplet-doublet transition of first order when V increases to a critical point V(c) ≈ U, where U is the on-site repulsion. Beyond the p-h symmetry, the sequence of the QPTs depends on ϵ. For small ϵ, a first order doublet-singlet transition is observed. For middle ϵ, we find the quadruplet-triplet transition of first order at V(c1) and the triplet-singlet transition of the Kosterlitz-Thouless type at V(c2). For large ϵ, there are two kinds of first order QPT with phase sequence quadruplet-triplet-doublet. The magnetic field B compensates for the effect of V. For V > U, as B increases we find a first order or second order QPT from a low-spin state to a high-spin state. The restoring of the Kondo effect and a perfect spin filtering is realized in the appropriate regime of the magnetic field.

Physics of lateral triple quantum-dot molecules with controlled electron numbers

We review the recent progress in theory and experiments with lateral triple quantum dots with controlled electron numbers down to one electron in each dot. The theory covers electronic and spin properties as a function of topology, number of electrons, gate voltage and external magnetic field. The orbital Hund's rules and Nagaoka ferromagnetism, magnetic frustration and chirality, interplay of quantum interference and electron-electron interactions and geometrical phases are described and related to charging and transport spectroscopy. Fabrication techniques and recent experiments are covered, as well as potential applications of triple quantum-dot molecule in coherent control, spin manipulation and quantum computation.

The tunnel magnetoresistance in chains of quantum dots weakly coupled to external leads

We analyze numerically the spin-dependent transport through coherent chains of three coupled quantum dots weakly connected to external magnetic leads. In particular, using the diagrammatic technique on the Keldysh contour, we calculate the conductance, shot noise and tunnel magnetoresistance (TMR) in the sequential and cotunneling regimes. We show that transport characteristics greatly depend on the strength of the interdot Coulomb correlations, which determines the spatial distribution of the electron wavefunction in the chain. When the correlations are relatively strong, depending on the transport regime, we find both negative TMR as well as TMR enhanced above the Julliere value, accompanied with negative differential conductance (NDC) and super-Poissonian shot noise. This nontrivial behavior of tunnel magnetoresistance is associated with selection rules that govern tunneling processes and various high-spin states of the chain that are relevant for transport. For weak interdot correlations, on the other hand, the TMR is always positive and not larger than the Julliere TMR, although super-Poissonian shot noise and NDC can still be observed.

Spin-selective Aharonov-Bohm oscillations in a lateral triple quantum dot

We present a theory of spin-selective Aharonov-Bohm oscillations in a lateral triple quantum dot. We show that to understand the Aharonov-Bohm (AB) effect in an interacting electron system within a triple quantum dot molecule (TQD) where the dots lie in a ring configuration requires one to not only consider electron charge but also spin. Using a Hubbard model supported by microscopic calculations we show that, by localizing a single electron spin in one of the dots, the current through the TQD molecule depends not only on the flux but also on the relative orientation of the spin of the incoming and localized electrons. AB oscillations are predicted only for the spin singlet electron complex resulting in a magnetic field tunable "spin valve."

Tuning kinetic magnetism of strongly correlated electrons via a staggered flux

An interplay between kinetic process and magnetic ordering is manifested when strong correlation and electronic frustration are present: tuning a staggered flux phi from 0 to pi makes the ground state (GS) of an infinite-U Hubbard model change abruptly from a Nagaoka-type ferromagnet to a Haerter-Shastry-type antiferromagnet at a phi_(c), with both states being metallic and of kinetic origin. Intraplaquette spin correlation, as well as nonanalyticity in the GS energy, signals such a novel quantum criticality. This tunable kinetic magnetism is generic and may be experimentally realized.