To confirm the Majorana signatures, significant effort has been devoted to distinguishing between Majorana zero modes (MZMs) and spatially separated quasi-Majorana modes (QMMs). Because both MZMs and QMMs cause a quantized zero-bias peak in the condu
ctance measurement, their verification task is thought to be very difficult. Here, we proposed a simple device with a single nanowire, where the device could develop clear evidence of the topological Kondo effect in the topologically trivial phase with four QMMs. On the other hand, in the topological superconducting phase with MZMs, the transport signatures are significantly different. Therefore, our scheme provides a simple way to distinguish Majorana and quasi-Majorana modes.
The non-local coherent nature of the Majorana devices is one of the key factors for realizing decoherence-free topological qubits. Direct observation of this coherent nature could provide a first-step benchmarking scheme to validate Majorana qubit qu
ality. We propose a simple transport scheme with a Majorana island device along with a dissipative environment in the electrodes. We found that the dissipative environment renormalizes the quantum transport in significant different ways: As reducing temperature, while the conductance for Majorana coherent teleportation increases, all other incoherent signals are strongly suppressed due to dissipation. This special conductance scaling behavior is a clear benchmark to reveal the non-local coherent nature of Majorana devices.
A quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. The built-in spin flip mechanism is a consequence of the spin-v
ibration interaction resulting from the interplay between the intrinsic spin-orbit coupling and the vibrational modes of the suspended carbon nanotube. On the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. We find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin-vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. Moreover, in the linear response regime, the kinetic coefficient is non-monotonic in the temperature $T$ and it reaches its maximum when $k_BT$ is about one phonon energy. The existence of a strong intradot Coulomb interaction is irrelevant for our spin battery, provided that high-order cotunneling processes are suppressed.
Phonon-assisted electronic tunnelings through a vibrating quantum dot embedded between normal and superconducting leads are studied in the Kondo regime. In such a hybrid device, with the bias applied to the normal lead, we find a series of Kondo side
bands separated by half a phonon energy in the differential conductance, which are distinct from the phonon-assisted sidebands previously observed in the conventional Andreev tunnelings and in systems with only normal leads. These Kondo sidebands originate from the Kondo-Andreev cooperative cotunneling mediated by phonons, which exhibit a novel Kondo transport behavior due to the interplay of the Kondo effect, the Andreev tunnelings, and the mechanical vibrations. Our result could be observed in a recent experiment setup [J. Gramich emph{et al.}, PRL textbf{115}, 216801 (2015)], provided that their carbon nanotube device reaches the Kondo regime at low temperatures.
Motivated by experimental observation of the Kondo-enhanced Andreev transport [R. S. Deacon textit{et al.}, PRB textbf{81}, 121308(R) (2010)] in a hybrid normal metal-quantum dot-superconductor (N-QD-S) device, we theoretically study the Kondo effect
in such a device and clarify the different roles played by the normal and superconducting leads. Due to the Andreev reflection in a QD-S system, a pair of Andreev energy levels form in the superconducting gap, which is able to carry the magnetic moment if the ground state of the QD is a magnetic doublet. In this sense, the Andreev energy levels play a role of effective impurity levels. When the normal lead is coupled to the QD-S system, on the one hand, the Andreev energy levels broaden to form the so-called Andreev bound states (ABSs), on the other hand, it can screen the magnetic moment of the ABSs. By tuning the couplings between the QD and the normal (superconducting) leads, the ABSs can simulate the Kondo, mixed-valence, and even empty orbit regimes of the usual single-impurity Anderson model. The above picture is confirmed by the Greens function calculation of the hybrid N-QD-S Anderson model and is also able to explain qualitatively experimental phenomena observed by Deacon textit{et al.}. These results can further stimulate related experimental study in the N-QD-S systems.
Thermoelectric effect is exploited to optimize the Cooper pair splitting efficiency in a Y-shaped junction, which consists of two normal leads coupled to an $s$-wave superconductor via double noninteracting quantum dots. Here, utilizing temperature d
ifference rather than bias voltage between the two normal leads, and tuning the two dot levels such that the transmittance of elastic cotunneling process is particle-hole symmetric, we find currents flowing through the normal leads are totally contributed from the splitting of Cooper pairs emitted from the superconductor. Such a unitary splitting efficiency is significantly better than the efficiencies obtained in experiments so far.
Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $chi_{textrm{imp}}$ to susceptibility, defined or
iginally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $chi_{textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility $chi_{textrm{loc}}$ and to compare them with $chi_{textrm{imp}}$ obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in $chi_{textrm{imp}}$ are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding $chi_{textrm{loc}}$ less accurate than $chi_{textrm{imp}}$, the FDM method allows a high-precision dynamical calculation of $chi_{textrm{loc}}$ at much reduced computational cost, with an accuracy at least one order higher than $chi_{textrm{imp}}$. Moreover, artifacts in the FDM algorithm to $chi_{textrm{imp}}$, and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilsons definition to such cases.
We propose a scheme to detect the Majorana bound states (MBSs) by a thermodynamically stable D.C. Josephson current with $4pi$-periodicity in the superconducting phase difference, which is distinct from the previous A.C. $4pi$-periodicity found in to
pological superconducting Josephson junctions. The scheme, consisting of a quantum dot coupled to two s-wave superconducting leads and a floating topological superconductor supporting two MBSs at its ends, only exploits the interplay of a local Zeeman field and the exotic helical and self-Hermitian properties of MBSs, without requiring the conservation of fermion parity and not relying on the zero-energy property of MBSs. Our D.C. $4pi$-periodicity is thus robust against the overlap between the two MBSs and various system parameters, including the local Coulomb interaction, the tunneling asymmetry, and the width of superconducting gap, which facilitates experimentally detection of the MBSs.
