Elastic Cotunneling Research Articles

Light-modulated 8-Pmmn borophene-based pure crossed Andreev reflection

Abstract We investigate the off-resonant circularly polarized light-modulated crossed Andreev reflection in an 8-Pmmn borophene-based normal conductor/superconductor/normal conductor junction. When the signs of Fermi energies in two normal regions are opposite, the pure crossed Andreev reflection without the local Andreev reflection and the elastic cotunneling occurs. By using the Dirac-Bogoliubov-de Gennes equation and the Blonder-Tinkham-Klapwijk formula, the pure crossed Andreev reflection conductance and its oscillation as a function of the junction length and the Fermi energy in the superconducting regions are discussed. It is found that the value of pure crossed Andreev reflection conductance peak value and its corresponding value of light-induced gap increase with the increase of incident energy of electron. Furthermore, the valley splitting for the transmitted hole is found due to the presence of tilted velocity of borophene. Our findings are beneficial for designing the high efficiency 8-Pmmn borophene-based nonlocal transistor and nonlocal valley splitter without local and non-entangled processes.

Electrically controlled nonlocal transport in antiferromagnet/superconductor junctions with Rashba spin-orbital coupling

Abstract We theoretically investigate nonlocal transport phenomena at an antiferromagnet/normal/superconductor/antiferromagnet junction. Both parallel and antiparallel configurations are considered, with the N\'{e}el vector aligned with the $z$ axis in the left antiferromagnet and with the $z$ and -$z$
 axes in the right antiferromagnet, respectively.
In the parallel configuration, only equal-spin crossed Andreev reflection (CAR) is allowed, as the conventional CAR is forbidden. As the Rashba spin-orbital coupling strength increases in the normal region, the amplitude of equal-spin CAR increases while the amplitude of electron elastic cotunneling (EC) decreases, resulting in equal-spin CAR-dominant nonlocal transport. In the antiparallel configuration, a CAR-dominant nonlocal transport is observed at low Rashba spin-orbital coupling strength, with the conventional CAR process being finite. Furthermore, our results indicate that increasing the staggered sublattice potential enhances the conventional CAR in the parallel configuration, and conversely, in the antiparallel configuration at high Rashba spin-orbital coupling strength, it reduces CAR dominance in favor of EC processes. Therefore, by adjusting the Rashba spin-orbital coupling strength and staggered sublattice potential, CAR-dominant nonlocal transport can be achieved in both the parallel and antiparallel configurations.

Electrically controlled crossed Andreev reflection in altermagnet/superconductor/altermagnet junctions

Altermagnets are a novel class of magnetic materials with a significant non-relativistic spin splitting band structure but zero net macroscopic magnetization. We here investigate the interplay between altermagnetism and superconductivity and how the band structures of the altermagnet affect nonlocal transport across altermagnet/superconductor/altermagnet junctions. The two types of spin-momentum coupling: anisotropic and valley-dependent spin-momentum couplings are considered. The pure crossed Andreev reflection (CAR) can be observed by tuning the chemical potential and a switch effect between pure CAR and pure electron elastic cotunneling (EC) can be realized by reversing the Néel vector of the right altermagnet. For the anisotropic spin-momentum coupling, increasing the altermagnetism strength decreases the amplitude of EC while increases that of CAR. Furthermore, a switch between pure EC and pure CAR is predicted for the Néel vectors of the altermagnets in the parallel configuration for the valley-dependent spin-momentum coupling by tuning the on-site energy.

Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors.

The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.

Minimal quantum dot based Kitaev chain with only local superconducting proximity effect

The possibility to engineer a Kitaev chain in quantum dots coupled via superconductors has recently emerged as a promising path toward topological superconductivity and possibly non-Abelian physics. Here we show that it is possible to avoid some of the main experimental hurdles on this path by using only local proximity effect on each quantum dot in a geometry that resembles a two-dot version of the proposal in Fulga []. There is no need for narrow superconducting couplers, additional Andreev bound states, or spatially varying magnetic fields; it suffices with spin-orbit interaction and a constant magnetic field in combination with control of the superconducting phase to tune the relative strengths of elastic cotunneling and an effective crossed-Andreev-reflection-like process generated by higher-order tunneling. We use a realistic spinful, interacting model and show that high-quality Majorana bound states can be generated already in a double quantum dot. Published by the American Physical Society 2024

Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires

Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires

Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device

Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device

Retro and specular Andreev reflections and valley-spin switching effect in graphene superconducting heterojunction

We investigated Andreev reflection of graphene-based normal/superconductor single and double junctions under the modulation of non-resonant circularly polarized light, staggered potential, and exchange field. In the graphene-based normal/superconductor single junction, we discovered that the circularly polarized light can adjust the bandgap of retro Andreev reflection and specular Andreev reflection. The exchange field can change the position of the transition point between retro Andreev reflection and specular Andreev reflection. In the graphene-based normal/superconductor/normal double junction, when the light field is modulated from left circularly polarized light to right circularly polarized light, the valley-spin switching effect between pure elastic co-tunneling and pure crossed Andreev reflection can be realized. By changing the exchange field, we achieved the conversion of non-local transport between pure elastic co-tunneling and pure crossed Andreev reflection. In addition, the energy location and range of crossed Andreev reflection and elastic co-tunneling can be controlled by the staggered potential and the exchange field. Our results suggest that the device can implement light and exchange field control of the Andreev reflection process and the spin-valley switch.

Realization of a minimal Kitaev chain in coupled quantum dots.

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.

Optimal thermoelectric induced by Cooper pair splitting

We study the optimal output power and efficiency of the thermoelectric induced by Cooper pair splitting(CPS). Due to its particular properties such as additional electron injection to the Quantum Dots system, Cooper pair splitting has been regarded as a powerful and available candidate of quantum heat engine. It is well known that elastic cotunnelling process coexist with CPS and several parameters such as temperature difference, bias voltage, Coulomb interaction. Which is most important is one of the key problems to determine the performance of the heat engine. We show the parametric dependence of the output power and efficiency and find the optimal performance of this heat engine with CPS through genetic algorithm.

Local and Nonlocal Two-Electron Tunneling Processes in a Cooper Pair Splitter.

We measure the rates and coupling coefficients for local Andreev, nonlocal Andreev, and elastic cotunneling processes. The nonlocal Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic cotunneling whereas the local Andreev process is more than 2 orders of magnitude stronger than the corresponding nonlocal one. Theory estimates describe the findings and explain the large difference in the nonlocal and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.

Direct coupling-induced pseudoparity nonconservation scattering: bipolar spin diode and unipolar spin entanglement pairing

The zigzag graphene nanoribbon (ZR) is characterized by the distinct pseudoparity combined with valley-selection rule, which could feature exotic transport phenomena, especially in ZR-based superconducting spintronic devices. However, the ZR with superconductivity induced by proximity of a bulk superconductor (SC) on it still keeps original band properties. Herein, we present a superconducting heterostructure with an SC directly coupling to two ZRs, which is characteristic of pseudoparity-mixing, resulting in pseudoparity nonconservation elastic cotunneling (EC) and crossed Andreev reflection (CAR) processes. It is shown that the mixing leads to the switch effect of the EC and CAR processes manipulated by the SC length, particularly the full spin polarization. In the context of only one magnetized ZR lead, a novel bipolar spin diode behavior on a scale of small SC length and unipolar spin entanglement pairing at some large SC lengths, are both exhibited on a large scale of forward and/or reverse bias voltages. More importantly, the spin-diode can be combined with the quantum spin Hall (QSH) insulator to provide smoking gun evidence for the helical spin texture of the (QSH) insulator, which is still lacking.

Conductance and shot noise in a silicene-based superconducting superlattice with two ferromagnetic electrodes

Using the scattering matrix method and the Blonder–Tinkham–Klapwijk formalism, we theoretically study the transport properties and the shot noise in a silicene-based superconducting superlattice (SCSL) with two ferromagnetic electrodes . It is found that for the antiparallel (AP) magnetization configuration, the crossed Andreev reflection (CAR) probability for spin-up electron from the K valley shows the nearly perfect transmission peak at the superconducting energy gap. With increasing the exchange splitting energy, the transmission probabilities of the elastic cotunneling and CAR processes for spin-up electron from the K valley around zero incident angle show the valley–peak–valley transitions. For the AP magnetization configuration, the local Fano factor shows the super-Poissonian value and the nonlocal Fano factor forms a Poissonian value plateau with weak oscillation within a suitable parameter regime. Compared to the local Fano factor, the nonlocal Fano factor is always sub-Poissonian for the parallel magnetization configuration, but for the AP magnetization configuration its maximum value increases and becomes super-Poissonian as the number of layers in the SCSL increases. • The crossed Andreev reflection probability shows nearly perfect transmission peak. • The transmission probabilities are symmetric about the incident angle of electron. • The super-Poissonian Fano factor is found. • The Poissonian value plateaus of the local and nonlocal Fano factors are formed. • The energy range with pure crossed Andreev reflection is robust to layer number.

Phase-modulated thermoelectric transport in a four-terminal ferromagnet/superconductor junction

We theoretically investigate the spuerconducting phase-modulated thermoelectric transport in a four-terminal ferromagnet/superconductor junction driven by a thermal gradient, in which a central quantum dot (QD) is coupled to two superconductors and two ferromagnetic leads. Both the Cooper pair splitting (CPS) and the elastic cotunneling (EC) can contribute to electric and heat currents. When the thermally induced electric current only originates from the CPS (EC), it is an even (odd) function of the QD level. The relative contributions of the CPS and EC can be modulated by the Zeeman field in the QD and the superconducting phase difference. Intriguingly, a Zeeman field controlled heat switch effect has been demonstrated. Furthermore, by varying the Zeeman field direction the heat current exhibits a conversion from a dip to a peak. These features can help us to distinguish the CPS from the EC and to design phase-coherent caloritronics devices.

Electrical control of crossed Andreev reflection and spin-valley switch in antiferromagnet/superconductor junctions

We study the subgap transport through the antiferromagnet/superconductor (AF/S) and antiferromagnet/superconductor/antiferromagnet (AF/S/AF) junctions controlled by electric field in a generic buckled honeycomb system, such as silicene, germanene, and stanene. In the presence of electric field and antiferromagnetic exchange field, the spin-valley polarized half-metallic phase can be achieved in the honeycomb system due to the spin-orbit coupling, which affords an opportunity to generate the pure crossed Andreev reflection (CAR). It is found that the pure CAR can be generated without local Andreev reflection (AR) and elastic cotunneling (EC) over a wide range of electric field. A spin-valley switch effect can be realized between the pure CAR and the pure EC by adjusting the electric field. The properties of AR process and CAR process strongly depend on the spin-valley polarized states. Our results suggest that the device can implement an electrical measurement of the CAR process and spin-valley switch.

Thermoelectric current in a graphene Cooper pair splitter

Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

Noise and full counting statistics of a Cooper pair splitter

We investigate theoretically the noise and the full counting statistics of electrons that are emitted from a superconductor into two spatially separated quantum dots by the splitting of Cooper pairs and further on collected in two normal-state electrodes. With negatively-biased drain electrodes and a large superconducting gap, the dynamics of the Cooper pair splitter can be described by a Markovian quantum master equation. Using techniques from full counting statistics, we evaluate the electrical currents, their noise power spectra, and the power-power correlations in the output leads. The current fluctuations can be attributed to the competition between Cooper pair splitting and elastic cotunneling between the quantum dots via the superconductor. In one regime, these processes can be clearly distinguished in the cross-correlation spectrum with peaks and dips appearing at characteristic frequencies associated with elastic cotunneling and Cooper pair splitting, respectively. We corroborate this interpretation by analyzing the charge transport fluctuations in the time domain, specifically by investigating the $g^{(2)}$-function of the output currents. Our work identifies several experimental signatures of the fundamental transport processes involved in Cooper pair splitting and provides specific means to quantify their relative strengths. As such, our results may help guide and interpret future experiments on current fluctuations in Cooper pair splitters.

Valley controlled Andreev reflection and valley-switch effect in graphene-based superconducting hybrid structures

The presence of the valley degree of freedom in two-dimensional materials leads to the valleytronics, in which information is encoded by the valley quantum number of the electron. For graphene-based superconducting hybrid structures, with the incoming electron and the Andreev reflected hole belonging to two opposite valleys, the Andreev reflection (AR) can be controlled by the valley degree of freedom. Here, we investigate theoretically the AR in graphene-based normal/supercondcutor junctions. Due to the interplay of the staggered potentials and the off-resonant circularly polarized light, the conductances demonstrate rich features. In particular, when the Fermi level of the normal lead is smaller than the superconducting gap, the retro AR and specular AR are well separated in energy, so we can easily distinguish them by studying the conductance spectra. More importantly, for normal/supercondcutor/normal junctions, the local AR is forbidden due to the vanishing density of states in one valley, and one may observe a valley-switch effect between perfect elastic cotunneling and perfect crossed AR, by reversing the handedness of the circularly polarized light.

Heat switch and thermoelectric effects based on Cooper-pair splitting and elastic cotunneling

In this paper, we demonstrate that the hybrid normal-superconducting-normal (NSN) structure has potential for a multifunctional thermal device which could serve for heat flux control and cooling of microstructures. By adopting the scattering matrix approach, we theoretically investigate thermal and electrical effects emerging in such structures due to the Cooper pair splitting (CPS) and elastic cotunneling phenomena. We show that a finite superconductor can, in principle, mediate heat flow between normal leads, and we further clarify special cases when this seems contradictory to the second law of thermodynamics. Among other things, we demonstrate that the CPS phenomenon can appear even in the simple case of a ballistic NSN structure.

Transport signatures of an Andreev molecule in a quantum dot-superconductor-quantum dot setup.

Hybrid devices combining quantum dots with superconductors are important building blocks of conventional and topological quantum-information experiments. A requirement for the success of such experiments is to understand the various tunneling-induced non-local interaction mechanisms that are present in the devices, namely crossed Andreev reflection, elastic co-tunneling, and direct interdot tunneling. Here, we provide a theoretical study of a simple device that consists of two quantum dots and a superconductor tunnel-coupled to the dots, often called a Cooper-pair splitter. We study the three special cases where one of the three non-local mechanisms dominates, and calculate measurable ground-state properties, as well as the zero-bias and finite-bias differential conductance characterizing electron transport through this device. We describe how each non-local mechanism controls the measurable quantities, and thereby find experimental fingerprints that allow one to identify and quantify the dominant non-local mechanism using experimental data. Finally, we study the triplet blockade effect and the associated negative differential conductance in the Cooper-pair splitter, and show that they can arise regardless of the nature of the dominant non-local coupling mechanism. Our results should facilitate the characterization of hybrid devices, and their optimization for various quantum-information-related experiments and applications.