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Spintronics Takes Advantage of the Electronic Spin In I. MOTIVATION Spintronics takes advantage of the electronic spin in designing a variety of applications, in- cluding for giant magnetoresistance sensing, quantum computing, and quantum-information processing [1, 2]. The spins of mobile electrons can be manipulated by the spin-orbit interac- tion (SOI), which causes the spin of an electron moving through a spin-orbit active material to rotate. Transport properties of spin-active electric weak links has been the subject of our ASG's at PCS in 2018 and 2019. The main results obtained so far during one and a half year's work, where the emphasis has been on new functionalities of spin-active devices, can be grouped depending on the area of research as follows: A. Electric transport in spin-orbit-interaction (SOI) active electric weak links a) The theoretical concept of \Rashba splitting" of electrons transferred through an SOI- active electric weak link was formulated and applied to a supercurrent flowing through a superconducting weak link [3, 4]. We have shown that a transfer of Cooper pairs through an SOI-active weak links results in their spin-polarization, which makes it possible to generate a supercurrent that carries a finite spin. b) Extra spin and charge can be accumulated in a small quantum dot by letting a super- current of spin-polarized Cooper pairs flow through it. New types of superconducting proximity states carrying both charge and spin were theoretically considered [5]. c) Electric- and magnetic gating effects on electron- and spin transport through a spin- orbit-active nanowire were suggested as tools for detecting and measuring spin-orbit coupling in nanomaterials [6]. B. Spin generation in mechanically driven SOI devices We have predicted theoretically that a non-zero spin current can be generated in me- chanically driven SOI-active electric weak links [7]. As a result a nanometer size point-like spin current-source is suggested for possible nano-spintronic applications. 1 C. Heat transport in magnetic shuttle structures We predicted theoretically that heat transport through an electric weak link made of magnetic material can be controlled via the spin of the electrons that carry the heat [8]. This is due to the strong coupling of the electronic spin to the mechanical vibrations of the electric weak link, a coupling which causes a mechanical instability which can be seen as a thermal breakdown, similar to the electric breakdown occurring in electric transport. This prediction has important consequences for applications including those addressing the important issue of heat removal from electronic nanodevices. The electric charge of electrons becomes an important player in the physics of mesoscopic transport if discrete electron tunneling events are important elements of the process. If a weak link is connected to electrodes by high-resistance tunneling barriers, the picture of a continuous charge flow valid for bulk conductors is replaced by the image of discrete tun- neling events between spatially localized electronic states. In such a picture the discrete nature of the charge carried by single electrons qualitatively change the physics of small size conductors. The charging energy U needed to accumulate an extra electric charge e in the small volume of a mesoscopic conductor determines the role of the Coulomb correlations dominating the physics of mesoscopic nanodevices. At low temperatures, T U, thermal fluctuations of the number of electrons accumulated in a conductor is suppressed and new physical phenomena come into play. In this case the parity of the number of electrons be- comes a good quantum number, allowing for qualitatively new physical phenomena. Two examples of such phenomena relevant for the present application are: 1) the parity effect in superconducting quantum dots [9, 10] and 2) parity controlled spin-accumulation in a dot [11]. The first example amounts to the quantization of charge in a superconducting quantum dot in units of 2e, which allows for the formation of a superconducting \Cooper pair box" a key ingredient for the implementation of a qubit for quantum computing using supercon- ducting devices. The second example allows for electrostatic control of the spin-dependent magnetic exchange force determining mechanically assisted charge- and heat transport in magnetic nanodevices. Our previous theoretical predictions and recent results obtained within the ongoing ASG program demonstrate qualitatively new performances occurring from the electrostatically controlled [13] electron number parity, such as the phenomenon 2 of Coulomb promotion of mechanically assisted transport and mechanically assisted Cooper pair transfer through superconducting Josephson junctions [12, 13]. The interplay between the two fundamental electronic degrees of freedom, charge and spin, and the quantum orbital motion of electrons in mesoscopic nanodevices will be in fo- cus of the proposed research program for the new ASG. Possible nanodevice applications employing mechanical degrees of freedom of normal metals, semiconductors, magnets and superconductors will be explored in in close cooperation with experimentalists in two labo- ratories that we collaborate with. The very choice of the directions of our planned research is significantly affected by the desire to establish such a close cooperation as well as looser cooperation with the members of PCS. II. OBJECTIVES: (a) To build collaborative scientific research with the experimental group of Dr. Junho Suh (through a theoretical study SOI-induced nanomechanics; microwave induced spin- current generations, etc.). (b) To build collaborative scientific research with the experiment group of Dr. Chulki Kim (KIST, Seoul) (through the formulation of a theory of superconducting nanomechan- ics). (c) To develop theoretical studies of the interplay of spin and charge in many-body struc- tures with SOI. (d) To extend further the cooperation and collaborative research with PCS members (pre- liminary discussions show a significant potential in involving such PCS members as Drs. M. Fistul, A. Parafilo, Sang-Jun Choi, Kunwoo Kim, and Sungjong Woo in the planned research on the nanoelectromechanics of magnetic and superconducting nanodevices, and Nojoon Myoung (Chosun University) and Sejoong Kim (UST) for spin-active 2D materials). (d) To organize an International workshop on Mesoscopic Nanoelectromechanics, which we consider as a special objective of the planned ASG activity for the year 2020. Such an international event, which will be held at PCS IBS, is specially motivated by the 3 obvious advantage for the ASG in particular and for the wider community of Korean scientists in general, especially the younger ones in Daejeon, in getting some of the leading world experts in our field to Daejeon for an intensive period of interaction. Further collaboration with theoreticians and experimentalists at the cutting edge of our field would be a both desirable and probable outcome. Moreover, the format of an ASG-related Workshops at PCS would provide an ideal opportunity to advertise to the relevant international community the quite considerable progress we have been fortunate to make since the launch of our ASG one year ago. This progress has been achieved in the broad area of functional spin-driven mesoscopics, which is the basis for the operation of a number of possible future nanodevices. It involves, e.g., spin-orbit- interaction driven transport in semiconductors, metals, magnets and superconductors, where the interplay between quantum coherence and electron-electron correlations are crucial, and many-body effects in Kondo transport. III. RESEARCH DIRECTIONS A. High frequency properties of SOI-active weak links: a) Spin generation and charge accumulation in AC-driven Rashba weak links; - ASG members responsible for the research: M. Jonson, O. Entin-Wohlman, A. Aharony, J. Suh b) DC charge transport controlled by AC driven SOI; - ASG members responsible for the research: M. Jonson, O. Entin-Wohlman, A. Aharony, H.C. Park, D. Radi´c,J. Suh c) Nano-mechanics of suspended nano-wires, driven by high frequency SOI; - ASG members responsible for the research: I. Krive, H.C. Park, M. Jonson, O. Entin-Wohlman, J. Suh. B. Properties of SOI-active NEM devices with coupled spintronic, electric and mechanical degrees of freedom (Spintro-electro-mechanics of SOI-active NEM devices): a) Mechanically generated spin-currents in SOI-active weak links; - ASG members responsible for the research: O. Entin-Wohlman, A. Aharony, M. Jonson, J. Suh 4 b) SOI-induced mechanical force and Rashba pumping of nanovibrations; - ASG members responsible for the research: O. Entin-Wohlman, A. Aharony, H.C. Park, D. M. Jonson, J. Suh. C. Nano-electro-mechanics of superconducting weak links: a) Electro-mechanics of a superconducting Cooper-pair box (CPB) (formulation of approach); - ASG members responsible for the research: L. Gorelik, D. Radi´c,H.C. Park, C. Kim b) Cohesive and Coulomb forces driving mechanical CPB vibrations; - ASG members responsible for the research: L. Gorelik, D. Radi´c,H.C. Park, C. Kim c) Resonant generation of pronounced CPB vibrations in a DC voltage biased device; - ASG members responsible for the research: L. Gorelik, D. Radi´c,H.C. Park, C. Kim d) Shuttle instability due to mechanical transportation of Cooper pairs; - ASG members responsible for the research: L. Gorelik, H.C. Park, C. Kim. D. Coulomb promotion of spintro-mechanics in magnetic shuttle devices - ASG members responsible for the research: I. Krive, D. Radi´c,H.C. Park, M. Jonson. E. Electron number parity-controlled thermoelectricity in spin-active NEM devices - ASG members responsible for the research: I. Krive, D. Radi´c,H.C. Park, M. Jonson. A. High frequency properties of SOI-active weak links One aim of spintronics is to build logic devices [14], which produce spin-polarized elec- trons, so that one can use their electronic spinors as qubits. In the simplest device, electrons move between two large electronic reservoirs, via a nano-scale quantum network. For this two-terminal case, time-reversal symmetry and unitarity of the Hamiltonian prevent any spin splitting of the transport between the reservoirs [15].
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