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Topological band theory has contributed to some of the most astonishing developments in solid-state physics. The unique attributes that arise from topological effects are at the focus of modern experimental and theoretical research. Weyl point, a topological defect at the Fermi surface, enables topological transitions and transport phenomena. Its existence is considerably restricted in natural materials due to the tuning and dimension constraint. Recently, The Weyl points have been predicted to accommodate within superconducting nanostructures in the spectrum of Andreev bound states. Theoretically, one can easily manipulate the dimensionality and the tuning process through elementary approaches with specially designed structures. This opens up a new window for explorations in a higher dimension, high-order topological effects,Majorana states, and other complications even though it may be still experimentally challenging. One realization of such structures is the multi-terminal Josephson junction. The parameters are the superconducting phase differences of the terminals and theWeyl points reside at low energies within the superconducting gap. Chapter 2 of this thesis investigates the topological effect in the quantized transconductance of such a structure considering the presence of the continuous spectrum that is intrinsic to superconductors. This research is based on scattering formalism and relates the Landauer conductance to the continuous spectrumas a background field in the regular topological charge picture. Chapter 3 is based on a very generic superconducting nanostructure setup so long as it hosts Weyl points in it. The research proposes a unit that tunnel-couples such a setup with a quantum dot. The distinct feature of the spectrum, especially the distinction between its spin-singlet and spin-doublet due to spin-orbit coupling, leads to an exploration of the state manipulation. Eventually, through adiabatic and diabatic approaches, one can feasibly realize a full unitary transformation of the spectrum. Because of this, the unit could easily find its promising application in entangled qubits. Chapter 4 also relies on the generic low-energy Weyl point setup in the superconducting nanostructure, but instead, it is weakly tunnel-coupled to regularmetallic leads. We know that spintronics explores the intrinsic spin degree of freedom. It is usually realized on magnetic materials. In the setup of this research, the energy spectrum contains a natural spin-orbit that creates a minimalistic magnetic state in the vicinity of theWeyl point. The spin structure of the spectrum allows fine-controls over the spin and switch between magnetic/non-magnetic state. Hence this chapter’s research focuses on the possible spintronics features based on master equations. Chapter 5 furthers the research of chapter 4. It considers a universal energy scale sets up by the tunnel coupling strength. In the language of the Green’s function, this chapter studies the topological effect through the response function. This set up is a suitable example of low energy Weyl points situated in the presence of a low-energy continuous spectrum brought by electrons in the leads. We have seen in Chapter 1 how the continuous spectrum above the gap modifies the topology leading to a non-quantized contribution to the transconductance. The peculiarity of couplingWeyl points to a low energy continuous spectrum is that the dissipation gives rise to a redefinition of the Berry curvature, whichmanifests as a continuous density of topological charge instead of a pointlike one. This unusual characteristic can be captured by the tunnel current and thus can assist the detection ofWeyl points experimentally.
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Topological band theory has contributed to some of the most astonishing developments in solid-state physics. The unique attributes that arise from topological effects are at the focus of modern experimental and theoretical research. Weyl point, a topological defect at the Fermi surface, enables topological transitions and transport phenomena. Its existence is considerably restricted in natural materials due to the tuning and dimension constraint. Recently, The Weyl points have been predicted to accommodate within superconducting nanostructures in the spectrum of Andreev bound states. Theoretically, one can easily manipulate the dimensionality and the tuning process through elementary approaches with specially designed structures. This opens up a new window for explorations in a higher dimension, high-order topological effects,Majorana states, and other complications even though it may be still experimentally challenging. One realization of such structures is the multi-terminal Josephson junction. The parameters are the superconducting phase differences of the terminals and theWeyl points reside at low energies within the superconducting gap. Chapter 2 of this thesis investigates the topological effect in the quantized transconductance of such a structure considering the presence of the continuous spectrum that is intrinsic to superconductors. This research is based on scattering formalism and relates the Landauer conductance to the continuous spectrumas a background field in the regular topological charge picture. Chapter 3 is based on a very generic superconducting nanostructure setup so long as it hosts Weyl points in it. The research proposes a unit that tunnel-couples such a setup with a quantum dot. The distinct feature of the spectrum, especially the distinction between its spin-singlet and spin-doublet due to spin-orbit coupling, leads to an exploration of the state manipulation. Eventually, through adiabatic and diabatic approaches, one can feasibly realize a full unitary transformation of the spectrum. Because of this, the unit could easily find its promising application in entangled qubits. Chapter 4 also relies on the generic low-energy Weyl point setup in the superconducting nanostructure, but instead, it is weakly tunnel-coupled to regularmetallic leads. We know that spintronics explores the intrinsic spin degree of freedom. It is usually realized on magnetic materials. In the setup of this research, the energy spectrum contains a natural spin-orbit that creates a minimalistic magnetic state in the vicinity of theWeyl point. The spin structure of the spectrum allows fine-controls over the spin and switch between magnetic/non-magnetic state. Hence this chapter’s research focuses on the possible spintronics features based on master equations. Chapter 5 furthers the research of chapter 4. It considers a universal energy scale sets up by the tunnel coupling strength. In the language of the Green’s function, this chapter studies the topological effect through the response function. This set up is a suitable example of low energy Weyl points situated in the presence of a low-energy continuous spectrum brought by electrons in the leads. We have seen in Chapter 1 how the continuous spectrum above the gap modifies the topology leading to a non-quantized contribution to the transconductance. The peculiarity of couplingWeyl points to a low energy continuous spectrum is that the dissipation gives rise to a redefinition of the Berry curvature, whichmanifests as a continuous density of topological charge instead of a pointlike one. This unusual characteristic can be captured by the tunnel current and thus can assist the detection ofWeyl points experimentally.
We investigate transport in a superconducting nanostructure housing a Weyl point in the spectrum of Andreev bound states. A minimum magnet state is realized in the vicinity of the point. One or more normal-metal leads are tunnel-coupled to the nanostructure. We have shown that this minimum magnetic setup is suitable for realization of all common goals of spintronics: detection of a magnetic state, conversion of electric currents into spin currents, potentially reaching the absolute limit of one spin per charge transferred, and detection of spin accumulation in the leads. The peculiarity and possible advantage of the setup is the ability to switch between magnetic and nonmagnetic states by tiny changes of the control parameters: superconducting phase differences. We employ this property to demonstrate the feasibility of less common spintronic effects: spin on demand and alternative spin current.
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We investigate transport in a superconducting nanostructure housing a Weyl point in the spectrum of Andreev bound states. A minimum magnet state is realized in the vicinity of the point. One or more normal-metal leads are tunnel-coupled to the nanostructure. We have shown that this minimum magnetic setup is suitable for realization of all common goals of spintronics: detection of a magnetic state, conversion of electric currents into spin currents, potentially reaching the absolute limit of one spin per charge transferred, and detection of spin accumulation in the leads. The peculiarity and possible advantage of the setup is the ability to switch between magnetic and nonmagnetic states by tiny changes of the control parameters: superconducting phase differences. We employ this property to demonstrate the feasibility of less common spintronic effects: spin on demand and alternative spin current.
Recently, it has been shown that multiterminal superconducting nanostructures may possess topological properties that involve Berry curvatures in the parametric space of the superconducting phases of the terminals, and associated Chern numbers that are manifested in quantized transconductances of the nanostructure. In this paper, we investigate how the continuous spectrum that is intrinsically present in superconductors, affects these properties. We model the nanostructure within scattering formalism deriving the action and the response function that permits a redefinition of Berry curvature for continuous spectrum. We have found that the redefined Berry curvature may have a nontopological phase-independent contribution that adds a nonquantized part to the transconductances. This contribution vanishes for a time-reversible scattering matrix. We have found compact expressions for the redefined Berry curvature for the cases of weak energy dependence of the scattering matrix and investigated the vicinity of Weyl singularities in the spectrum.
...
Recently, it has been shown that multiterminal superconducting nanostructures may possess topological properties that involve Berry curvatures in the parametric space of the superconducting phases of the terminals, and associated Chern numbers that are manifested in quantized transconductances of the nanostructure. In this paper, we investigate how the continuous spectrum that is intrinsically present in superconductors, affects these properties. We model the nanostructure within scattering formalism deriving the action and the response function that permits a redefinition of Berry curvature for continuous spectrum. We have found that the redefined Berry curvature may have a nontopological phase-independent contribution that adds a nonquantized part to the transconductances. This contribution vanishes for a time-reversible scattering matrix. We have found compact expressions for the redefined Berry curvature for the cases of weak energy dependence of the scattering matrix and investigated the vicinity of Weyl singularities in the spectrum.
Journal article(2017)
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S Meyer, Y. Chen, G. E.W. Bauer, R Gross, S. T.B. Goennenwein, S. Wimmer, M Althammer, T. Wimmer, Richard Schlitz, S Geprags, H Huebl, D. Kodderitzsch, H. Ebert
The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, which so far has been discussed only on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent yttrium iron garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal and transverse thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.
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The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, which so far has been discussed only on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent yttrium iron garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal and transverse thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.
