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Topological Superconductivity
Published in David A. Cardwell, David C. Larbalestier, I. Braginski Aleksander, Handbook of Superconductivity, 2023
From the very beginning of its discovery, the phenomenon of superconductivity has been a source of inspiration for numerous breakthrough concepts and applications. One of the most recent and exciting developments in the field relates to the possibility of spontaneously formed or artificially engineered topological superconductors (TSCs). TSCs constitute systems which harbor exotic charge-neutral excitations termed Majorana fermions (MFs) [1–3]. These are closely related to the particles that Ettore Majorana put forward in 1937 [4] as self-conjugate solutions of the Dirac equation, with the neutrino being considered as the most prominent candidate for a Majorana particle. The crucial difference is that Majorana particles are fundamental and indivisible, while Majorana excitations encountered in TSCs define quasiparticles emerging only in the presence of electron-electron interactions.
Superconducting Qubits
Published in David A. Cardwell, David C. Larbalestier, Aleksander I. Braginski, Handbook of Superconductivity, 2022
Britton Plourde, Frank K. Wilhelm-Mauch
A radical approach to do this is to use a system whose microscopic quasiparticles are Majorana Fermions, which are topologically protected, as decohering them requires a rare nonlocal fluctuation. A clear pathway to this is the use of one-dimensional superconductors with a strong spin-orbit interaction (Lutchyn et al., 2010; Oreg et al., 2010). As these have so far not been realized as bulk materials, they are realized instead using nanowires from rather heavy semiconductors that acquire superconducting properties due to the proximity effect. While there is by now clear evidence that Majorana quasiparticles have been observed (Mourik et al., 2012; Aasen et al., 2016), qubits requiring at least a pair of Majoranas are still outstanding.
History and Mental State Examination
Published in Richard Kerslake, Elizabeths Templeton, Lisanne Stock, Revision Guide for MRCPsych Paper A, 2018
Since the TSS is protected by the time-reversal symmetry [1–8], the TSS can coexist with the nonmagnetic impurities doped into the TI matrix. Thus, the coexistence of the TSS and other broken-symmetry states becomes possible. This possibility offers the chance to study Majorana quasiparticles, which is of great interest in fundamental physics and quantum computation [15]. The first superconducting TI was discovered by the research groups of Hasan [15] and Cava [16]. In the Cu intercalated TI Bi2Se3, the superconducting transition temperature Tc is approximately 3.8 K for Cu0.12Bi2Se3 crystal (Figure 16.3(a)] [15, 16).
Quantum Berezinskii–Kosterltz–Thouless transition for topological insulator
Published in Phase Transitions, 2020
Ranjith Kumar R, Rahul S, Surya Narayan Sahoo, Sujit Sarkar
Here, we consider an interacting helical liquid system at the edge of the quantum spin Hall system as our model Hamiltonian. Quantum spin Hall systems with or without Landau levels describe the helical edge states and it also describes the connection between spin and momentum. The left movers in the edge of quantum spin Hall systems are associated with down spin and right movers with up spin [28–34]. In the non-interacting case, the helical liquid is characterized by the symmetry indicating that the even and odd TR components are topologically distinct [28]. In the interacting case, it is observed that helical liquid with odd number of components can not be constructed in the one-dimensional lattice [17]. Low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry has been explored [35]. The formation of these one-dimensional states which can be controlled by the gate voltage on the topological surface has been studied and found the energy dispersion is almost linear in the momentum [36]. The impact of interaction on the helical liquid system has been studied explicitly, which results in the forming of Mojorana fermion states with a high degree of stability [37]. The scattering process between fermion bands conserving momentum of helical liquid system opens a gap against interaction effect, which leads to the stabilization of Majorana fermion mode [38]. The existence of the Majorana fermion mode and the characterization of Majorana–Ising transition has also been studied extensively [39,40].
Effects of the long-range neutrino-mediated force in atomic phenomena
Published in Molecular Physics, 2022
Phillip Munro-Laylim, Vladimir Dzuba, Victor Flambaum
The convergence of the integral in the matrix elements on the distance indicates that this interaction in atoms may be treated as a contact interaction (see Figure 1). We can replace by its contact limit, where we assume . Note that if we used the potential with the cut-off , the result would be six times bigger: Using Equation (4), the potential in Equation (1) in the contact limit may be presented as, using natural units , In Ref. [16], the potential was obtained for a Majorana neutrino loop instead of a Dirac neutrino loop. Using these results, we conclude that the neutrino-exchange potential for Majorana neutrinos requires the adjustment to as follows: This indicates that the nature of neutrinos may, in principle, be detected from the difference in Dirac and Majorana potentials. At small distance, the Dirac neutrino and Majorana neutrino potentials are practically the same, the difference is proportional to and is very small. In the contact interaction limit, the relative difference is . However, the asymptotic expression at large distance changes: for Majorana neutrinos we have , whereas for Dirac neutrinos. Therefore, the ratio of Dirac potential to Majorana potential is [16]. Thus the difference between potentials is negligible at small distances and only becomes significant at large distances . Unfortunately, effects of the neutrino-exchange potential are many orders of magnitude smaller than sensitivity of current macroscopic experiments [6–10], motivating future experimental work.