Majorana ϕ 0 -junction in a disordered spin-orbit coupling nanowire with tilted magnetic field

Abstract

Majorana Josephson junctions in nanowire systems exhibit a pseudo-4π period current-phase relation in the clean limit. In this work, we study how this current-phase relation responds to a tilted magnetic field in a disordered Majorana Josephson junction within the Bogoliubov-de Gennes approach. We show that the tilted magnetic field induces a φ 0 phase shift to the currentphase relation. Most importantly, we find that this φ 0 -junction behavior is robust even in the presence of disorders.

Universal Majorana thermoelectric noise

“…T is still universal even at low bias voltages because it does not depend on d in this voltage range. As expected, we find that outside the validity of the Majorana tunneling condition (19), e.g., |eV | > |η|, the thermoelectric ratio between…”

“…Here d may be tuned by an external gate voltage to satisfy (19). Similarly, the bias voltage V , thermal voltage V T and temperature T may be externally adjusted to satisfy (19). The Majorana overlap ξ will be small if the topological superconductor in the setup is chosen to be long enough so that the two Majorana fermions do not merge into a single Dirac fermion during the tunneling into the quantum dot.…”

“…In this situation the value of the plateau saturates at the asymptotic limit (e 3 /h)[1 + ln(2)] and the width of the plateau gets extremely wide. Therefore, when the Majorana tunneling is strong enough, so that (19) is satisfied, the fluctuation thermoelectric coefficient ∂S > (V, V T )/∂V T becomes independent of d , Γ and η, that is it becomes truly universal with the value (e 3 /h)[1 + ln(2)] (the black horizontal line in Fig. 4).…”

“…Here d may be tuned by an external gate voltage to satisfy (19). Similarly, the bias voltage V , thermal voltage V T and temperature T may be externally adjusted to satisfy (19).…”

“…The majority of transport proposals focus on mean electric current often providing low-energy behavior of the system's electrical conductance. Examples are given by superconductor-Luttinger liquid junctions [11], Kondo effect in quantum dots side coupled to a topological superconductor supporting Majorana fermions at its ends [12], driven topological superconductors [13], Josephson junctions on surfaces of three-dimensional topological insulators [14], Kondo effect in topological superconductorquantum dot-normal lead junction [15], normal metalsuperconducting semiconductor-normal metal structures [16], spinon-antispinon systems [17], Coulomb blockaded systems [18], disordered Josephson junctions in tilted magnetic fields [19] and many others.…”