Josephson ϕ0-junction in nanowire quantum dots

Szombati, Daniel; Nadj-Perge, Stevan; Car, Diana; Plissard, Sébastien; Bakkers, Epam Erik; Kouwenhoven, Leo P.

doi:10.1038/nphys3742

Cited by 266 publications

(236 citation statements)

References 38 publications

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“…Substituting (20) into the Ferrell-Prange equation (5), expanding the sine on the right-hand side up to O(w 2 /λ 2 J ), and collecting the terms in each order of the perturbation theory separately, we find…”

Section: Phase Transitions Due To the Shifting Of The Vortexmentioning

confidence: 99%

“…For example, in S|F|S junctions the transition between 0 and π states can occur by changing the temperature [10,[24][25][26], but this transition requires the presence of magnetic impurities and very precise choice of the F-layer thickness. A more realistic situation is realized in the Josephson systems containing ballistic Bi nanowires or InSb quantum dots where the interplay between strong spin-orbit and Zeeman interactions enables the formation of π and ϕ 0 states, which can be tuned by an external magnetic field [18,20,27]. …”

Section: Introductionmentioning

confidence: 99%

“…Such situation is realized in the S|F|S junctions with strong spin-orbit coupling (see Refs. [17][18][19][20] and references therein) or complicated noncollinear distribution of the magnetization (see Refs. [21][22][23] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Anomalous Josephson effect controlled by an Abrikosov vortex

et al. 2017

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The possibility of a fast and precise Abrikosov vortex manipulation by a focused laser beam opens the way to create laser-driven Josephson junctions. We theoretically demonstrate that a vortex pinned in the vicinity of the Josephson junction generates an arbitrary ground state phase which can be equal not only to 0 or π but to any desired ϕ 0 value in between. Such ϕ 0 junctions have many peculiar properties and may be effectively controlled by the optically driven Abrikosov vortex. Also we theoretically show that the Josephson junction with the embedded vortex can serve as an ultrafast memory cell operating at sub THz frequencies. I. INTRODUCTIONJosephson junctions (JJs) with nonzero spontaneous phase difference between the superconducting electrodes in the ground state (the so-called π , ϕ 0 , and ϕ JJs) have become the subject of intensive theoretical and experimental study during the past decade [1,2]. The most striking feature of such junctions is their ability to generate a current in the superconducting circuit, thus acting as a phase battery [3][4][5][6]. In addition, relatively small variation of the system parameters may provoke dramatic changes in the ground state phase difference, which is believed to provide new effective tools for controlling the currents in microelectronic devices (see, e.g., Refs. [7,8]).There are several generic mechanisms leading to the spontaneous appearance of nonzero Josephson phase. The basic one reveals when the superconducting (S) electrodes are separated by a ferromagnetic (F) layer. The exchange field inside the ferromagnet produces the spatial oscillations of the Cooper pair wave function, and depending on the ratio between the oscillation period and the F-layer thickness the ground state phase is equal to 0 or π (these cases are referred as 0 or π JJs, respectively) [9][10][11]. A peculiar situation is realized when the thickness d of the ferromagnet varies along the junction in a way that in some parts of the ferromagnet the value of d corresponds to the 0 state while in other parts to the π state (see Ref. [12] and references therein). If there is only a slight difference between the areas of the "0" and "π " regions the phase frustration can result in the appearance of a state with the spontaneous phase difference φ = ±ϕ = 0,π which is degenerate (ϕ JJ) (see Ref.[13] and references therein). A similar effect takes place in Josephson junctions with the current injectors acting as an effective source of the phase jumps along the junction (see and references therein). One can also obtain a ϕ 0 JJ, where the ground state phase φ = ϕ 0 is not degenerate, e.g., using the JJs with broken inversion symmetry [17]. In this case the superconducting current I through the junction should not be necessarily an odd function of the phase difference φ and can take the form I = I c sin(φ + ϕ 0 ) [17]. Such situation is realized in the S|F|S junctions with strong spin-orbit coupling (see and references therein) or complicated noncollinear distribution of the magnetization (see an...

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Section: Phase Transitions Due To the Shifting Of The Vortexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anomalous Josephson effect controlled by an Abrikosov vortex

et al. 2017

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“…Depending on the polarization of the STM probe, a current will flow or not in the trivial phase and the opposite situation will occur in the topological phase. The second possibility is to couple the nanowire to a quantum dot [20,30,36,48,49], which then can be used for energy-selective spin read-out [50].…”

Section: Figmentioning

confidence: 99%

Spin and charge signatures of topological superconductivity in Rashba nanowires

Szumniak¹,

Chevallier²,

Loss³

et al. 2017

Phys. Rev. B

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We consider a Rashba nanowire with a proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological superconductivity that can be accessed experimentally. We find a similar behavior for the charge of the bulk quasiparticle states, also exhibiting a sign reversal at the transition. We show that these signatures are robust against random static disorder. DOI: 10.1103/PhysRevB.96.041401Introduction. Topological phases of condensed matter systems [1,2] have attracted a lot of attention over many years due to their high promise for applications such as topological quantum computation [3,4]. One of the hallmarks of such phases, in particular of topological superconductivity, are zero-energy modes such as Majorana fermions (MF) that emerge at the edges of the system. Various candidate materials can host such topological states [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but one of the most promising platforms are semiconducting nanowires of InAs or InSb material, with strong Rashba spin orbit interaction (SOI), subjected to an external magnetic field and in proximity to an s-wave superconductor [22,23]. Experimental evidence has been reported for topological phases in such wires [24][25][26][27][28][29][30][31] as well as in magnetic atomic chains on superconducting substrates [32][33][34]. However, most of the work so far has focused on the detection of the MFs in these nanowires and not on their bulk properties. This is quite surprising given the fact that the unambiguous identification of MFs from transport data alone can be challenging [35][36][37][38][39][40][41][42][43]. It is thus of great interest to look for alternative signatures of topological phases and to address the question how the bulk states change when passing from trivial to topological phase and if these changes appear in physically observable quantities.In this work, we show that the phase of a topological superconductor can be monitored by bulk states, in particular by certain spin and charge degrees of freedom. Quite remarkably, we find that the sign of the spin component along the magnetic field reverses for low-momentum states close to the Fermi level when the system passes through the phase transition, and similarly for the charge of such bulk states. This sign reversal is a direct consequence of the band inversion at the transition point and is directly accessible by spin-and energy resolved measurements. Another remarkable feature is that this signature is independent of boundary effects and thus unrelated to the presence of MFs. To demons...

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“…So far, the possibility of ϕ junction has been discussed theoretically in various Josephson junctions with X being multilayered ferromagnets [13,14], quantum point contacts [15], quantum dots [16][17][18], nanowires [11,19], topological materials [20,21], and a ferromagnet without inversion symmetry [22]. In experiments, on the other hand, the realization of a ϕ junction has been reported only in a Josephson junction with a nanowire quantum dot [23]. At present, it is not easy to control the phase shift ϕ after fabricating Josephson junctions.…”

Section: Introductionmentioning

confidence: 99%

Tunable- φ Josephson junction with a quantum anomalous Hall insulator

2017

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We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current J flows without a phase difference across the junction θ . The phase shift ϕ appearing in the current-phase relationship J ∝ sin(θ − ϕ) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains the physical origin of ϕ. In a quantum anomalous Hall insulator, time-reversal symmetry and mirror-reflection symmetry are broken simultaneously. However, magnetic mirror-reflection symmetry is preserved. Such characteristic symmetry properties enable us to have a tunable ϕ junction with a quantum Hall insulator.

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Josephson ϕ0-junction in nanowire quantum dots

Cited by 266 publications

References 38 publications

Anomalous Josephson effect controlled by an Abrikosov vortex

Anomalous Josephson effect controlled by an Abrikosov vortex

Spin and charge signatures of topological superconductivity in Rashba nanowires

Tunable- φ Josephson junction with a quantum anomalous Hall insulator

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