Josephson junction detectors for Majorana modes and Dirac fermions

Maiti, Moitri; Kulikov, Kostyantyn; Sengupta, K.; Shukrinov, Yu. M.

doi:10.1103/physrevb.92.224501

Cited by 18 publications

(7 citation statements)

References 55 publications

(61 reference statements)

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“…Shapiro steps as a phenomenon have wide applications from technological to scientific, and Kolmogorov complexity could be a practical tool for scientists in those fields. To illustrate that, let us look at the recent studies that attracted great attention: application of Josephson junctions in detection of Majorana fermions [35][36][37]. In Ref.…”

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confidence: 99%

“…Thus, detection of Majorana fermions requires very precise observation and measurement of subharmonic Shapiro steps, which in experiments could be a real problem due to noise (all analysis in Ref. [37] were performed at the zero temperature). We believe that application of KC could help in the solution of this and similar problems.…”

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confidence: 99%

“…In Ref. [37], it was shown that the current-voltage characteristics exhibits subharmonic odd Shapiro steps, where particular sequence of subharmonic steps in the devil's staircase structure represents a signature of the Majorana states. Thus, detection of Majorana fermions requires very precise observation and measurement of subharmonic Shapiro steps, which in experiments could be a real problem due to noise (all analysis in Ref.…”

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confidence: 99%

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Complexity of Shapiro steps

et al. 2020

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We demonstrate on the example of the dc+ac driven overdamped Frenkel-Kontorova model that an easily calculable measure of complexity can be used for the examination of Shapiro steps in presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function we were able to detect Shapiro steps, measure their size with desired precision and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, an unconventional but a practical and easy tool for examination of Shapiro steps in real systems.

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Complexity of Shapiro steps

et al. 2020

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“…A particularly interesting Josephson effect is the phenomenon of Shapiro steps/plateaus. These typically appear when we consider a resistively and capacitively shunted Josephson junction in which a resistance R and a capacitance C are placed in parallel with a Josephson junction [80][81][82][83][84]. When such a device is exposed to an external radio-frequency (rf ) excitation, the rf drive can phase-lock with the internal dynamics of the Josephson junction and manifest as steps in the current versus voltage (I − V) characteristics.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional spin–orbit coupled Dirac system with extended s-wave superconductivity: Majorana modes and Josephson effects

Udupa

Banerjee

Sengupta

et al. 2021

J. Phys.: Condens. Matter

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Motivated by the spin–momentum locking of electrons at the boundaries of certain topological insulators, we study a one-dimensional system of spin–orbit coupled massless Dirac electrons with s-wave superconducting pairing. As a result of the spin–orbit coupling, our model has only two kinds of linearly dispersing modes, and we take these to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the s-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two s-wave superconductors with different phases of the pairing, with a δ-function potential barrier lying at the junction of the two superconductors. Remarkably, we find that the system has a single Andreev bound state (ABS) which is localized at the junction. When the pairing phase difference crosses a multiple of 2π, an ABS touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant V 0 and a term which oscillates with a frequency ω. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency ω J = 2eV 0/ℏ is a rational fraction of ω. We discuss experiments which can realize such junctions.

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“…For example, the interplay between topology and instabilities has been recently analyzed in bosonic systems under ac driving [36] and junction arrays mimicking the SSH model [37]. The Shapiro experiment in a topological Josephson junction has been theoretically analyzed by means of a semiclassical RSJ model [38][39][40], and with a finite capacitance in the high ac-bias limit [41]. showing Shapiro steps corresponding to the phase-locked regime (PL, orange) and a linear I0 − V section for the quasiperiodic regime (QP, blue).…”

Section: Introductionmentioning

confidence: 99%

Signatures of a 4π -periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions

2017

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We investigate theoretical aspects of the detection of Majorana bound states in Josephson junctions using a semiclassical model of the junction. The influence of a 4π-periodic supercurrent contribution can be detected through its effect on the width of the Shapiro steps and the Fourier spectrum of the voltage. We explain how the inclusion of a capacitance term results in a strong quenching of the odd steps when the junction is underdamped, which may be used to effectively detect Majorana bound states. Furthermore, in presence of capacitance the first and third steps are quenched to a different degree, as observed experimentally. We examine the emission spectrum of phase-locked solutions, showing that the presence of period-doubling may complicate the measurement of the 4π-periodic contribution from the Fourier spectrum. Finally, we study the voltage response in the quasiperiodic regime and indicate how the Fourier spectra and the first-return maps in this regime reflect the change of periodicity in the supercurrent.

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Josephson junction detectors for Majorana modes and Dirac fermions

Cited by 18 publications

References 55 publications

Complexity of Shapiro steps

Complexity of Shapiro steps

One-dimensional spin–orbit coupled Dirac system with extended s-wave superconductivity: Majorana modes and Josephson effects

Signatures of a 4π -periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions

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