Spontaneous fractional Josephson current from parafermions

Physical review, 2023

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, ν = 1/m, m ∈ 2Z + 1, this leads to an electrical control of either Majorana (m = 1) or parafermion (m = 1) zero modes.

physica status solidi (RRL) - Rapid Research Letters

arXiv (Cornell University), 2022

Robust and tunable topological Josephson junctions (TJJs) are highly desirable platforms for investigating the anomalous Josephson effect and topological quantum computation applications. Experimental demonstrations have been done in hybrid superconducting-two dimensional topological insulator (2DTI) platforms, sensitive to magnetic disorder and interactions with phonons and other electrons. In this work, we propose a robust and electrostatically tunable TJJ by combining the physics of the integer quantum Hall (IQH) regime and of superconductors. We provide analytical insights about the corresponding Andreev bound state spectrum, the Josephson current and the anomalous current. We demonstrate the existence of protected zero-energy crossings, that can be controlled through electrostatic external gates. This electrostatic tunability has a direct advantage to compensate for non-ideal interfaces and undesirable reflections that may occur in any realistic samples. TJJs in the IQH regime could be realized in graphene and other 2D materials. They are of particular relevance towards scalable and robust Andreev-qubit platforms, and also for efficient phase batteries.

Low Temperature Physics, 2004

The modern physics of superconductivity can be called the physics of unconventional superconductivity. The discovery of the d-wave symmetry of the order parameter in hightemperature superconductors and the triplet superconductivity in compound Sr 2 RuO 4 has caused a huge stream of theoretical and experimental investigations of unconventional superconductors. In this review we discuss some novel aspects of the Josephson effect which are related to the symmetry of the order parameter. The most intriguing of them is spontaneous current generation in an unconventional weak link. The example of a Josephson junction in the form of a grain boundary between two disorientated d-wave or f-wave superconductors is considered in detail. Josephson current-phase relations and the phase dependences of the spontaneous current that flows along the interface are analyzed. The spontaneous current and spontaneous phase difference are manifestations of the time-reversal symmetry ͑T ͒ breaking states in the system. We analyzed the region of appearance of T-breaking states as function of temperature and mismatch angle. A review of the basics of superconducting qubits with emphasis on specific properties of d-wave qubits is given. Recent results in the problem of decoherence in d-wave qubits, which is the major concern for any qubit realization, are presented.

Bulletin of the American Physical Society, 2018

The ability to measure and manipulate complex particles in the solid state is a cornerstone of modern condensed-matter physics. Typical excitations of a sea of electrons, called quasiparticles, have properties similar to those of free electrons. However, in recent years exotic excitations with very different properties have been created in designer quantum materials, including Dirac fermions in graphene 1 and fractionally-charged quasiparticles in fractional quantum Hall systems 2. Here we report signatures of a new quasiparticle-the Majorana fermion-in Josephson junctions consisting of two superconducting leads coupled through a three-dimensional topological insulator 3. We observe two striking departures from the common transport properties of Josephson junctions: a characteristic energy that scales inversely with the width of the junction, and a low characteristic magnetic field for suppressing supercurrent. To explain these effects, we propose a phenomenological model in which a one-dimensional wire of Majorana fermions is present along the width of the junction, similar to a theoretical prediction by Fu and Kane 4. These results present an opening into the investigation of Majorana fermions in the solid state and their exotic properties, including non-Abelian statistics 5 , a suggested basis for fault-tolerant quantum computation 6 .

Journal of Physics: Condensed Matter, 2022

Topological Josephson junctions (TJJs) have been a subject of widespread interest due to their hosting of Majorana zero modes. In long junctions, i.e. junctions where the junction length exceeds the superconducting coherence length, TJJs manifest themselves in specific features of the critical current \cite{Beenakker2013}. Here we propose to couple the helical edge states mediating the TJJ to additional channels or quantum dots, by which the effective junction length can be increased by tunable parameters associated with these couplings, so that such measurements become possible even in short junctions. Besides effective low-energy models that we treat analytically, we investigate realizations by a Kane-Mele model with edge passivation and treat them numerically via tight binding models. In each case, we explicitly calculate the critical current using the Andreev bound state spectrum and show that it differs in effective long junctions in the cases of strong and weak parity changing...

Physical Review Letters, 2020

We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applying a finite voltage bias smaller than the superconducting gap to a relatively long junction, the finite-frequency interference pattern in the non-equilibrium transport current is qualitatively different for helical edge states as compared to nonhelical ones.

2004

For certain orientations of Josephson junctions between two px-wave or two d-wave superconductors, the subgap Andreev bound states produce a 4π-periodic relation between the Josephson current I and the phase difference φ: I ∝ sin(φ/2). Consequently, the ac Josephson current has the fractional frequency eV /h, where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction.

Physical Review Letters, 1999

In the presence of phase fluctuations the dc Josephson effect is modified and the supercurrent at zero voltage is replaced by a peak at small but finite voltages. It is shown that at zero temperature this peak is determined by two complementary expansions of finite radius of convergence. The leading order expressions are related to results known from the regimes of Coulomb blockade and of macroscopic quantum tunneling. The peak positions and the suppression of the critical current by quantum fluctuations are discussed. 74.50.+r, 73.23.Hk, The dc Josephson effect allows a Cooper pair current to flow through a superconducting tunnel junction in the absence of an external voltage. The current is determined by the difference ϕ of the condensate phases on the two sides of the junction through I = I c sin(ϕ) and is limited by the critical current I c . While this feature in the current-voltage characteristic has zero weight, it acquires a finite width due to either thermal or quantum fluctuations of the phase difference. Here, we analyze the role of quantum fluctuations and concentrate on the Josephson peak at zero temperature.

Physics Letters A, 1992

An effective Josephson coupling energy for a one-dimensional Josephson junction is renormalized due to quantum fluctuations of the phase difference. In a longjunction at T-.0 a Kosterlitz-Thouless phase transition takes place. The state with a logarithmically divergent phase-phase correlation function shows a nontrivial combination of phase disorder on a junction surface with phase order in the bulk. For finitesize junctions the renormalized value ofthe Josephson coupling energy turns out to be strongly suppressed for small Josephson-to-charging energy ratio. The implications of this effect for Bloch oscillations are discussed. The prediction [1] of the effect of Bloch oscilla-pacitance Cci.: S should be small enough to allow for tions in ultrasmall superconducting tunnel junctions an experimentally accessible temperature interval. induced substantial theoretical and experimental ac-Typical experimental parameters for "quantum" tivity in the field (see e.g. refs. [2,3] for a review). Josephson junctions are S-S l0~-l0'°cm and Recently reliable experimental evidence of this ef-C-i 10-'~-l0 16 F. Then if we assume the junction fect was reported [4-6].Most of these experimental size in the x-direction Lto be of the order of that results turn out to be in good quantitative agreement in the y-direction L~(x and y are coordinates in the with the theory [7,8]. junction plane) we can estimate L~-~L~- .-' l0~cm.