Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9505096 · Physical Review Letters

ac Josephson Effect in a Single Quantum Channel

D. V. Averin, Athanassios Bardas

Published Aug 28, 1995• 442 citations
arXivHTMLPDF

Abstract

We have calculated all the components of the current in a short one-dimensional channel between two superconductors for arbitrary voltages and transparencies $D$ of the channel. We demonstrate that in the ballistic limit ( $D\ensuremath{\simeq}1$) the crossover between the quasistationary evolution of the Josephson phase difference $\ensuremath{\phi}$ at small voltages and transport by multiple Andreev reflections at larger voltages can be described as the Landau-Zener transition induced by finite reflection in the channel. For perfect transmission and vanishing energy relaxation rates the stationary current-phase relation is never recovered, and $I(\ensuremath{\phi}){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}I}_{c}\ensuremath{\mid}\mathrm{sin}\ensuremath{\phi}/2\ensuremath{\mid}\mathrm{sgn}V$ for arbitrary small voltages.

DOI
10.1103/physrevlett.75.1831

Related papers

ac Josephson effect in asymmetric superconducting quantum point contacts

Shin-Tza Wu, Sungkit Yip

We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic $(D=1)$ limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to nonzero sine components. We also demonstrate that in this limit, the temperature dependence of the dc component follows $\mathrm{tanh}({\ensuremath{\Delta}}_{s}∕2T)$, where ${\ensuremath{\Delta}}_{s}$ is the smaller gap, with the contribution coming entirely from the bound state.

arXiv:cond-mat/0407163•Physical Review B•Sep 20, 2004•7 citations

dc and ac Josephson effect in a superconductor–Luttinger-liquid–superconductor system

Rosario Fazio, F. W. J. Hekking, A. A. Odintsov

We calculate both the dc and the ac Josephson current through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-1/2 Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At zero temperature, the critical current is found to decay algebraically with increasing distance d between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures T, lower than the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$, there is a crossover from algebraic to exponential decay of the critical current as a function of d, at a distance of the order of \ensuremath{\Elzxh}${\mathit{v}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{BT}}$. Moreover, the dependence of critical current on temperature shows nonmonotonic behavior. If the Luttinger liquid is confined to a ring of circumference L, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a \ensuremath{\pi} junction. These features are robust against thermal fluctuations up to temperatures on the order of \ensuremath{\Elzxh}${\mathit{v}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{BL}}$. For the wire geometry, we have also studied the ac-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the ac-Josephson effect can be used as a tool for the observation of spin-charge separation. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9509135•Physical review. B, Condensed matter•Mar 1, 1996•47 citations

Analytic approach to transport in Josephson junctions beyond the Andreev approximation: General theory and applications to the BEC-BCS crossover

F. Setiawan, Johannes Hofmann

Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal reflections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic $analytical$ framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even $negative$ conductance at specific voltages.

•Aug 23, 2021•0 citations

Coulomb effects in a ballistic one-channel S-S-S device

Dmitri A. Ivanov, M. V. Feigel’man

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy $E_C \ll Δ$. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to $π$, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge $Q_x=C V_g$ with period $2e$.

arXiv:cond-mat/9712074•Physics-Uspekhi•Feb 28, 1998•1 citation

Andreev scattering and Josephson current in a one-dimensional electron liquid

Ian K. Affleck, Jean-Sébastien Caux, Alexandre M. Zagoskin

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are reexamined. We first present some apparently new results on the noninteracting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e., zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters, a fine-tuning which is possible even with bandwidth mismatch between superconductor and normal metal. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low-energy properties of a junction $(E\ensuremath{\ll}\ensuremath{\Delta},$ the superconducting gap) can be obtained by ``integrating out'' the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization-renormalization group-boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interations but to the Andreev one for attractive interations. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior. We calculate the critical exponents, which are different at these two different fixed points.

arXiv:cond-mat/0001375•Physical review. B, Condensed matter•Jul 1, 2000•116 citations

Coulomb effects in a ballistic one-channel S-S-S device

Dmitri A. Ivanov, M. V. Feigel’man

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q x =CV g .

Journal of Experimental and Theoretical Physics•Aug 1, 1998•18 citations
We have calculated all the components of the current in a short one-dimensional channel between two superconductors for arbitrary voltages and transparencies DDD of the channel. We demonstrate that in the ballistic limit ( D\ensuremath≃1D\ensuremath{\simeq}1D\ensuremath≃1) the crossover between the quasistationary evolution of the Josephson phase difference \ensuremathϕ\ensuremath{\phi}\ensuremathϕ at small voltages and transport by multiple Andreev reflections at larger voltages can be described as the Landau-Zener transition induced by finite reflection in the channel. For perfect transmission and vanishing energy relaxation rates the stationary current-phase relation is never recovered, and I(\ensuremathϕ)=Ic\ensuremath∣sin\ensuremathϕ/2\ensuremath∣sgnVI(\ensuremath{\phi}){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}I}_{c}\ensuremath{\mid}\mathrm{sin}\ensuremath{\phi}/2\ensuremath{\mid}\mathrm{sgn}VI(\ensuremathϕ)=Ic​\ensuremath∣sin\ensuremathϕ/2\ensuremath∣sgnV for arbitrary small voltages.
We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission DDD of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1)(D=1)(D=1) limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to nonzero sine components. We also demonstrate that in this limit, the temperature dependence of the dc component follows $\mathrm{tanh}({\ensuremath{\Delta}}_{s}∕2T)$, where ${\ensuremath{\Delta}}_{s}$ is the smaller gap, with the contribution coming entirely from the bound state.
We calculate both the dc and the ac Josephson current through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-1/2 Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At zero temperature, the critical current is found to decay algebraically with increasing distance d between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures T, lower than the superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​, there is a crossover from algebraic to exponential decay of the critical current as a function of d, at a distance of the order of \ensuremath{\Elzxh}vF{\mathit{v}}_{\mathit{F}}vF​/kBT{\mathit{k}}_{\mathit{BT}}kBT​. Moreover, the dependence of critical current on temperature shows nonmonotonic behavior. If the Luttinger liquid is confined to a ring of circumference L, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a \ensuremath{\pi} junction. These features are robust against thermal fluctuations up to temperatures on the order of \ensuremath{\Elzxh}vF{\mathit{v}}_{\mathit{F}}vF​/kBL{\mathit{k}}_{\mathit{BL}}kBL​. For the wire geometry, we have also studied the ac-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the ac-Josephson effect can be used as a tool for the observation of spin-charge separation. \textcopyright{} 1996 The American Physical Society.
Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal reflections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic analyticalanalyticalanalytical framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even negativenegativenegative conductance at specific voltages.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy EC≪ΔE_C \ll ΔEC​≪Δ. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to πππ, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge Qx=CVgQ_x=C V_gQx​=CVg​ with period 2e2e2e.
Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are reexamined. We first present some apparently new results on the noninteracting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e., zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters, a fine-tuning which is possible even with bandwidth mismatch between superconductor and normal metal. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low-energy properties of a junction $(E\ensuremath{\ll}\ensuremath{\Delta},$ the superconducting gap) can be obtained by ``integrating out'' the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization-renormalization group-boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interations but to the Andreev one for attractive interations. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior. We calculate the critical exponents, which are different at these two different fixed points.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q x =CV g .