Broken time-reversal symmetry in Josephson junction involving two-band superconductors (original) (raw)
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Physical Review B
We determine the current-phase relation (CPR) of two-terminal configurations of Josephson junctions containing two-dimensional (2D) time-reversal invariant topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as junctions between topological and non-topological superconductors (TRITOPS-S). We focus on wide junctions for which several channels intervene in the tunneling coupling. We derive effective Hamiltonians to describe the topological edge modes for different TRITOPS models, including Hamiltonians with p-wave pairing and Hamiltonians combining s-wave pairing with spin-orbit coupling. We also derive effective low-energy Hamiltonians to describe the Josephson junction. These can be solved analytically and explain the contribution of the edge states to the Josephson current as a function of the phase bias. We find that edge-modes yield peculiar features to the CPR for both junction types. The primary effects occur for the response of the Majorana zero-modes at half-flux quantum phase φ ≈ π in TRITOPS-TRITOPS junctions and for integer flux quantum phase φ ≈ 0 for TRITOPS-S junctions, respectively. The former effect is particularly strong for two-component nematic superconductors. The second effect leads to a spontaneously broken timereversal symmetry in the TRITOPS-S junction and to a breakdown of the bulk-boundary correspondence. We analyze in this case the role of the phase fluctuations. For weakly-coupled junctions, we show that time-reversal symmetry is restored for large enough stiffness in these fluctuations. I. INTRODUCTION.
arXiv (Cornell University), 2022
We determine the current-phase relation (CPR) of two-terminal configurations of Josephson junctions containing two-dimensional (2D) time-reversal invariant topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as junctions between topological and non-topological superconductors (TRITOPS-S). We focus on wide junctions for which several channels intervene in the tunneling coupling. We derive effective Hamiltonians to describe the topological edge modes for different TRITOPS models, including Hamiltonians with p-wave pairing and Hamiltonians combining s-wave pairing with spin-orbit coupling. We also derive effective low-energy Hamiltonians to describe the Josephson junction. These can be solved analytically and explain the contribution of the edge states to the Josephson current as a function of the phase bias. We find that edge-modes yield peculiar features to the CPR for both junction types. The primary effects occur for the response of the Majorana zero-modes at half-flux quantum phase φ ≈ π in TRITOPS-TRITOPS junctions and for integer flux quantum phase φ ≈ 0 for TRITOPS-S junctions, respectively. The former effect is particularly strong for two-component nematic superconductors. The second effect leads to a spontaneously broken timereversal symmetry in the TRITOPS-S junction and to a breakdown of the bulk-boundary correspondence. We analyze in this case the role of the phase fluctuations. For weakly-coupled junctions, we show that time-reversal symmetry is restored for large enough stiffness in these fluctuations. I. INTRODUCTION.
Time-reversal symmetry-breaking superconductivity
Physical review, 1999
We study time reversal symmetry breaking superconductivity with ∆ k = ∆ x 2 −y 2 (k)+e iθ ∆α (α = s or dxy) symmetries. It is shown that the behavior of such superconductors could be qualitatively different depending on the minor components (α) and its phase at lower temperatures. It is argued that such qualitatively different behaviors in thermal as well as in angular dependencies could be a source of consequences in transport and Josephson physics. Orthorhombicity is found to be a strong mechanism for mixed phase (in case of α = s). We show that due to electron correlation the order parameter is more like a pure d x 2 −y 2 symmetry near optimum doping.
Time-reversal anomaly and Josephson effect in time-reversal invariant topological superconductors
arXiv preprint arXiv:1208.3928, 2012
Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. In this paper, we study the Josephson coupling between time-reversal invariant topological superconductors and s-wave superconductors. The Majorana edge/surface states of time-reversal invariant topological superconductors in all physical dimensions 1, 2, 3 have a generic topological property which we named as time-reversal anomaly. Due to the time-reversal anomaly, the Josephson coupling prefers a nonzero phase difference between topological and trivial superconductors. The nontrivial Josesphon coupling leads to a current-flux relation with a half period in a SQUID geometry, and also a half period Fraunhofer effect in dimension higher than one. We also show that an in-plane magnetic field restores the ordinary Josephson coupling, as a sharp signature that the proposed effect is a consequence of the unique time-reversal property of the topological edge/surface states. Our proposal provides a general approach to experimentally verify whether a superconductor is topological or not.
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.
We discuss the phase diagram and phase transitions in U (1)×Z2 three-band superconductors with broken time reversal symmetry. We find that beyond mean field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken Z2 time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different Z2 states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures. arXiv:1306.2313v1 [cond-mat.supr-con]
Josephson detection of time-reversal symmetry broken superconductivity in SnTe nanowires
npj Quantum Materials, 2021
A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. In this work, we present such a case: we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in JJs and observe a deviation from the standard CPR. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. The analysis examines how multiban...
Spontaneously broken time-reversal symmetry in high-temperature superconductors
Nature Physics, 2015
Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal symmetry broken states have been proposed for the high-temperature superconductors, but their identification remains experimentally controversial. Here we show a route to a low-temperature superconducting state with broken time-reversal symmetry that may accommodate currently conflicting experiments. This state is characterised by an unusual vortex pattern in the form of a necklace of fractional vortices around the perimeter of the material, where neighbouring vortices have opposite current circulation. This vortex pattern is a result of a spectral rearrangement of current carrying states near the surfaces. arXiv:1411.0886v1 [cond-mat.supr-con]
Phase transitions and anomalous normal state in superconductors with broken time-reversal symmetry
Using Monte Carlo simulations, we explore the phase diagram and the phase transitions in U(1) × Z2 n-band superconductors with spontaneously broken time-reversal symmetry (also termed s + is superconductors), focusing on the three-band case. In the limit of infinite penetration length, the system under consideration can, for a certain parameter regime, have a single first order phase transition from a U(1) × Z2 broken state to a normal state due to a nontrivial interplay between U(1) vortices and Z2 domain walls. This regime may also apply to multicomponent superfluids. For other parameters, when the free energy of the domain walls is low, the system undergoes a restoration of broken Z2 time reversal symmetry at temperatures lower than the temperature of the superconducting phase transition.We show that inclusion of fluctuations can strongly suppress the temperature of the Z2-transition when frustration is weak. The main result of our paper is that for relatively short magnetic field penetration lengths, the system has a superconducting phase transition at a temperature lower than the temperature of the restoration of the broken Z2 symmetry.
2021
We examine the stability of mixed-symmetry superconducting states with broken time-reversal symmetry in spatialsymmetry-broken systems, including chiral states, on the basis of the free-energy functional derived in the weakcoupling theory. We consider a generic α1 + iα2 wave state, with α1 and α2 being different symmetry indices such as (α1, α2) = (d, s), (px, py), and (d, d ′). The time-reversal symmetry of the mixed-symmetry state with the α1and α2-wave components is broken when the phases of these components differ, and such a state is called the time-reversal-symmetry breaking (TRSB) state. However, their phases are equated by Cooper-pair scattering between these components if it occurs; i.e., when the off-diagonal elements S α1α2 = S α2α1 of the scattering matrix are nonzero, they destabilize the TRSB state. Hence, it has often been believed that the TRSB state is stable only in systems with a spatial symmetry that guarantees S α1α2 = 0. We note that, contrary to this belief, t...