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We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994)], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions. [ABSTRACT FROM AUTHOR]

We investigate the nature of the magnetic phase transition induced by the short-ranged electron-electron interactions in a Weyl semimetal by using the perturbative renormalization-group method. We find that the critical point associated with the quantum phase transition is characterized by a Gaussian fixed point perturbed by a dangerously irrelevant operator. Although the low-energy and long-distance physics is governed by a free theory, the velocities of the fermionic quasiparticles and the magnetic fluctuations suffer from nontrivial renormalization effects. In particular, their ratio approaches one at low energies, which indicates an emergent Lorentz symmetry at the quantum critical point. We further investigate the stability of the fixed point in the presence of weak disorder preserving the chiral symmetry. We show that while the fixed point is generally stable against weak disorder, a moderately strong random chemical potential and/or random vector potential may induce a quantum phase transition towards a disorder-dominated phase. We propose a global phase diagram of the Weyl semimetal in the presence of both electron-electron interactions and disorder based on our results. [ABSTRACT FROM AUTHOR]

We study the behavior of a topological Josephson junction in which two topological superconductors are coupled through a quantum dot. We focus on the case with the bulk superconducting gap being the largest energy scale. Two parameter regimes are investigated: a weak tunneling between the dot and the superconductors, with the dot near its charge degeneracy point, and a strong-tunneling regime in which the transmission between the dot and the superconductors is nearly perfect. We show that in the former situation, the Andreev spectrum for each sector with fixed fermion parity consists of only two levels, which gives rise to the nontrivial current-phase relation. Moreover, we study the Rabi oscillation between the two levels and indicate that the corresponding frequency is a 4π-periodic function of the phase difference between the two superconductors, which is immune to the quasiparticle poisoning. In the latter case, we find that the Coulomb charging energy enhances the effect of backscattering at the interfaces between the dot and the superconductors. Both the temperature and the gate-voltage dependence of the critical Josephson current are examined. [ABSTRACT FROM AUTHOR]

In a superconducting nanostructure, phase fluctuations are prominent and give rise to finite resistance below superconducting transition temperature Tc. By using a monolayer polymer/nanosphere hybrid we developed previously, we fabricated a large array of interconnected niobium (Nb) honeycomb lattices with the thinnest interconnected linewidth d ranging from 36 nm to 89 nm. The honeycomb cells form a highly ordered triangular lattice with more than 108 unit cells extending over few mm² area, which enables the detailed transport study at nanometer scales. We found Tc gradually drops with decreasing d due to the phase-slip effect, while the critical field at lower temperature tends to follow that of a continuous Nb thin film. One likely scenario is to consider a model system of numerous superconducting islands interconnected by short phase-slip junctions, where the phase coherence is dictated by the phase slippage in the nanoconstriction. This was strongly supported by the excellent fitting to the thermally activated phase-slip model and also the unusual phenomena of transition width narrowing in high fields. [ABSTRACT FROM AUTHOR]