Tunneling transport in NSN junctions made of Majorana nanowires across the topological quantum phase transition

We theoretically consider transport properties of a normal metal (N)- superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in the context of the possible existence of Majorana bound states in disordered semiconductor-superconductor hybrid systems in the presence of spin-orbit coupling and Zeeman splitting induced by an external magnetic field. We study in details the transport signatures of the topological quantum phase transition as well as the existence of the Majorana bound states in the electrical transport properties of the NSN structure. Our theory includes the realistic nonperturbative effects of disorder, which is detrimental to the topological phase (eventually suppressing the superconducting gap completely), and the effects of the tunneling barriers (or the transparency at the tunneling NS contacts), which affect (and suppress) the zero bias conductance peak associated with the zero energy Majorana bound states. We show that in the presence of generic disorder and barrier transparency the interpretation of the zero bias peak as being associated with the Majorana bound state is problematic since the nonlocal correlations between the two NS contacts at two ends may not manifest themselves in the tunneling conductance through the whole NSN structure. We establish that a simple modification of the standard transport measurements using conductance differences (rather than the conductance itself as in a single NS junction) as the measured quantity can allow direct observation of the nonlocal correlations inherent in the Majorana bound states and enables the mapping out of the topological phase diagram (even in the presence of considerable disorder) by precisely detecting the topological quantum phase transition point.Comment: 34 pages, 7 figures, 1 table. New version with minor modifications and more physical discussion

Parity effect in a mesoscopic Fermi gas

We develop a quantitative analytic theory that accurately describes the odd-even effect observed experimentally in a one-dimensional, trapped Fermi gas with a small number of particles [G. Z\"urn et al., Phys. Rev. Lett. 111, 175302 (2013)]. We find that the underlying physics is similar to the parity effect known to exist in ultrasmall mesoscopic superconducting grains and atomic nuclei. However, in contrast to superconducting nanograins, the density (Hartree) correction dominates over the superconducting pairing fluctuations and leads to a much more pronounced odd-even effect in the mesoscopic, trapped Fermi gas. We calculate the corresponding parity parameter and separation energy using both perturbation theory and a path integral framework in the mesoscopic limit, generalized to account for the effects of the trap, pairing fluctuations, and Hartree corrections. Our results are in an excellent quantitative agreement with experimental data and exact diagonalization. Finally, we discuss a few-to-many particle crossover between the perturbative mesoscopic regime and non-perturbative many-body physics that the system approaches in the thermodynamic limit.Comment: 7 pages, 1 figur

Spectral evolution of the SU(4) Kondo effect from the single impurity to the two-dimensional lattice

We describe the evolution of the SU(4) Kondo effect as the number of magnetic centers increases from one impurity to the two-dimensional (2D) lattice. We derive a Hubbard-Anderson model which describes a 2D array of atoms or molecules with two-fold orbital degeneracy, acting as magnetic impurities and interacting with a metallic host. We calculate the differential conductance, observed typically in experiments of scanning tunneling spectroscopy, for different arrangements of impurities on a metallic surface: a single impurity, a periodic square lattice, and several sites of a rectangular cluster. Our results point towards the crucial importance of the orbital degeneracy and agree well with recent experiments in different systems of iron(II) phtalocyanine molecules deposited on top of Au(111) [N. Tsukahara et al., Phys. Rev. Lett. 106, 187201 (2011)], indicating that this would be the first experimental realization of an artificial 2D SU(4) Kondo-lattice system.Comment: 17 pages, 4 figures. New version contains an Appendix with details of the derivation of the Hamiltonian Eq.(2), derivation of the slave-boson mean-field equations, and an estimation of the upper bounds of the RKKY interactio

Magnetic phases in the one-dimensional Kondo chain on a metallic surface

We study the low-temperature properties of a one-dimensional spin-1/2 chain of magnetic impurities coupled to a (normal) metal environment by means of anisotropic Kondo exchange. In the case of easy-plane anisotropy, we obtain the phase diagram of this system at T=0. We show that the in-plane Kondo coupling destabilizes the Tomonaga-Luttinger phase of the spin-chain, and leads to two different phases: i) At strong Kondo coupling, the spins in the chain form Kondo singlets and become screened by the metallic environment, and ii) At weak and intermediate Kondo coupling, we find a novel dissipative phase characterized by diffusive gapless spin excitations. The two phases are separated by a quantum critical point of the Wilson-Fisher universality class with dynamical exponent $z\simeq2$.Comment: 15 pages, 3 figures. New version contains clarifications about the specific approximations. Accepted for publication in PR

Valence fluctuations in a lattice of magnetic molecules: application to iron(II) phtalocyanine molecules on Au(111)

We study theoretically a square lattice of the organometallic Kondo adsorbate iron(II) phtalocyanine (FePc) deposited on top of Au(111), motivated by recent scanning tunneling microscopy experiments. We describe the system by means of an effective Hubbard-Anderson model, where each molecule has degenerate effective $d-$orbitals with $xz$ and $yz$ symmetry, which we solve for arbitrary occupation and arbitrary on-site repulsion $U$. To that end, we introduce a generalized slave-boson mean-field approximation (SBMFA) which correctly describes both the non-interacting limit (NIL) $U=0$ and the strongly-interacting limit $U \rightarrow \infty$, where our formalism reproduces the correct value of the Kondo temperature for an isolated FePc molecule. Our results indicate that while the isolated molecule can be described by an SU(4) Anderson model in the Kondo regime, the case of the square lattice corresponds to the intermediate-valence regime, with a total occupation of nearly 1.65 holes in the FePc molecular orbitals. Our results have important implications for the physical interpretation of the experiment.Comment: 7 pages, 2 figure

Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator

Topological Kondo insulators are strongly correlated materials, where itinerant electrons hybridize with localized spins giving rise to a topologically non-trivial band structure. Here we use non-perturbative bosonization and renormalization group techniques to study theoretically a one-dimensional topological Kondo insulator. It is described as a Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel - a strongly correlated version of the prototypical Tamm-Shockley model. We derive and solve renormalization group equations at two-loop order in the Kondo parameter, and find that, at half-filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a non-interacting conduction band (Hubbard parameter $U=0$). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-$1$ chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-$1/2$ end states for chains with open boundary conditions. Our analysis allows to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.Comment: 13 pages, 2 figures, 1 appendix. New version with typos correcte