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Register a new userTopological states in normal and superconducting $p$-wave chains
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Added by
Mucio A. Continentino
Publication date
2014
fields
Physics
and research's language is
English
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We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the $sp$-chain maps formally into a $p$-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the $T$-matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.
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We study low temperature electron transport in p-wave superconductor-insulator-normal metal junctions. In diffusive metals the p-wave component of the order parameter decays exponentially at distances larger than the mean free path $l$. At the superconductor-normal metal boundary, due to spin-orbit interaction, there is a triplet to singlet conversion of the superconducting order parameter. The singlet component survives at distances much larger than $l$ from the boundary. It is this component that controls the low temperature resistance of the junctions. As a result, the resistance of the system strongly depends on the angle between the insulating boundary and the ${bf d}$-vector characterizing the spin structure of the triplet superconducting order parameter. We also analyze the spatial dependence of the electric potential in the presence of the current, and show that the electric field is suppressed in the insulating boundary as well as in the normal metal at distances of order of the coherence length away from the boundary. This is very different from the case of the normal metal-insulator-normal metal junctions, where the voltage drop takes place predominantly at the insulator.
The energy spectrum of cake shape normal - superconducting systems is calculated by solving the Bogoliubov-de Gennes equation. We take into account the mismatch in the effective masses and Fermi energies of the normal and superconducting regions as well as the potential barrier at the interface. In the case of a perfect interface and without mismatch, the energy levels are treated by semi-classics. Analytical expressions for the density of states and its integral, the step function, are derived and compared with that obtained from exact numerics. We find a very good agreement between the two calculations. It is shown that the spectrum possesses an energy gap and the density of states is singular at the edge of the gap. The effect of the mismatch and the potential barrier on the gap is also investigated.
In this paper we present scanning tunneling microscopy of a large $textrm{Bi}_2textrm{Se}_3$ crystal with superconducting PbBi islands deposited on the surface. Local density of states measurements are consistent with induced superconductivity in the topological surface state with a coherence length of order 540 nm. At energies above the gap the density of states exhibits oscillations due to scattering caused by a nonuniform order parameter. Strikingly, the spectra taken on islands also display similar oscillations along with traces of the Dirac cone, suggesting an inverse topological proximity effect.
The Hall resistivity rho_{xy} of LuNi_2B_2C is negative in the normal as well as in the mixed state and has no sign reversal typical for high-T_c superconductors. A distinct nonlinearity in the rho_{xy} dependence on field H was found in the normal state for T < 40K, accompanied by a large magnetoresistance reaching +90% for mu_0H=16T at T=20K. The scaling relation rho_{xy} ~ rho_{xx}^beta (rho_{xx} is the longitudinal resistivity) was found in the mixed state, the value of beta being dependent on the degree of disorder.
In this work, the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a current flux injected into the system using an external normal lead and derived from it via a superconducting electrode. After discussing the topological phase diagram of the isolated systems, using a scattering technique within the Bogoliubov de Gennes formulation, we analyze the differential conductance properties of these topological devices as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize topological systems is also addressed by studying the system electrical response as a function of the position and the distance of the normal electrode (tip). The results show how the signatures of topological order affect the electrical response of the analyzed systems, a subset of which being robust also against the effects of a moderate amount of disorder. The analysis of the internal modes of the nanodevices demonstrates that topological protection can be lost when quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. The conclusions of this work could be useful in understanding the topological phases of nanowire-based mesoscopic devices.
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