Spin polarised scanning tunneling probe for helical Luttinger liquids

We propose a three terminal spin polarized stm setup for probing the helical nature of the Luttinger liquid edge state that appears in the quantum spin Hall system. We show that the three-terminal tunneling conductance strongly depends on the angle ($\theta$) between the magnetization direction of the tip and the local orientation of the electron spin on the edge while the two terminal conductance is independent of this angle. We demonstrate that chiral injection of an electron into the helical Luttinger liquid (which occurs when $\theta$ is zero or $\pi$) is associated with fractionalization of the spin of the injected electron in addition to the fractionalization of its charge. We also point out a spin current amplification effect induced by the spin fractionalization.Comment: Final version to appear in Phys. Rev. Let

Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic property of these surface states, namely the spin-momentum locking. We show that the information regarding the spin textures, so extracted, for different surfaces can be put together to reconstruct the parameters characterizing the bulk band structure of the material, hence acting as a hologram. For specific TI materials like, $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$, the planar surface states are distinct from one another with regard to their spectrum and the associated spin texture for each angle ($\theta$), which the normal to the surface makes with the crystal growth axis. We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin polarized STM which provides a unique fingerprint of the dispersion and the associated spin texture corresponding to each $\theta$. Additionally, the theory presented in this article can be used to extract value of $\theta$ for a given arbitrary planar surface from the STM spectra itself hence effectively mimicking X-ray spectroscopy.Comment: 11 pages, 8 figures, version accepted in Phys. Rev.

Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can give a clear experimental signal of this region.Comment: 5 pages, 4 figure

A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parameterization of a S-matrix representing small deviations from a given fixed point S-matrix (obtained earlier in Phys. Rev. B 77, 155418 (2008)), and we then perform a comprehensive stability analysis. In particular, for the non-trivial fixed point which has intermediate values of transmission, reflection, Andreev reflection and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are non-linear functions of V(0) and V(2k_{F}) (where V(k) represents the Fourier transform of the inter-electron interaction potential at momentum k). We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.Comment: Final version to appear in Phys. Rev.

Spintronics with NSN Junction of one-dimensional quantum wires : A study of Pure Spin Current and Magnetoresistance

We demonstrate possible scenarios for production of pure spin current and large tunnelling magnetoresistance ratios from elastic co-tunnelling and crossed Andreev reflection across a superconducting junction comprising of normal metal-superconductor-normal metal, where, the normal metal is a one-dimensional interacting quantum wire. We show that there are fixed points in the theory which correspond to the case of pure spin current. We analyze the influence of electron-electron interaction and see how it stabilizes or de-stabilizes the production of pure spin current. These fixed points can be of direct experimental relevance for spintronics application of normal metal-superconductor-normal metal junctions of one-dimensional quantum wires. We also calculate the power law temperature dependence of the crossed Andreev reflection enhanced tunnelling magnetoresistance ratio for the normal metal-superconductor-normal metal junction.Comment: Final version to appear in Euro. Phys. Let