Sourin Das

Spin-polarized 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 depends on the angle (θ) 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 (when θ is zero or π) 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.

Enhancement of Tunneling Density of States at a Junction of Three Luttinger Liquid Wires

We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x=v/(2omega), where v is the plasmon velocity and omega is the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enhancement in each wire individually.

Transport and accumulation of spin anisotropy

We show that spin anisotropy can be transferred to an isotropic system by transport of spin quadrupole moment. We derive the quadrupole moment current and continuity equation and study a high-spin valve structure consisting of two ferromagnets coupled to a quantum dot probing an impurity spin. The quadrupole back-action on their coupled spin results in spin torques and anisotropic spin relaxation which do not follow from standard spin current considerations. We demonstrate the detection of the impurity spin by charge transport and its manipulation by electric fields.

Duality between normal and superconducting junctions of multiple quantum wires

We study junctions of single-channel spinless Luttinger liquids using bosonization. We generalize earlier studies by allowing the junction to be superconducting and find new charge nonconserving low-energy fixed points. We establish the existence of g 1/g duality (where g is the Luttinger liquid parameter) between the charge-conserving (normal) junction and the charge nonconserving (superconducting) junction by evaluating and comparing the scaling dimensions of various operators around the fixed points in both the normal and superconducting sectors of the theory. For the most general two-wire junction, we show that there are two conformally invariant one-parameter families of fixed points which are also connected by a duality transformation. We also show that the stable fixed point for the two-wire superconducting junction corresponds to the situation where the crossed Andreev reflection (an incoming electron is transmitted as an outgoing hole) is perfect between the wires. For the three-wire junction, we study, in particular, the superconducting analogs of the chiral D-P and the disconnected fixed points obtained earlier in the literature in the context of charge-conserving three-wire junctions. We show that these fixed points can be stabilized for g < 1 (repulsive electrons) within the superconducting sector of the theory which makes them experimentally relevant.

Magnetic-field-induced Fabry-Perot resonances in helical edge states

We study electronic transport across a helical edge state exposed to a uniform magnetic ((B) over right arrow) field over a finite length. We show that this system exhibits Fabry-Perot-type resonances in electronic transport. The intrinsic spin anisotropy of the helical edge states allows us to tune these resonances by changing the direction of the (B) over right arrow field while keeping its magnitude constant. This is in sharp contrast to the case of nonhelical one-dimensional electron gases with a parabolic dispersion, where similar resonances do appear in individual spin channels (up arrow and down arrow) separately which, however, cannot be tuned by merely changing the direction of the (B) over right arrow field. These resonances provide a unique way to probe the helical nature of the theory. We study the robustness of these resonances against a possible static impurity in the channel.

Probing the Neutral Edge Modes in Transport across a Point Contact via Thermal Effects in the Read-Rezayi Non-Abelian Quantum Hall States

Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.

Fingerprints of Majorana Bound States in Aharonov-Bohm Geometry.

We study a ring geometry, coupled to two normal metallic leads, which has a Majorana bound state (MBS) embedded in one of its arms and is threaded by Aharonov-Bohm (AB) flux ϕ. We show that by varying the AB flux, the two leads go through resonance in an anticorrelated fashion while the resonance conductance is quantized to 2e^{2}/h. We further show that such anticorrelation is completely absent when the MBS is replaced by an Andreev bound state (ABS). Hence this anti-correlation in conductance when studied as a function of ϕ provides a unique signature of the MBS which cannot be faked by an ABS. We contrast the phase sensitivity of the MBS and ABS in terms of tunneling conductances. We argue that the relative phase between the tunneling amplitude of the electrons and holes from either lead to the level (MBS or ABS), which is constrained to 0,π for the MBS and unconstrained for the ABS, is responsible for this interesting contrast in the AB effect between the MBS and ABS.

Systematic stability analysis of the renormalization 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 parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial 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 nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron 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.

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,

Spin-polarized STM spectra of Dirac electrons on the surface of a topological insulator

\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3