arXiv subjects

Sourin Das

Publications and source records attributed to Sourin Das.

At least 73 records · Page 4Linked to original sources

arXiv2016

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 arm and is threaded by Aharonov Bohm ($\mathcal{A}\mathcal{B}$) flux $ϕ$. We show that by varying the $\mathcal{AB}$ flux, the two leads go through resonance in an anti-correlated fashion while the resonance conductance is quantized to $2 e^2/h$. We further show that such anti-correlation 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 $\mathcal{AB}$ effect between the MBS and ABS.

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arXiv2016

Transport signatures of surface potentials on three-dimensional topological insulators

The spin-momentum locked nature of the robust surface states of three dimensional topological insulators (3D TI) make them promising candidates for spintronics applications. Surface potentials which respect time reversal symmetry can exist at the surface between a 3D TI and the trivial vacuum. These potentials can distort the spin texture of the surface states while retaining their gapless nature. In this work, the effect of all such surface potentials on the spin textures is studied. Since, a tunnel magnetoresistance signal carries the information of the spin texture, it is proposed that spin-polarized tunneling of electrons to a 3D TI surface can be used to uniquely identify the surface potentials and quantitatively characterize them.

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arXiv2015

Majorana fermions: Anholonomy of bound states

Majorana bound states appearing in 1-D $p$-wave superconductor ($\cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($\cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$\ddot{\rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $\cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition.

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arXiv2015

Topological p-n junctions in helical edge states

Quantum spin Hall effect is endowed with topologically protected edge modes with gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with opposite parity for winding of spin texture for conduction and valence band. Using Pancharatnam's prescription for geometric phase it is shown that mismatch of this parity across a $p$-$n$ junction, which could be engineered into the edge by electrical gate induced doping, leads to a phase dependence in the two-terminal conductance which is purely topological (0 or $π$). This fact results in a ${\mathbb{Z}}_2$ classification of such junctions with an associated duality. Current asymmetry measurements which are shown to be robust against electron-electron interactions are proposed to infer this topology.

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arXiv2015

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 ($θ$), 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 $θ$. Additionally, the theory presented in this article can be used to extract value of $θ$ for a given arbitrary planar surface from the STM spectra itself hence effectively mimicking X-ray spectroscopy.

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arXiv2015

Tunnel Magnetoresistance scan of a pristine three-dimensional topological insulator

Though the Fermi surface of surface states of a 3D topological insulator (TI) has zero magnetization, an arbitrary segment of the full Fermi surface has a unique magnetic moment consistent with the type of spin-momentum locking in hand. We propose a three-terminal set up, which directly couples to the magnetization of a chosen segment of a Fermi surface hence leading to a finite tunnel magnetoresistance (TMR) response of the nonmagnetic TI surface states, when coupled to spin polarized STM probe. This multiterminal TMR not only provides a unique signature of spin-momentum locking for a pristine TI but also provides a direct measure of momentum resolved out of plane polarization of hexagonally warped Fermi surfaces relevant for $Bi_2Te_3$, which could be as comprehensive as spin-resolved ARPES. Implication of this unconventional TMR is also discussed in the broader context of 2D spin-orbit (SO) materials.

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arXiv2013

Transport of spin-anisotropy without spin currents

We revisit the transport of spin-degrees of freedom across an electrically and thermally biased tunnel junction between two ferromagnets with non-collinear magnetizations. Besides the well-known charge and spin currents we show that a non-zero spin-quadrupole current flows between the ferromagnets. This tensor-valued current describes the non-equilibrium transport of spin-anisotropy relating to both local and non-local multi-particle spin correlations of the circuit. This quadratic spin-anisotropy, quantified in terms of the spin-quadrupole moment, is fundamentally a two-electron quantity. In spin-valves with an embedded quantum dot such currents have been shown to result in a quadrupole accumulation that affects the measurable quantum dot spin and charge dynamics. The spin-valve model studied here allows fundamental questions about spin-quadrupole storage and transport to be worked out in detail, while ignoring the detection by a quantum dot. This physical understanding of this particular device is of importance for more complex devices where spin-quadrupole transport can be detected. We demonstrate that, as far as storage and transport are concerned, the spin anisotropy is only partly determined by the spin polarization. In fact, for a thermally biased spin-valve the charge- and spin-current may vanish, while a pure exchange spin-quadrupole current remains, which appears as a fundamental consequence of Pauli's principle. We extend the real-time diagrammatic approach to efficiently calculate the average of multi-particle spin-observables, in particular the spin-quadrupole current. Although the paper addresses only leading order and spin-conserving tunneling we formulate the technique for arbitrary order in an arbitrary, spin-dependent tunnel coupling in a way that lends itself to extension to quantum-dot spin-valve structures.

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arXiv2012

Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime

The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counter-propagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact (QPC) as was experimentally established in Nature 466, 585 (2010). We show that replacing the QPC by a quantum dot provides a natural way for detecting the neutral modes via the finite current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theories (CFTs) describing these states, induce asymmetries in the thermoelectric current peaks. This in turn provides a direct fingerprint of the corresponding CFT.

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arXiv2012

Magnetic field induced Fabry-Pérot resonances in helical edge states

We study electronic transport across a helical edge state exposed to a uniform magnetic ({$\vec B$}) field over a finite length. We show that this system exhibits Fabry-Pérot 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 {$\vec B$} field while keeping its magnitude constant. This is in sharp contrast to the case of non-helical one dimensional electron gases with a parabolic dispersion, where similar resonances do appear in individual spin channels ($\uparrow$ and $\downarrow$) separately which, however, cannot be tuned by merely changing the direction of the {$\vec B$} field. These resonances provide a unique way to probe the helical nature of the theory.

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arXiv2011

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

We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low bias voltages $V$. We show that $G(V)$ exhibits an unconventional dependence on the direction of magnetization of the tip and can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac Fermions on the surface. We also demonstrate that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field, then $G(V)$ acquires a dependence on the azimuthal angle of the magnetization of the tip. We explain the role of the Dirac Fermions in this unconventional behavior and suggest experiments to test our theory.

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arXiv2011

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 ($θ$) 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 (which occurs 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.

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arXiv2010

Spin quadrupoletronics: moving spin anisotropy around

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.

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arXiv2010

Power dissipation for systems with junctions of multiple quantum wires

We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi liquid leads) or non-interacting electrons. We show that for a given matrix M, the eigenvalues of M^T M characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M-matrix whose entries depends on the tunneling amplitudes between the different edges.

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arXiv2009

Resonant charge and spin transport in a t-stub coupled to a superconductor

We study transport through a single channel t-stub geometry strongly coupled to a superconducting reservoir. In contrast to the standard stub geometry which has both transmission resonances and anti-resonances in the coherent limit, we find that due to the proximity effect, this geometry shows neither a T=1 resonance (T is the transmission probability for electrons incident on the t-stub) nor a T=0 anti-resonance as we vary the energy of the incident electron. Instead, we find that there is only one resonant value at T=1/4, where charge transport vanishes while the spin transport is perfect.

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arXiv2009

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/(2 ω), where v is the plasmon velocity and ωis 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.

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arXiv2009

Effect of inter-edge Coulomb interactions on transport through a point contact in a ν= 5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a ν= 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).

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arXiv2009

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.

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arXiv2008

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 quasi-particle excitations obeying non-abelian statistics. In general, it is hard to probe the neutral modes in charge transport measurements and a thermal transport measurement seems to be inevitable. Here we propose a setup which can get around this problem 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 non-trivial signature of the presence of the neutral mode hence leading to its indirect detection. 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.

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