Propagation of Phonon in a Curved Space Induced by Strain Fields Instantons

We show that for a \textbf{multiple-connected} space the low energy strain fields excitations are given by instantons. Dirac fermions with a chiral mass and a pairing field propagates effectively in a multiple conected space. When the elastic strain field response is probed one finds that it is given by the \textbf{Pointriagin} characteristic. As a result the space time metric is modified. Applying an external stress field we observe that the phonon path bends in the transverse direction to the initial direction

A green's function approach for surface state photoelectrons in topological insulators

The topology of the surface electronic states is detected with photoemission. We explain the photoemission from the topological surface state . This is done by identifying the effective coupling between surface electrons-photons and vacuum electrons. The effective electron photon coupling is given by $e\tau^2$ where $\tau$ is the dimensionless tunneling amplitude of the zero mode surface states to tunnel into the vacuum. We compute the polarization and intensity of the emitted photoelectrons. We introduce a model which takes in account the Dirac Hamiltonian for the surface electron to photons coupling and the tunneling of the zero mode into the vacuum. Within the Green's function formalism we obtain exact results for the emitted Photoelectrons to second order in the laser field. The number of the emitted photoelectrons is sensitive to the laser coherent state intensity, the polarization is sensitive to the surface topology of the electronic states and the incoming photon polarization. The calculation is performed for the helical, Zeeman and warping case allowing to study spin textures.Comment: arXiv admin note: text overlap with arXiv:1501.0656

Tunnelling of Polarized Electrons in Magnetic Wires

We investigate the tunnelling between an electronic gas with two different velocities $V_\uparrow \neq V_\downarrow$ and a regular metal. We find that at the interface between the two systems that the tunnelling conductance for spin up and spin down are different. As a result a partly polarized gas (``magnetic wire'') is obtained. This result is caused by the e-e interaction, $g_2'' - g_1'' \neq 0$, which in the presence of $V_\uparrow \neq V_\downarrow$ gives rise to two different tunnelling exponents.Comment: 9 page

The Non-Dissipative Spin-Hall Current

A theory based on the Aharonov -Bohm effect in the momentum space for the Spin-Hall conductivity without a magnetic field is presented. The two dimensional Rashba Hamiltonian is diagonalized in the momentum spinor basis. This spinor is singular at K=0. The representation of the cartesian coordinates in the spinor momentum basis obey non-commutative rules. The non-commuting relations are a result of an effective Aharonov-Bohm vortex at K=0. We find the exact value of $\frac{e}{4\pi}$ for the Spin-Hall conductivity. The effect of a time reversal scattering potential on the Spin-Hall current causes the current to vanishes for an infinite system.Comment: submitted to P.R.

The Non-Dissipative Spin-Hall Conductivity and The Identification of the Conserved Current

The two dimensional Rashba Hamiltonian is investigated using the momentum representation.One finds that the SU(2) transformation which diagonalizes the Hamiltonian gives rise to non commuting Cartesian coordinates for K=0 and zero otherwise.This result corresponds to the Aharonov -Bohm phase in the momentum space. The Spin -Hall conductivity is given by $\frac{e}{4\pi}$ which disagree with the result $\frac{e}{8\pi}$ given in the literature.Using Stokes theorem we find that the Spin -Hall current is carried equally by the up and down electrons on the Fermi surface. We identify the Magnetic current and find that for an electric field with a finite Fourier component in the momentum space a non zero Spin -Hall current is obtained.For the electric field which is constant in space, the orbital magnetic current cancels the spin current. In order to measure the Spin-Hall conductance we propose to apply a magnetic field gradient $\Delta H_{2}$ in the $i=2$ direction and to measure a Charge- Hall current $\frac{e}{h}(\frac{g}{2})\mu_{B}\Delta H_{2}$ in the $i=1$ direction.Comment: 9 pages, 1 figure, submitted to PR

Electrodynamics effects in 3+1 dimensions induced by interactions in Topological Insulators

We investigate the effect of interactions in the Topological Insulator in 3+1 dimensions. We show that for a particular type of interactions, the Electrodynamics response is equivalent to the response of non-interacting Topological Insulator in 4+1 dimensions

The Marginal Fermi Liquid - An Exact Derivation Based on Dirac's First Class Constraints Method

Dirac's method for constraints is used for solving the problem of exclusion of double occupancy for Correlated Electrons. The constraints are enforced by the pair operator $Q(\vec{x})=\psi_{\downarrow}(\vec{x})\psi_{\uparrow}(\vec{x})$ which annihilates the ground state $|\Psi^0>$. Away from half fillings the operator $Q(\vec{x})$ is replaced by a set of $first$ $class$ Non-Abelian constraints $Q^{(-)}_{\alpha}(\vec{x})$ restricted to negative energies. The propagator for a single hole away from half fillings is determined by modified measure which is a function of the time duration of the hole propagator. As a result: a) The imaginary part of the self energy - is linear in the frequency. At large hole concentrations a Fermi Liquid self energy is obtained. b) For the Superconducting state the constraints generate an asymmetric spectrum excitations between electrons and holes giving rise to an asymmetry tunneling density of states.Comment: 33 pages, 5 figure

Fractional Topological Insulators- A Bosonization Approach

A metallic disk with strong spin orbit interaction is investigated . The finite disk geometry introduces a confining potential. Due to the strong spin-orbit interaction and confining potential the metal disk is described by an effective one dimensional with a harmonic potential. The harmonic potential gives rise to classical turning points. As a result open boundary conditions must be used. We Bosonize the model and obtain chiral Bosons for each spin on the edge of the disk. When the filling fraction is reduced to $\nu=\frac{k_{F}}{k_{so}}=\frac{1}{3}$ the electron- electron interactions are studied using the Jordan Wigner phase for composite fermions which gives rise to a Luttinger liquid. When the metallic disk is in the proximity with a superconductor a Fractional Topological Insulators is obtained. An experimental realization is proposed. We show that by tunning the chemical potential we control the classical turning points for which a Fractional Topological Insulator is realized.Comment: Keywords: spin-orbit, chiral bosons, chains, metallic disk, topological insulator

Probing Topological Superconductors with Sound Waves

A new method is introduced for probing Topological Superconductors. The integration of the superconding fermions generates a topological $\mathbf{Chern-Simons}$ sound action . Dislocations induce Majorana zero modes inside the sample, resulting in a new Hamiltonian which couple the Majorana modes, the electron field and the non-Abelian strain field sound. This Hamiltonian is used to compute the anomalous sound absorption. The Topological superconductor absorbs sound below the superconducting gap due to the transition between the quasi particles and the Majorana fermions. The sound waves offers a new tool for detecting Majorana fermions

Topological spin current

We present an exact derivation for non-commuting coordinates induced by the SU(2) transformation used to diagonalize the spin-orbit hamiltonian in two dimension.As a result an exact non-dissipative Hall current less sensitive to disorder and complementary to the dissipative conductivity is found. We compute the non-dissipative charge and spin-Hall conductance for the spin-orbit problem.We find that the spin-Hall conductance is quantized in units of $\frac{eg\mu_{B}}{h}$ .In the presence of a Zeeman interaction the charge-Hall conductivity is proportional to the magnetic field. We propose an experiment to test our theory