arXiv subjects

M. Franz

Publications and source records attributed to M. Franz.

At least 55 records · Page 3Linked to original sources

arXiv2012

Surface magnetic ordering in topological insulators with bulk magnetic dopants

We show that a three dimensional topological insulator doped with magnetic impurities in the bulk can have a regime where the surface is magnetically ordered but the bulk is not. This is in contrast to conventional materials where bulk ordered phases are typically more robust than surface ordered phases. The difference originates from the topologically protected gapless surface states characteristic of topological insulators. We study the problem using a mean field approach in two concrete models that give the same qualitative result, with some interesting differences. Our findings could help explain recent experimental results showing the emergence of a spectral gap in the surface state of Bi2Se3 doped with Mn or Fe atoms, but with no measurable bulk magnetism.

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arXiv2012

Flat bands with non-trivial topology in three dimensions

We construct a simple model for electrons in a three-dimensional crystal where a combination of short-range hopping and spin-orbit coupling results in nearly flat bands characterized by a non-trivial Z2 topological index. The flat band is separated from other bands by a bandgap much larger than the bandwidth. We discuss the fate of the many-body ground state of electrons in the flat band in the presence of repulsive interactions at partial filling and conjecture that it may become a three-dimensional fractional topological insulator if conventional magnetic instabilities can be avoided.

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arXiv2012

Spin Response of Electrons on the Surface of a Topological Insulator

The surface of a topological insulator hosts a very special form of a quasi-two dimensional metallic system when it is embedded in a topologically trivial medium like the vacuum. The electronic properties of this unusual 2D metal are distinct in many aspects from both the conventional two-dimensional electron gas systems in quantum well heterostructures as well as those of a single layer graphene. In this paper, we study one of these distinct features i.e., the response of the electronic spins to an applied magnetic field perpendicular to the surface. We find an unusual behaviour of the spin magnetization and susceptibility as a function of both the magnetic field and the chemical potential for a generic topological surface. We propose that this behavior could be studied by the recently developed experimental technique called βNMR which is highly sensitive to the surface electron spins. We explain how this technique could be used to probe for spontaneous magnetic ordering caused by magnetic dopants or interactions discussed in the recent literature.

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arXiv2011

Majorana Fermions in Proximity-coupled Topological Insulator Nanowires

A topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, is shown to realize a one-dimensional topological superconductor with unpaired Majorana fermions localized at both ends. This situation occurs under a wide range of conditions and constitutes what is possibly the most easily accessible physical realization of the elusive Majorana particles in a solid-state system.

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arXiv2011

Excitons and Optical Absorption on the Surface of a Strong Topological Insulator with a Magnetic Energy Gap

We present a theoretical study of interacting electron-hole pairs located on a magnetized surface of a strong topological insulator (TI). The excitonic energy levels and the optical absorption on such surface display unique and potentially measurable features such as (i) an enhanced binding energy for excitons whose total angular momentum is aligned with the magnetic exchange field, (ii) a stark dependence of the optical absorption on the direction of the magnetic exchange field as well as on the chirality of the incident light, and (iii) a tunable center-of-mass motion of spinful excitons induced by particle-hole asymmetry in the exchange field. Our predictions are relevant to surfaces of magnetically doped TIs or surfaces coated with magnetic films, in addition to TI nanowires placed under longitudinal magnetic fields.

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arXiv2010

Quantization and $2π$ Periodicity of the Axion Action in Topological Insulators

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form 'θE dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under 'θ-> θ+2π'. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space-time, assuming only that the vector potential is consistent with single-valuedness of the electron wavefunctions in the underlying insulator.

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arXiv2010

Detection of large acoustic energy flux in the solar atmosphere

We study the energy flux carried by acoustic waves excited by convective motions at sub-photospheric levels. The analysis of high-resolution spectropolarimetric data taken with IMaX/Sunrise provides a total energy flux of ~ 6400--7700 Wm$^{-2}$ at a height of ~ 250 km in the 5.2-10 mHz range, i.e. at least twice the largest energy flux found in previous works. Our estimate lies within a factor of 2 of the energy flux needed to balance radiative losses from the chromosphere according to Anderson & Athay (1989) and revives interest in acoustic waves for transporting energy to the chromosphere. The acoustic flux is mainly found in the intergranular lanes but also in small rapidly-evolving granules and at the bright borders, forming dark dots and lanes of splitting granules.

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arXiv2010

Bright points in the quiet Sun as observed in the visible and near-UV by the balloon-borne observatory Sunrise

Bright points (BPs) are manifestations of small magnetic elements in the solar photosphere. Their brightness contrast not only gives insight into the thermal state of the photosphere (and chromosphere) in magnetic elements, but also plays an important role in modulating the solar total and spectral irradiance. Here we report on simultaneous high-resolution imaging and spectropolarimetric observations of BPs using Sunrise balloon-borne observatory data of the quiet Sun at disk center. BP contrasts have been measured between 214 nm and 525 nm, including the first measurements at wavelengths below 388 nm. The histograms of the BP peak brightness show a clear trend toward broader contrast distributions and higher mean contrasts at shorter wavelengths. At 214 nm we observe a peak brightness of up to five times the mean quiet-Sun value, the highest BP contrast so far observed. All BPs are associated with a magnetic signal, although in a number of cases it is surprisingly weak. Most of the BPs show only weak downflows, the mean value being 240 m/s, but some display strong down- or upflows reaching a few km/s.

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arXiv2010

Surface waves in solar granulation observed with {\sc Sunrise}

Solar oscillations are expected to be excited by turbulent flows in the intergranular lanes near the solar surface. Time series recorded by the IMaX instrument aboard the {\sc Sunrise} observatory reveal solar oscillations at high resolution, which allow studying the properties of oscillations with short wavelengths. We analyze two times series with synchronous recordings of Doppler velocity and continuum intensity images with durations of 32\thinspace min and 23\thinspace min, resp., recorded close to the disk center of the Sun to study the propagation and excitation of solar acoustic oscillations. In the Doppler velocity data, both the standing acoustic waves and the short-lived, high-degree running waves are visible. The standing waves are visible as temporary enhancements of the amplitudes of the large-scale velocity field due to the stochastic superposition of the acoustic waves. We focus on the high-degree small-scale waves by suitable filtering in the Fourier domain. Investigating the propagation and excitation of $f$- and $p_1$-modes with wave numbers $k > 1.4$\thinspace 1/Mm we find that also exploding granules contribute to the excitation of solar $p$-modes in addition to the contribution of intergranular lanes.

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arXiv2010

Detection of vortex tubes in solar granulation from observations with Sunrise

We have investigated a time series of continuum intensity maps and corresponding Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar observatory Sunrise. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. From cross sections through the computational domain of the simulation, we conclude that these `granular lanes' are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. We propose that the observed vortex tubes may represent only the large-scale end of a hierarchy of vortex tubes existing near the solar surface.

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arXiv2010

Sunrise: instrument, mission, data and first results

The Sunrise balloon-borne solar observatory consists of a 1m aperture Gregory telescope, a UV filter imager, an imaging vector polarimeter, an image stabilization system and further infrastructure. The first science flight of Sunrise yielded high-quality data that reveal the structure, dynamics and evolution of solar convection, oscillations and magnetic fields at a resolution of around 100 km in the quiet Sun. After a brief description of instruments and data, first qualitative results are presented. In contrast to earlier observations, we clearly see granulation at 214 nm. Images in Ca II H display narrow, short-lived dark intergranular lanes between the bright edges of granules. The very small-scale, mixed-polarity internetwork fields are found to be highly dynamic. A significant increase in detectable magnetic flux is found after phase-diversity-related reconstruction of polarization maps, indicating that the polarities are mixed right down to the spatial resolution limit, and probably beyond.

astro-ph.SR↗

arXiv2010

Topological Anderson Insulator in Three Dimensions

Disorder, ubiquitously present in solids, is normally detrimental to the stability of ordered states of matter. In this letter we demonstrate that not only is the physics of a strong topological insulator robust to disorder but, remarkably, under certain conditions disorder can become fundamentally responsible for its existence. We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological `Anderson' insulator, a new topological phase of quantum matter in three dimensions.

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arXiv2010

Witten effect in a crystalline topological insulator

It has been noted a long time ago that a term of the form theta (e^2/2πh) B dot E may be added to the standard Maxwell Lagrangian without modifying the familiar laws of electricity and magnetism. theta is known to particle physicists as the 'axion' field and whether or not it has a nonzero expectation value in vacuum remains a fundamental open question of the Standard Model. A key manifestation of the axion term is the Witten effect: a unit magnetic monopole placed inside a medium with non-zero theta is predicted to bind a (generally fractional) electric charge -e(theta/2 pi+n) with n integer. Here we conduct a first test of the Witten effect, based on the recently established fact that the axion term with theta=pi emerges naturally in the description of the electromagnetic response of a new class of crystalline solids called topological insulators - materials distinguished by strong spin-orbit coupling and non-trivial band structure. Using a simple physical model for a topological insulator, we demonstrate the existence of a fractional charge bound to a monopole by an explicit numerical calculation. We also propose a scheme for generating an 'artificial' magnetic monopole in a topological insulator film, that may be used to facilitate the first experimental test of Witten's prediction.

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arXiv2010

Topological Insulators on the Lieb and Perovskite Lattices

Electrons hopping on the sites of a two-dimensional Lieb lattice and three-dimensional edge centered cubic (perovskite) lattice are shown to form topologically non-trivial insulating phases when spin-orbit coupling is introduced. These simple models on lattices with cubic symmetry show a Dirac-like structure in the excitation spectrum but with the unusual feature that there is a dispersionless band through the center of the spectrum and only a single Dirac cone per Brillouin zone.

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arXiv2010

Magnetoelectric Response of the Time-Reversal Invariant Helical Metal

We derive compact analytical expressions for the coupled spin-charge susceptibility of a clean helical metal at the surface of a three dimensional topological insulator (TI). These expressions lead to unconventional non-collinear RKKY interactions between two impurity magnetic moments placed on the surface of a TI, and predict the generation of electric currents by time-dependent magnetic moments. We determine the influence of gate and bias voltages on the interlayer exchange coupling between two single-domain ferromagnetic monolayers deposited on top of a TI.

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arXiv2010

Wormhole Effect in a Strong Topological Insulator

An infinitely thin solenoid carrying magnetic flux Phi (a `Dirac string') inserted into an ordinary band insulator has no significant effect on the spectrum of electrons. In a strong topological insulator, remarkably, such a solenoid carries protected gapless one-dimensional fermionic modes when Phi=hc/2e. These modes are spin-filtered and represent a distinct bulk manifestation of the topologically non-trivial insulator. We establish this `wormhole' effect by both general qualitative considerations and by numerical calculations within a minimal lattice model. We also discuss the possibility of experimental observation of a closely related effect in artificially engineered nanostructures.

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arXiv2010

Theory of quasiparticle interference on the surface of a strong topological insulator

Electrons on the surface of a strong topological insulator, such as Bi2Te3 or Bi1-xSnx, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and non-magnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from non-magnetic impurities observed in recent experiments and predict new interference features, uniquely characteristic of the helical liquid, when the scatterers are magnetic.

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arXiv2009

Three-dimensional Topological Insulators on the Pyrochlore Lattice

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically non-trivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling undistorted pyrochlore lattice with SO term yields a 'pristine' strong topological insulator with Z2 index (1;000). At quarter filling various strong and weak topological phases are obtained provided that both SO coupling and uniaxial lattice distortion are present. Our analysis suggests that many of the non-magnetic insulating pyrochlores should be topological insulators.

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