Edge states in graphene

Graphene offers more [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.236806]:

In condensed matter systems, topology often gives rise to gapless excitations at the edge (in 2D) or the surface (in 3D). Such excitations in the 2D fractional quantum Hall state should manifest in the edge behaving as a Luttinger liquid, in which tunneling is determined by a universal power law related to an attribute—the filling factor—of the magnetic flux through, and the number of electrons in, the 2D state.

However, no such behavior has yet been observed at the edges of 2D semiconductor heterostructures, the most-studied quantum Hall systems. Theorists say that in these systems the conflicting interplay between the confinement potential, attracting each electron towards the center, and the Coulomb force, pushing them apart from each other, modifies the edge itself. This process—edge reconstruction—disturbs the universal Luttinger liquid picture in the experimentally accessible distance scales.

In a paper in Physical Review Letters, Zi-Xiang Hu, at Princeton University, and his colleagues tell us that we may, after all, be able to see chiral Luttinger behavior in another system in which fractional quantum Hall effect has been observed—graphene. In graphene, electrons are confined by metallic gates that are placed a specific distance away. By contrast, in semiconductors, electrons are confined by dopants. This one difference should make graphene less susceptible to edge reconstruction and reveal the fractional quantum Hall state. The authors say that experimentalists should therefore finally see the elusive universal edge behavior in the experimentally accessible state with filling factor 1/3. – Sami Mitra

Majorana fermions possibly in topological insulators

This is a wonderful short review of the work done in looking for those elusive fermions in condensed matter community. I'll almost utterly post it here.

The search for Majorana fermions is quickly becoming an obsession in the condensed-matter community. To understand the intense interest, I will begin with a practical definition: a Majorana fermion is a fermion that is its own antiparticle. While sophisticated particle physics experiments are testing for Majorana character in neutrinos propagating in three dimensions [1], solid state physicists are more interested in lower dimensional counterparts. The most interesting Majorana fermions that are predicted to appear in materials are zero-dimensional bound states confined to live on various types of topological defects [2]. In a paper published in Physical Review Letters, Pavan Hosur and collaborators from the University of California, Berkeley, predict that these bound states are found in the vortices of the superconductor Cu_xBi₂Se₃ [3] (Fig. 1). Once discovered, a set of zero-dimensional Majorana bound states (MBS) are predicted to exhibit exotic non-Abelian statistics when exchanged among each other. While of great fundamental interest, perhaps the biggest driving factor in the search is a well-regarded proposal for (topological) quantum computation, which uses this unique statistical property of the MBS to robustly process quantum information free from local sources of decoherence [4, 5].

....

Naively, this eliminates all fermions at play in conventional electronic systems from being Majorana. The key to getting around this obstacle is noting that one finds many different emergent fermionic vacua/ground states in electronic systems that are qualitatively different from the fundamental vacuum of spacetime. To illustrate this, consider a BCS superconductor ground state filled with a condensate of paired electrons. If we again scatter two electrons off each other, they can indeed bind into a Cooper pair and “annihilate” into the fermionic vacuum! However, if the vacuum is of s-wave character, the most common superconducting ground state, then the two electrons bound into the Cooper pair must have opposite spin and are thus not Majorana (the antiparticle of an electron with spin up, in this case, is one with spin down). The solution to this problem is manifest: we must find a way to get around the spin-quantum number. Currently, there are two primary mechanisms to do this: (i) the superconducting vacuum can have spin-triplet pairing, which pairs electrons with the same spin or (ii) the superconductivity can exist in the presence of spin-orbit coupling or some other mechanism which will remove the spin conservation. Solution (i) is the paradigm for the first proposals of the existence of MBS as quasiparticles of a fractional quantum Hall state which models a two-dimensional electron gas at filling ν=5/2 [6], and as vortex excitations in some theories of the unconventional superconducting state of Sr₂RuO₄ [7]. These proposals offer real material candidates for finding MBS, but experiments in both of these systems require utmost care in sample production and measurement precision. To date, MBS excitations have not been clearly distinguished in either of these systems. Recently, solution (ii), which was first implemented by Fu and Kane in topological insulator/superconductor heterostructures [8], has been garnering attention due to more inherent practicality. This has been followed up nicely with further predictions of MBS in low-dimensional spin-orbit-coupled heterostructures in proximity to s-wave superconductors [9].

The seminal proposal of Fu and Kane predicts that if the surface of a three-dimensional topological insulator is proximity-coupled to an s-wave superconductor, then vortex lines in the superconductor will trap MBS where the lines intersect the topological insulator surface [8]. This proposal requires two main ingredients: (i) a topological insulator and (ii) an s-wave superconductor that can effectively proximity-couple to the surface of the topological insulator. Despite all of the recent publicity about the discovery of three-dimensional topological insulators [10], finding a suitable topological insulator for these experiments is still a difficult task. The reason being that, as of yet, there are no topological insulator materials that are completely insulating in the bulk, despite intense experimental programs dedicated to this task. The most commonly studied topological insulators are variations of either Bi₂Se₃ or Bi₂Te₃ , in which it has been difficult to tune the bulk to a completely insulating state [11]. Thus, while many experiments have confirmed the robust nature and structure of the surface states, these materials, having bulk carriers, are not true topological insulators.

It is then natural to ask, What is a doped topological insulator good for? While one hopes that many of the topological phenomena of the true insulating state might be manifested in some form in a doped system, many questions still remain unanswered. However, Hosur et al. have made a striking prediction that MBS can still be realized in doped topological insulators under certain mild conditions [3]. A true insulating state is important in the Fu-Kane proposal because if the bulk contains low-energy states then the MBS can tunnel away from the surface and delocalize into the bulk, which effectively destroys the MBS. Hosur et al. circumvent this delocalization by requiring that the entire doped topological insulator become superconducting. They show that as long as the doping is not too large, vortices in superconducting topological insulators will bind MBS at the places where the vortex lines intersect the material surfaces. While this might seem like a big leap in complexity, experimental evidence already shows that, indeed, copper-doped Bi₂Se₃ is a superconductor below 3.8 K [12]. In this context, Hosur et al. make a strong prediction that vortex lines in superconducting Cu_xBi₂Se₃ can harbor MBS.

To understand the prediction, we begin with the Fu-Kane proximity effect scenario, as mentioned above, with a vortex line stretched between two surfaces. MBS are trapped where each end of the vortex line meets the topological insulator surface (see Fig. 1). If we tune the bulk chemical potential to lie in the conduction band, as opposed to the nominal insulating gap, then the MBS on each end of the vortex line could tunnel through the bulk and hybridize with the state on the opposite end. This is prevented in Hosur et al.’s work by inducing a superconducting gap in the entire bulk so that the MBS remain trapped. If the superconducting state were homogeneous, then the MBS would be trapped on the ends of the vortex line for any doping level. However, the superconducting order parameter varies rapidly near the vortex core, which is essentially a thin tube of normal metal (doped topological insulator) containing bound states with energies that lie below the nominal superconducting gap. It is easiest for the MBS to tunnel through the “mini-gap” region in the vortex core, and in fact, Hosur et al. go on to show that there is a critical chemical potential level where a vortex-core bound state becomes gapless and the MBS can easily tunnel through the vortex line to annihilate. Beyond this critical doping, the vortex line re-enters a gapped phase, but the MBS are absent. See Fig. 1 for an illustration of this process. The critical chemical potential can be calculated solely from low-energy information about the Fermi surface, and depends on the orientation of the vortex line with respect to the crystal structure. It is estimated that vortex lines oriented along the c axis of Cu_xBi₂Se₃ are just on the trivial side of the transition, while vortices perpendicular to the c axis should be well within the nontrivial regime and should trap MBS.

Smectic Coexisting with nematic in cuprate

In the pseudogap phase of cuprate superconductors, incredibly rich and exotic things have been observed, among which are the checkerboard pattern that breaks the C4v symmetry within an unit cell and the stripes that break an additional translational symmetry. These are called electronic nematic and smectic phases, respectively. According to this study, there should be an interesting interplay between the two on cuprates, due to topological defects. The authors formalize the coupling in a gauge invariant way.

Coupling to the smectic fields can then occur either through phase or amplitude fluctuations of the smectic. Here, we focus on the former, which means that couples to local shifts of the wave vectors and . Replacing the gradient in the x direction by a covariant-derivative-like coupling gives(4)and similarly for the gradient in the y direction, to yield a GL term coupling the nematic to smectic states. The vector represents by how much the wave vector, , is shifted for a given fluctuation. Hence, we propose a GL functional (for modulations along ) based on symmetry principles and and being small:(5)where … refers to terms we can neglect for the present purpose (SOM d). If we were to replace by where is the electromagnetic vector potential, Eq. 5 becomes the GL free energy of a superconductor; its minimization in the long-distance limit yields and thus quantization of its associated magnetic flux (22, 23). Analogously, minimization of Eq. 5 implies surrounding each topological defect (SOM e). Here, the vector is proportional to and lies along the line where = 0. The resulting key prediction is that will vanish along the line in the direction of that passes through the core of the topological defect, with becoming greater on one side and less on the other (Fig. 4B). Additional coupling to the smectic amplitude can shift the location of the topological defect away from the line of = 0 (SOM e).

The mysterious Moire'- pattern-based electronic properties

Plenty of attention has been diverted to studying the bilayer graphene and hybrid structures consisting of patched mono-bi-layer graphene. A very fundamental problem in bi-layer graphene is how the electronic properties depend on the twisted angle. Theoretical study has been challenging. An interesting review in Nature on a recent PRL paper[http://www.nature.com/nature/journal/v474/n7352/full/474453a.html?WT.ec_id=NATURE-20110623#/references]:

In their study, Luican et al.⁴ find that, at small rotation angles, the local density of electronic states develops a dependence on position within the moiré-pattern unit cell and no longer exhibits the Dirac-like, decoupled-layer, Landau-level pattern. Layer coupling becomes strong in this sense for rotation angles less than about 2°, corresponding to moiré-pattern periods longer than about 10 nanometres. Here it is tempting to conjecture — from the spatial dependence of the density of electronic states — that bilayer wavefunctions have become localized, so that an STM measurement at one position reflects the stacking arrangement only at that position.
...
The extraordinary sensitivity of the electronic properties of few-layer graphene systems to the relative orientations of their layers could prove useful in various applications, for example in ultra-sensitive strain gauges, pressure sensors or ultra-thin capacitors. Further progress requires an improved understanding of both large and small rotation-angle limits, and also improved experimental control of rotation angles.

Closed Line Of dislocations in graphene

Defects are valuables in materials science. They are purported to generate novel physics in unexpected ways. Low dimensional systems are more prone to defects. In graphene, structural defects can exist in zero or one D, called point defect or line defect, respectively. A line defect can have tremendous impact upon the transport properties of graphene. Very common is the dislocations. In this new work[PHYSICAL REVIEW B 83, 195425 (2011)], closed line of dislocations were observed. They look like flowers. They are topologically different from open dislocations. What kind of effects can be expected on electronic properties ? Let's see.

Topological defects can affect the physical properties of graphene in unexpected ways. Harnessing their influence may lead to enhanced control of both material strength and electrical properties. Here we present a class of topological defects in graphene composed of a rotating sequence of dislocations that close on themselves,
forming grain boundary loops that either conserve the number of atoms in the hexagonal lattice or accommodate vacancy or interstitial reconstruction, while leaving no unsatisfied bonds. One grain boundary loop is observed as a “flower” pattern in scanning tunneling microscopy studies of epitaxial graphene grown on SiC(0001).We show that the flower defect has the lowest energy per dislocation core of any known topological defect in graphene, providing a natural explanation for its growth via the coalescence of mobile dislocations.

Cellular networks

Cellular networks are common in nature, such as seen in the cells, bubbles, and polycrystals. In all these problems, a central question is, how do the cell boundaries distribute in time in their geometric structures and textures ? A key phenomena is that, at large times, the evolution of the distribution ubiquitously leads to a steady state that follows Boltzman's law. Here is an attempt to address this problem. The approach is traditional and phenomenological.

Mesoscale experiment and simulation permit harvesting information about both geometric features and texture in polycrystals. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length [in two dimensions (2D)] or area (in 3D) of an interface with a given lattice misorientation and normal. During the growth process, an initially random distribution of boundary types reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, it is found that if the given energy density depends only
on lattice misorientation, then the steady-state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest nonrandom distributions, corresponding to independent trials with respect to the energy. In this paper, we derive an entropy-based theory that suggests that the evolution of the GBCD satisfies a Fokker-Planck equation, an equation whose stationary state is a Boltzmann distribution. Cellular structures coarsen according to a local evolution law, curvature-driven growth, and are limited by space-filling constraints. The interaction between the evolution law and the constraints is governed primarily by the force balance at triple junctions, the natural boundary condition associated with curvature-driven growth, and determines a dissipation relation. A simplified coarsening model is introduced that is driven by the boundary conditions and reflects the network level dissipation relation of the grain growth system. It resembles an ensemble of inertia-free spring-mass dash pots. Application is made of the recent characterization of Fokker-Planck kinetics as a gradient flow for a free energy in deriving the theory. The theory predicts the results of large-scale two-dimensional simulations and
is consistent with experiment. [PHYSICAL REVIEW B 83, 134117 (2011)]

Topological insulators reviewed

In Review Of Modern Physics this month, an article appears to cover the fundamentals and frontiers in the research in topological insulators, to which more information can be found in earlier blog entries. [REVIEWS OF MODERN PHYSICS, VOLUME 82, OCTOBER–DECEMBER 2010]

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum
Hall state. A three-dimensional 3D topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on HgTe/CdTe quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall
insulator. Experiments on Bi1−xSbx, Bi2Se3, Bi2Te3, and Sb2Te3 are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana
fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

Pinwheel magnetic structure

Solid black lines are magnetic exchange interactions with three different strengths. The ellipses show the main spin correlations of the pinwheel valence-bond solid state found by Matan and co-workers in Rb₂Cu₃SnF₁₂. Spin singlets form between spin pairs linked by the dominant exchange interactions.


[Nature Physics Volume:6 ,Pages:837–838 Year published: 2010]

Better surface Dirac states

Topological insulators are insulators that house gapless surface states. These states provide playground for a host of Dirac physics. Although a couple of such materials have been found, this newly examined one has some better features:

In summary, our ARPES experiment of TlBiSe2 has revealed three important aspects: First, the surface state Dirac cone is confirmed to be present at the Gamma point. Second, the Dirac cone is practically ideal, especially near the DP, and its velocity is larger than for Bi2Se3. Finally, according to both experiment and theory, there are no bulk continuum states that energetically overlap with the DP. This means that the scattering channel from the topological surface state to the bulk continuum is suppressed. Our experimental results favor the realization of the topological spin-polarized transport with high mobility and long spin lifetime in TlBiSe2. [PRL 105, 146801 (2010)]

Topological Insulators used to determine fundamental constants

Topological phenomena (TP) play crucial role in determining the precise values of fundamental constants such as elementary charge, Planck constant and speed of light. This is so because of the robustness of topological phenomena against local variation in samples and also weak disorder and interactions between particles. Some famous TP have already been in use to this end: the quanta of magnetic flux has been measured with circular superconducting devices; the electrical conductance has been measured with the help of quantum Hall effect. Recently, a new TP was discovered in materials now known as topological insulators (TI). These materials are characterized by their bulky band gap and gapless surface states that are topologically robust. Examples include Te-Bi type compounds. It is expected that, such TP may also be employed to improve the precision of measurement. This came to realization in a latest publication [PRL 105, 166803 (2010)]:

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant ¼ e2=@c. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.

Hysterisis loops and the motions of domians

A ferromagnet (or other like materials) exists usually in domains and their polarization makes a loop with varying external polling field. These domains reflect the microscopic symmetry of the systems. The formation of domains is due to long-range interactions, while the intra-domain texture is dominated by short-range behaviors, as expected by the definition. Without long range force, a single domain will be randomly selected, due to spontaneous symmetry breaking. Long range force then modifies this and result in richer structure, with all possible domains occurring conforming to the symmetry. Domains are separated by domain walls, which are usually very thin and allow the order parameter to change gradually from the value of one domain to that of another domain. Domains form randomly (usually think so), in the course of thermal fluctuations, but can be modified by applying external field. The behavior of domains is therefore history dependent. A very quantitative understanding of the dynamics of domains is not easy, especially in the presence of impurities and other factors. A recent study reveals more new aspects of this behavior: Phys. Rev. B 82, 104423 (2010).

Two-sentence review of topological insulators

Creativity comes when one finds something interesting where the situation seems rather normal or when one makes a breakthrough where the difficulty seems so considerable that no progress can be made. The discovery of topological insulators is surely of the former type. It is just a combination of two factors:
(1) band structure invariant under time reversal operation;
(2) surface states that exist and cross and expand the whole bulk band gap.

A good article is: Liang Fu and C.L.Kane, cond-mat/0611341

Electrons on the surface of topological insulators

Topological insulators are featured with massless surface states that are protected from impurity scattering. Electrons in such states move on the surface, which are usually curved. How would this curvature affect the motions ? This article [Phys. Rev. B 82, 085312 (Published August 12, 2010)] shows that, the electrons shall feel gravity-like force.

Electron scattering in solids is normally associated with impurities, defects, lattice vibrations, and electron-electron Coulomb scattering. Now, in an article published in Physical Review B, Jan Dahlhaus and collaborators from the Instituut-Lorentz at the University of Leiden in the Netherlands show that for surface electrons on a topological insulator, electron scattering can be dominated by a completely different mechanism: geodesic scattering. Geodesics are the generalization of straight lines in curved space. In general relativity, gravitational fields curve four-dimensional spacetime, and particle motion follows geodesic lines shaped by gravity. Strong enough fields cause the phenomenon known as gravitational lensing, an observable deflection of massless particles such as photons.

The surface electrons of a topological insulator behave as massless particles and are constrained to move in a two-dimensional curved space. The curvature is caused by random surface deformations that appear naturally during the growth of the material. Such a bump on the surface acts like a gravitational lens for surface electrons, resulting in trajectories that are analogous to geodesic motion. Considering that due to the special nature of topological insulators these surface electrons are protected from the ubiquitous impurity backscattering, this article likely reveals a previously unsuspected and important contribution to the resistivity on the surface of these materials. – Athanasios Chantis

Surface states

A latest fervent topic in condensed matter physics is the so-called topological insulators. An essential feature of these compounds is their having unique surface states. Surface states are states that decay into the vacuum as well as the bulk, thus qualitatively different from bulk states. These states always show up in the bulk forbidden gap, much the way as impurity states. In a sense they are indeed impurity states, because they are created by breaking periodic boundary conditions. Suppose you have a ring of N identical atoms. Now you break it, and you obtain two end atoms which have different surrounding than other bulk atoms. The breaking bond can be expressed as a perturbation, and thus leading to two impurity states. In history, they are called Shockley-Tamm states.

Introduction to surface states:
[1]http://philiphofmann.net/surflec3/surflec015.html
[2]http://en.wikipedia.org/wiki/Surface_states

Topological insulators and one of its creators

This is a talk by Mr. Zhang, on the pogress and history of topological insulators and its relation to other subjects in condensed matter physics.

Below is the link of this talk:

http://www.youtube.com/watch?v=Qg8Yu-Ju3Vw&NR=1

And Below is the link of an conversation with the talker:

http://www.youtube.com/watch?v=d5s6nZtPAHE&feature=related

Boundary matters: topological insulators

It has become a habit for those who profess in solid state physics to consider a crystal as a periodic array of atoms. In reality, this is, however only an approximation. Any solid is limited by its surfaces, which means the periodicity terminates at these bounds. Despite this, people still in most cases take them as infinite and unbounded, so that exact periodicity can be used to obtain exact solutions of some models. Usually, such solutions indeed provide very good descriptions of the sample, provided the bulk is dominant over the boundaries. One such artificial boundary condition goes under 'Von Karmen periodic condition', which yields Bloch waves.

Nevertheless, surface (not film, [1]) states can display many exotic properties that are not supported by bulky solutions. These properties may be related to, let's say, impurities, dangling bonds, surface tensions, structural reconstructions and et al. Due to these properties, modern computers could be made. As we know, transistors and diodes just make use of the properties of interfaces between two semiconductors.

Surface states have not ceased to surprise people. Some ten years ago, people found a novel type of conducting channels in two dimensional electron gas systems. Such systems under strong magnetic field exhibit the famous quantum Hall effects. It was later suggested that, such Hall states possess edge states that can conduct electricity along the edges of the 2D sample. These states are squeezed out of and split from the insulating bulk states, by magnetic field.

In 2005, Kane and his collaborators suggested that [2], such edge states could exist even without magnetic field. The considered graphene, namely a single graphite layer. In such materials, they guessed, there might be strong spin-orbit coupling. Such couplings can actually play a similar role as a magnetic field, and thus may create edge states. In this case, new complexity arises due to the spin degrees of freedom (see the figure).

All the as-described edge states are 1D objects. Most recently, a kind of 2D edge states was discovered existing in Bi2Te3 compounds. Such compounds have complex crystal structures and strong spin orbit coupling. These states are able to conduct spin and charges along the surface. So, one has this very gorgeous phenomenon: insulating bulk+metallic surface. They are termed 'topological insulators'. Why topology ? Topological properties are the properties that are invariant under continuous transformations of parameter space. In Bi2Te3, that is the number of edge states, which is conserved, however the shape of the sample is changed.

Although something has been learned of these new properties, a realistic and analytically tractable solution still awaits to show up. More experiments need be done to confirm and explore our understanding.

[1]A surface is linked with a bulk, but a film has its own bulk and surface (edges). Interface can be deemed as a special surface.
[2]PRL 95, 226801 (2005)

New surge in topological insulators

[1]PRL 105, 076801 (2010)
[2]PHYSICAL REVIEW B 82, 081305 R 2010
[3]Physics 3, 66 (2010)

The prediction [1] and experimental discovery [2, 3] of a class of materials known as topological insulators is a major recent event in the condensed matter physics community. Why do two- and three-dimensional topological insulators (such as HgTe/CdTe [2] and Bi2Se3 [3], respectively) attract so much interest? Thinking practically, these materials open a rich vista of possible applications and devices based on the unique interplay between spin and charge. More fundamentally,
there is much to enjoy from a physics point of view, including the aesthetic spin-resolved Fermi surface topology [3], the possibility of hosting Majorana fermions (a fermion that is its own antiparticle) in a solid-state system [4], and the intrinsic quantum spin Hall effect, which can be thought of as two copies of the quantum Hall effect for spin-up and spin-down electrons [5]. Now, an exciting new addition to the above list comes from two teams that are reporting the first experimental observation of quantized topological surface states forming Landau levels in the presence of a magnetic field. The two papers - one appearing in Physical Review Letters by Peng Cheng and colleagues at Tsinghua University in China, and collaborators in the US, the other, appearing as a Rapid Communication in Physical Review B, by Tetsuo Hanaguri at Japan’s RIKEN Advanced Science Institute in Wako and scientists at the Tokyo Institute of Technology - pave the way for seeing a quantum Hall effect in topological insulators.

Topological insulators: next gold rush ?

At this year’s APS meeting, however, the hallways were filled with talk of a promising newcomer— an eccentric class of materials known as topological insulators. The most striking characteristic of these insulators is that they conduct electricity only on their surfaces. The reasons are mathematically subtle — so much so that one physicist, Zahid Hasan of Princeton University in New Jersey, tried to explain the behaviour using ‘simpler’ concepts such as superstring theory. (“It’s awfully beautiful stuff,”
he said reassuringly.) Yet the implications are rich, ranging from practical technology for quantum computing to laboratory tests of advanced particle physics.

Skymion observed in magnets

There came a paper [1] reporting the observation of individual skymions.

Skymion is a topological texture of certain physical order parameter, such as magnetization. One interesting property of topological texture is its stability against local perturbations. Such stability does not imply being low in energy. Rather, it means a big barrier preventing its demise into other configurations. This barrier exists because, to destroy a topological object needs a global change, which could happen only at very insignificant probability. Any local change cannot get rid of it.

[1]X. Z. Yu,Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui1, N. Nagaosa & Y. Tokura, Vol 465| 17 June 2010| doi:10.1038/nature09124