Topological Definition and 250 Threads

I would like to find the crystal structure of (Pb0.5Sn0.5)Te I was told it is similar to NaCl basically an XY crystal I think it is called Space Group: 225 I would like to know the first, second, third ...layer of atoms closest to a X atom...and perhaps their distance... I found...

Hi all My question: I have read: Topological Insulators: Dirac Equation in Condensed Matters But also I have read: Observation of a Discrete Time Crystal Is it different situations ?

Let ##(V, ||\cdot||)## be some finite-dimensional vector space over field ##\mathbb{F}## with ##\dim V = n##. Endowing this vector space with the metric topology, where the metric is induced by the norm, will ##V## become a topological vector space? It seems that this might be true, given that...

I went to an applied phd program in computational biology and got bored, so now I'm considering physics. Topological matter looks fancy/sort of interesting. Does it have anything to do with actual experiments (and I mean more than just insulators/superconductors) yet? I would assume that to...

I am reading "An Introduction to Differential Topology" by Dennis Barden and Charles Thomas ... I am focussed on Chapter 1: Differential Manifolds and Differentiable Maps ... I need some help and clarification on an apparently simple notational issue regarding the definition of a chart...

I have been learning topological insulators recently, and I become more and more curious about the link between topological insulators and mathematical theory these days. I know topological insulators have something to do with fiber bundles and K-theory. I have a relatively good background of...

Is there a topologist out there that wants to explain why exactly a branched line in R2 is not not a topological manifold? I know it's because there doesn't exist a chart at the point of branching, but I don't understand why not. I'm just starting to self study this, so go easy on me :).

Hello. Is there a review paper about topological insulator which is written for non-physics major people? If it will be helpful, I know classical physics, basics about band theory and little bit of modern physics, and have just finished learning quantum mechanics (with a book written by...

Hi every one, I face with a question on my works, As you know there in many articles Physicist introduce a material that has zero gap without spin-orbit coupling (SOC). By applying the SOC, a relatively small gap (0.1 eV) is opened and it becomes topological insulator. My question, Is that...

As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...

I've been checking a university's descriptions of its research groups and their interests, where I encountered the phrase "Topological effects in Particle Physics" which had no explanation. I searched in the internet, but I couldn't find anything. Could anyone explain about such effects and...

In chapter 2.3 in Nakahara's book, Geometry, Topology and Physics, the following definition of a topological space is given. Let X be any set and T=\{U_i | i \in I\} denote a certain collection of subsets of X. The pair (X,T) is a topological space if T satisfies the following requirements 1.)...

I know the solution for R2. That is a for an infinite plane you can have one of 2 things (from the classification of 2D surfaces): 1) cross cap (cut a circle out of the plane and identify opposite points). 2) a oriented handle (cut two circles out and identify points on one with reflected...

I have just been reading a classical paper on the formation of majorana edge states (MES) in quantum wires. The hamiltonian is Kitaev type with a superconducting and spin-orbit interacting and one finds that the energies have a gap that closes and reopens as we vary the magnetic field. According...

Hi every body, I faced a paradox. The topological insulator is robust against a potential that does not breaks the TRS. But in the original work of Kane-Mele (PRL 95, 146802), the "staggered sublattice potential" that does not breaks the TRS,, makes zigzag ribbon trivial insulator (figure 1 in...

Hello! (Wave) The topological sort of a graph can be considered as an order of its nodes along a horizontal line so that all the directed edges go from the left to the right. How could we show that all the directed edges go fom the left to the right? We suppose that it is: Then it holds...

I was wondering, how does a photon look like? What does it look like? I'm taking modern physics at the moment and I'm able to calculate lots of things quite well. Like DeBroglie wavelengths, I'm able to utilize the Schrodinger equation and the Heisenberg uncertainty principle and what not but I...

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal representation of the universe: "Neither does the theory of relativity, Bohr argued, provide us...

The extended plane (E2 U ∞) is a non-orientable surface, and yet topologically is a sphere which is orientable, can someone comment on how this is reconciled?

Homework Statement . Let ##X## be a topological space and let ##A,B \subset X##. Then (1) ##A \cap \overline{B} \subset \overline{A \cap B}## when ##A## is open (2) ##\overline{A} \setminus \overline{B} \subset \overline {A \setminus B}##. The attempt at a solution. In (1), using...

why the topological term in gauge theory, ε_{\mu\nu ρσ}F^{\mu \nu} F^{ρσ} ,is scale-independent?

Homework Statement Let ##X## be a topological space. Let ##A_1 \supseteq A_2 \supseteq A_3...## be a sequence of closed subsets of ##X##. Suppose that ##a_i \in Ai## for all ##i## and that ##a_i \rightarrow b##. Prove that ##b \in \cap A_i##. Homework Equations The Attempt at a Solution...

Hi All, This is a question on ergodic theory - not quite analysis, but as close as you can get to it, so I decided to post it here. Suppose I have a compact metric space $X$, with $([0,1], B, \mu)$ a probability space, with $B$ a (Borel) sigma algebra, and $\mu$ the probability measure...

Hello! I'm trying to teach myself some mathematics, and I want to see if I understand this concept correctly from what I've been reading. (And just to be clear, this isn't part of any coursework, so I assume it doesn't go under that section for that reason?) So, essentially, although...

In the definition of smooth manifolds we require that the transition functions between different charts be infinitely differentiable (a circle is an example of such a manifold). Topological manifolds, however, does not require transitions functions to be smooth (or rather no transition functions...

I understand that the centring of the Fermi energy at the Dirac point is a highly sought after property in Topological Insulators but I'm unsure as to exactly why? I see that the state at the conical intercept will be unique but I'm not sure of what is theorized to happen to the electrons...

The usual definition of an n-dimensional topological manifold M is a topological space which is 'locally Euclidean', by which we mean that: (1) every point in M is contained in an open set which is homeomorphic to ##\mathbb{R}^n##. (2) M is second countable. (3) M is an Hausdorff space...

In set theory a set is defined to be a collection of distinct objects (see http://en.wikipedia.org/wiki/Set_%28mathematics%29), i.e. we must have some way of distinguishing anyone element from a set, from any other element. Now a topological space is defined as a set X together with a...

Can anyone suggest any? I have all of the coursework for a PhD, So I'm not afraid of anything but I will have lots of questions.

Homework Statement Find a topological conjugation between g(x) and T(x) where g and T are mappings (both tent maps [graphically speaking]) Homework Equationsg:[-1, 1] → [-1,1] g(x) = 1-2|x| T:[0,1] → [0, 1] T(x) = 2x when x ≤ 1/2 and 2(1-x) when x ≥ 1/2 h ° T = g ° h (homeomorphism)The...

Homework Statement is it possible to have a topological space that is neither the indiscrete nor the discrete, and very set in the topology is clopen? Homework Equations The Attempt at a Solution let ##X## = {(0,1),(2,3)} with the ordinary topology on R. (0,1) is open, but...

Homework Statement Consider (R,C). Prove that a sequence converges in this topological space iff it is bounded below define ##C = ## ##\left \{ (a,\infty)|a\in R \right \} \bigcup \left \{ \oslash , R \right \}## Homework Equations The Attempt at a Solution So I am not very...

Isnt it invariant an adjective?

If X is a locally compact Haussorff space, then the set of continuous functions of compact support form a normal vector space C_c(X) with the supremum norm, and the completion of this space is the space C_0(X) of functions vanishing at infinity, i.e. the space of functions f such that f can be...

So, I have a topological group ##G##. This means that the functions m:G\times G\rightarrow G:(x,y)\rightarrow xy and i:G\rightarrow G:x\rightarrow x^{-1} are continuous. I have a couple of questions that seem mysterious to me. Let's start with this: I've seen a statement...

The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in the same fashion for a 3D TI). I can follow the argument up to defining the Chern parity $\nu$...

to get a 2D mercury telluride topological insulator, one has to construct a quantum well structure to get a bulk gap and most people use sandwiched structure with mercury cadmium telluride on top and the bottom. (so CdTe/HgTe/CdTe) and my question is can we get same or similar quantum...

Hi, I have a simple question: What is a Topological Action?

Hi, I am not a mathematician, but I have noticed some recent papers on this seemingly new field, called Topological Data Analysis (see this relevant paper). I have had an overview of the applications and it seems that when you have data points that were sampled from some source (e.g. an...

Determine the interior, boujdary, and closure for the set: { 1/n : n is in the positive integers Z}. Attempt: two things bothering me. 1) if i am in the set of positive integers, how does 1/n even exist? 2) now let's say it does exist, then the inteior would be empty because every...

Let X be a metric separable metric and zero dimensional space.Then X is homeomorphic to a subset of Cantor set. How can it be proved? Thank's a lot, Hedi

Hi I have been searching some papers online to find how practically we can approach for the fabrication of topological insulators. Can somebody please help me regarding this by providing some web links or some insight on the fabrication of topolopgical insulators...

Say we have a disconnected manifold with components C1, C2, C3. (I know in the threat title I said just topological space, but I'm actually thinking of manifolds here, sorry! Not sure how to change the title) It makes intuitive sense that if we're looking at just one of the components, then...

Author: John M. Lee Title: Introduction to Topological Manifolds Amazon Link: https://www.amazon.com/dp/1441979395/?tag=pfamazon01-20 Prerequisities: Real Analysis course involving epsilon-delta and preferebly metric spaces, group theory Level: Grad students Table of Contents: Preface...

Hi, I have a problem understanding something This is a snapshot of a book I am reading Point no. 2 concerns me, because it looks to me like it contradicts itself, with "this or this" The first part says \sum_{j}V_j = \mathbb{L^2(R)} which, to me, looks completely equivavalent...

Homework Statement Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. Homework Equations I have no idea. The Attempt at a Solution I seriously have no idea. This is for my analysis course, and I'm not...

In trying to get the Aharonov-effect right I've found something that I'm not sure how to sort out. Briefly put my understanding of the effect is that it shows something that cannot be explained by classical physics in the sense that makes observable a classical EM global gauge transformation...

Hello, I've found in some of the articles on experimental quantum physics the term "Topological cross section" Now I'm trying to understand what is it and in particular what the difference between topological and differential cross section? Thanks in advance for suggestions on any reading...

Hi I am studying how the spin orbit interaction in certain materials can lead to topological insulator effects and realize it has something to do with the effects of the SOC on the band structure of the material (Bi2Se3), possibly due to the inversion of the valence and conduction band but I...

It would be helpful if someone could please explain topological equivalence of functions in simple words? I am working on dynamical systems and chaos theory.In the underlying material,topological equivalence has taken a more complex definition involving orbits.Please be kind enough to explain...