Questions tagged [quantum-hall-effect]

Questions related to the quantum Hall effect (the quantisation of resistivity observed when a 2-dimensional electron gas system is subjected to a strong perpendicular magnetic field), as well as formulations of states, topological properties, and applications.

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What makes a topological insulator topological?

I understand that a topological insulator is one with an insulating bulk and conducting surface but I don't understand why or how the topological part comes into it. All of the resources I've found ...
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Localized and extended states in Landau levels due to disorder in Integer Quantum Hall Effect

In the presence of a random potential due to the presence of disorder, the degenerate Landau levels split into a band. It is given that the states in the middle of this band are extended and the ones ...
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Jump to next landau level

According to Landau quantization, the degeneracy of Landau level is approximately $n=\frac{B}{\Phi_0}$, where $\Phi_0$ is fundamental quantum of flux. My question is, as $B$ decreases, why rather ...
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Why do we go beyond two-body interaction?

Actually, my question is why do we study many-body interactions. I have just started working in Fractional quantum Hall systems. There we have Coulomb interactions between electrons, which we know is ...
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Composite Fermion Approach to Quantum Hall

I am following David Tong's notes on the Quantum Hall Effect (https://arxiv.org/abs/1606.06687). One of the approaches he takes to the FQHE is the composite fermion approach (Section 3.3.2). There are ...
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Deriving classical Hall effect from quantum Hall effect

I'm interested in the derivation of the classical Hall effect coefficient, given in cgs by $$R_{H}=-\frac{1}{nec},$$ where $n$ is the electron number density, $-e<0$ is the electron charge,and $c$ ...
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How to connect Maxwell's equations to quantum anomalous Hall effect?

The quantum anomalous Hall effect (QAHE) describes the response of a material resulting from topological properties of its band structure. These topological properties are often characterized by the ...
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Quantum Hall Effect: Why the spikes of the longitudinal resistance appear every time when Hall conductance jumps?

[ Let's focus on the longitudinal resistance, I have two confusions: Why it shows spike like feature every time the hall conductance jumps? Why its amplitude grows when the magnetic field grows? ...
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Literature Anyons [duplicate]

In a few months I have to give a talk about Identical Particles in Quantum Physics, which should answer the following questions or explain following concepts: Why are there only Fermions and Bosons ...
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Can we define Spin-Chern number for original QAHE Haldane model?

In Haldane's original paper [5], he discusses the quantum anomalous Hall effect as being characterized by the so-called Chern number that is the surface integral of Berry curvature over the entire ...
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Gapping out edge modes by backscattering

I was reading this paper by Michael Levin about protected edge states without symmetry. In the introduction, he makes the argument that backscattering terms or other perturbations gap out left and ...
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Quantization of Chiral Boson

I am trying to understand the edge modes of fractional quantum Hall(FQH) effect from ChernSmions theory picture. Chern-Simons action with a boundary along $y$ produces the following action $ \...
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What is the analog of quantifiable magnetic field in condensed matter systems?

What is the analog of the magnetic flux density B, which is an observable and quantifiable quantity (i.e. $|B|$ can be defined in Teslas), in the anomalous QHE? For instance in the Haldane model? In ...
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Statistics of a quasiparticle

I was trying to understand the Chern-Simons theory description of the fractional quantum Hall effect. I was trying to follow this article. After integrating out Lagrangian the mutual statistics of two ...
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Is there any instance when a current in Hall effect passes in the vertical direction?

In Hall effect when a magnetic field is applied in transverse direction (z) in sample (conductor/semiconductor) a vertical (y) voltage is developed, because some charges are deflected from the ...
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How to interpret Berry curvature in 2-band model?

While studying the 2-band Haldane model, I realized that I am missing an intuitive picture of how Berry curvature comes into play, especially when considering an adiabatic loop. A 2-band model has 2 ...
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Do Chern Insulators (QAHE) have topological order (long-range quantum entanglement)?

I know IQHE is a example having "invertible" topological order from Professor Wen's definition. And Topological Insulators is SRE because of necessary of underlying symmetry protection. After that, ...
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Landau level in particular cases

If we consider an array of identical uncoupled spinless non-interacting one-dimensional wires, as shown in Fig.(a) with a single-particle electronic dispersion E(k), which we can take to be parabolic ...
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Integer quantum Hall conductance and time-reversal symmetry

If we have a (2+1)-dimensional electronic gapped system with a unique ground state and it has a nonzero integer quantum Hall conductance, then the system (or its ground state) must break the time-...
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What exactly is “Landau level mixing” and how does it change the Hamiltonian?

I've read of Landau level mixing ("LL-mixing") in several papers, e.g. this one which in its supplementary information accounts for LL-mixing through the random-phase approximation, but I've yet to ...
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Magnetic flux changed by gauge transformation

This occurred to me when I was reviewing the Laughlin argument. Suppose a gauge transformation $A\rightarrow A+\nabla{\theta}$, where $\theta$ is the angle defined in a closed loop. When integrating ...
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Why do we consider spin degeneracy in graphene quantum hall effect and not in the conventional one?

When dealing with quantum hall effect in graphene we say that each landau level (with $n\neq 0$) has 4 times the degeneracy of a simple landau level derived for an electron in a magnetic field because ...
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How to Explicitly Calculate z-Component of Berry Curvature?

While numerically playing with the 2-level Haldane model recently, I wondered how I could analytically calculate the z-component of the Berry curvature $F$. I framed my problem as needing an ...
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Effective theory of hierarchial fractional quantum hall state

In describing the effective field theory picture of the hierarchical fractional quantum Hall states in Tong's lecture notes, page 165 he gives the expression for filling fraction, quasi-particle ...
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Why is the composite fermion not included in the anyon contents of FQH topological orders?

For example, both the $\nu=1/3$ Laughlin state and the Moore-Read state has a simple interpretation in terms of composite fermions, which are bound states of an electron and two fluxes. Both the ...
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Is the quantum Hall state a topological insulating state?

I am confused about the quantum Hall state and topological insulating states. Following are the points (according to my naive understanding of this field) which confuse me: Topological insulator has ...
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Circumstances that might happen in Hall-effect experiment

In Hall-effect experiment, is it possible that no transverse potential difference will be observed? Under what circumstances might this happen?
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Source Berry Curvature Chern Insulator

Why is there non-zero hall conductance for a Chern insulator? From section 2.3 of Bernevigs book 'Topological insulators and topological superconductors' I learned one can view degeneracies are ...
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Configuration space of identical particles - fractional statistics

In Khare's book of fractional statistics and quantum theory, when discussing why we need fractional statistics he arrives at the configuration space for a system of two identical particles in $d$ ...
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IQHE, quantized conductance, and zeeman splitting

I've been trying to understand IQHE by reading these lecture notes by David Tong. Mainly, I was trying to understand the quantized hall resistivity in terms of the number of Landau levels crossing ...
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filling factor, landau fan, and landau index

In the paper here, there is a plot of $R_{xx}$ as a function of magnetic field $B_{⊥}$ and carrier density, $n$. The filling factor jumps by 4 between adjacent lines. The set of lines where $R_{...
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1answer
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Laughlin state energy gap

I've been reading Girvin's lecture notes on quantum hall effect and in a section on Haldane pseudo-potentials (paragraphs beneath equation 1.108) he says: Because the relative angular momentum of a ...
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What is the closed-loop line integral of Berry curvature in a two-level model?

I am aware that integrating the Berry curvature over the entire Brillouin zone gives us the Chern number. However, I wonder what a closed loop line integral of the Berry curvature means. I think ...
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Visualizing k-space tori in 3D

In many introductions to topological insulators (in the exposition of Haldane’s model, for example), we represent the parameter space, a torus, on a plane with axes running from $0$ to $2\pi$. In an ...
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What is the physical significance of Gaussian curvature in condensed matter physics?

In basic models concerning two-level systems, we deal with manifolds such as the Bloch sphere and torus. I believe that the Chern number is what dominates the theory in terms of ties to differential ...
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How does Laughlin argument for hierarchical fractional quantum Hall effect work?

For 1 level and 1 layer $1/q$ FQHE let's say $q=5$ we have the following argument for Laughlin gauge principle. It says that if we adiabatically increase the flux from $0$ to $q\phi_0$ of a corbino ...
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Understanding the fractional quantum Hall effect in Chern-Simons formalism described in Wen's book

So I study fractional quantum hall effect with Chern-Simons formalism by using Wen's book, this is an excellent book, but it assumes that you know field theory very well thus it has gaps between steps....
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Why does the Hall Coefficient not hold for certain metals?

We know metals have electrons as their main charge carriers, so we can arrive at the conclusion that $R_H$ is negative. $R_H=\frac{1}{q n}$, where $q$ is the charge of carriers, which is negative for ...
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Help me understand a little bit about this abstract

I was reading a story on phys.org: Holographic image of a black hole proposed in a graphene flake (Lisa Zyga, 25 July 2018, phys.org) From there I followed a link to the paper Quantum ...
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Scalar product on the space of conformal blocks

Conformal blocks are extensively used as trial wave functions in the Quantum Hall Effect. The interpretation as wavefunctions implies that there is a scalar product on the space of relevant conformal ...
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Relationship between electronic current and electron momentum?

I remembered when reading Laughlin's famous argument for quantum Hall, it implied the actual current should be proportional to the electron's mechanical momentum ($p-eA/c$) instead of $p$ itself. Why ...
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What does negative filling mean for Landau levels?

I'm trying to read this paper, but I've never heard of Landau levels like $\nu=-1.$ What does it mean?
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Why does spin-orbit coupling lead to a nonzero Berry curvature?

Many theories consider spin orbit coupling to be a prerequisite for a nonzero Berry curvature, and therefore, for the classical anomalous Hall effect. Here, the spin orbit coupling is defined as: $$ ...
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Rigorous Laughlin pumping argument

Is there a way to justify formally the Laughlin pumping argument? It is often argued that the spectral flow of Landau levels while varying the flux inserted through the Corbino ring should account for ...
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Finding the generated magnetic field of a Hall generator

I've been using a Hall generator to generate a particular magnetic field by applying a current. I need to work out what field this corresponds to in Tesla. All I have to go on is what's in the photo ...
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Topologically proctected twist in the wave function (TKNN invariant)

In the famous TKNN paper and subsequents the authors wisely argue that the transversal conductance in the Integer Quantum Hall Effect has a topological interpretation as the integral of the curvature ...
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Proving that the Berry curvature is always zero

If we have an energy eigenstate $|\psi(\boldsymbol \lambda )\rangle$ which is a function of some external parameter $\boldsymbol \lambda = (a,b)$, then the associated Berry connection is defined to be ...
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Electron positions in the lowest Landau level

In the lowest Landau level, the position operators $\hat{x}$ and $\hat{y}$ do not commute. So in writing e.g. the Laughlin wave function $\Psi\left(z_1,...z_N\right) = \prod_{i<j} \left(z_i -z_j\...
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What are the implications that the Hamiltonian of a material lacks time reversal symmetry?

When reading about topological insulators and the quantum Hall effect, I've read that some Hamiltonians of the crystal structure representing the "materials" lack time reversal symmetry. My question ...
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Boundary Conditions giving Gauge Transformation a Physical Meaning?

I am currently reading Robert Laughlin's Nobel lecture. In the part where he uses gauge invariance to explain integer quantization of the Hall conductivity, he has a 2D rectangular surface which is ...