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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Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero?

Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero? I am puzzled about it. What's the physics meaning of it?
Yuan Fang
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Why average over fluxes when calculating Hall conductivity?

I am following David Tong's lecture notes on the quantum Hall effect and am confused by his derivation on page 60, where he shows a connection between the Hall conductivity and the Chern number. What is the motivation for and/or physical meaning of…
LSchoon
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why does Laughlin wave function have a relative angular momentum no less than n

The textbooks say, the relative angular momentum of any two particles i and j should be no less than n, n is the power of (zi-zj)^n in the equation below I don't see this is an obvious argument. Can anybody clarify why? Also, which one is a better…
Jian
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Why do I have spin splitting at 5 and 7 at the quantum hall effect?

I just learned something about the quantum hall effect, and was wondering about the spin splitting at a filling factor of 5 and 7, i.e. I have nearly equal sized plateaus for the filling factor of 2, 3 and 4, but I have only a small plateau at 5,…
arc_lupus
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What is the difference between hierarchy picture and composite Fermion in explaining FQHE

Are they equivalent? I came up this question because they both explain states beyond Loughlin state.
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Hall conductivity and edge response

The hall conductivity $\sigma_{xy}$ seems to reflect to some extent the response of a system in direction $\hat{y}$ to certain perturbation (electric field for example) restricted in $\hat{x}$ direction. My question is, does a nonzero…
lenowen
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Why the physical meaning of quantum hall effect is important?

I have read some paper about transport measurement of graphene. From classical hall effect, we can get some information about kind of charge carrier, charge density etc. So, it is important for understanding matter. But, I don't know why quantum…
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About Laughlin's argument in IQHE

If Laughlin's argument for IQHE is a non-interacting picture, then why it still works? Besides, what is the relation between Laughlin and Halperin's approach and TKNN (also the later work by Niu and Thouless)?
Kite.Y
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Laughlin's Gauge Argument and Quantum Spin Hall Effect

I'm reading C.L. Kane and E.J. Mele's original paper of QSHE(DOI:https://doi.org/10.1103/PhysRevLett.95.226801). When proving the existence of edge state, they use the Laughlin's gauge argument which I am familiar with. However, they also say that…
Xzy
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Current in linear combination of landau levels

I’m working through Girvin’s Quantum Hall Effect notes (https://arxiv.org/abs/cond-mat/9907002) And I came across the following problem: It is interesting to note that the exact eigenstates in the presence of the electric field can be viewed as…
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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 two things I am struggling with. First of all he…
YankyL
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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 $R_{xx}= 0$ seems to be defined as 'Landau…
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Quantum Hall Effect, Shubnikov de Haas oscillations

I have done a measurement at a HgTe 2DEG. I have measured nice plateaus in Rxy and Shubnikov de Haas Oscillations in Rxx. In the B field range between 1 and 3 Tesla I see some variation in the Shubnikov de Haas oscillations compared to bigger…
Leonard
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Why is the $1/3$ Fractional Quantum Hall Effect the most robust?

As far as I know, the $1/3$ plateau is the most wide one, and the $1/5$ plateau is ok, while the $1/7$ filling does not correspond to a well-developed plateau. So, why is the $1/3$ plateau the most robust one?
J.Bates
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Pair correlation function for a inhomogeneous Laughlin droplet

Pair correlation function for the usual Laughlin droplet is defined as $g(\vec{r})$: $$\rho_0 g(\vec{r})=\frac{1}{N}\langle\sum_i^N \sum_{j \neq i}^N \delta(\vec{r}-\vec{r_i}+\vec{r_j})\rangle$$, where $\rho_0=\frac{\nu}{2\pi l_0^2}$. So if now the…
huyichen
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