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138 views

Problem with quantum Hall effect and Berry curvature

I am having trouble proving that the Hall conductivity is equal to the integral over the Berry curvature in momentum space. In the TKNN (1982) paper, using the Kubo formula $$ \sigma_{xy} = \frac{ ie^...
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82 views

Fractional quantum Hall effect [duplicate]

Can someone explain the fractional quantum Hall effect in layman's terms, I'm having some difficulty understanding it?
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101 views

Is the Hall coefficient a resistance?

The Hall coefficient is defined as this: $$R_H=\frac{E_y}{j_xB_z}.$$ Always as $R_H$. I am currious as to how to use this coefficient? Is it the y-direction resistance/resistivity (it is very close ...
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23 views

How to confirm experimentally the effect of momentum space Berry curvature in solids?

I'm studying spin-orbit coupling and Berry curvature effects, especially on the spin Hall effect. However, Table 3 in a review paper http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.87.1213 ...
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15 views

Measurement of Quantum Hall Effect

I'm somewhat confused about the original measurement of the QHE in a Si-MOSFET, which might stem from my not understanding MOSFETs very well. In their measurement, von Klitzing et al. measure the ...
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27 views

Quantum Hall effect in a Corbino disk

I'm a little bit confused about the Quantum Hall effect. I follow a course in condensed matter physics and the Quantum Hall effect is seen as the mother of all effects in condensed matter physics ...
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33 views

Simplify $K$-matrix

2+1D Abelian topologically ordered states are believed to be described by multicomponent $U(1)$ Chern-Simons theories, with Lagrangian \begin{equation} \mathcal{L}=\frac{K_{IJ}}{4\pi}\epsilon^{\mu\nu\...
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12 views

Temperature dependence of phase transition in Quantum Hall Effect

Most phase transitions have a distinct critical temperature, depending on the parameters of the system. For example, the critical temperature of Bose-Einstein condensation depends on the particle ...
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93 views

why Hall conductance quantized

When I am studying quantum Hall effect, the quantum Hall conductance can be represented by Green function $\left(\text{up to}\ \frac{e^2}{h}\large \right)$: I cannot understand why it is an integer? ...
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66 views

Elementary introduction to (quantum) hall effect

Where can I find an elementary introduction to classical and quantum hall effect? Only physics I know is some basic quantum mechanics, EM and statistical physics. My goal eventually is to understand ...
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73 views

How do the compressible strips carry current in Quantum Hall effect?

I would be very grateful if anyone can answer this question on Quantum Hall effect According to most papers I have gone through, states at the fermi energy actually carry the current. The width of the ...
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1answer
91 views

Landau level for quadratic band touching in Dirac Hamiltonian

I wonder if there is anyone or any references that have solved the Landau level spectrum and eigenstates with respect to the following Hamiltonian: \begin{equation} H=\frac{k_x^2-k_y^2}{m}\sigma_x+\...
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55 views

incompressibility of fully filled Landau level

Suppose Landau level degeneracy is $10^9$, if we force to put ($10^9+1$) particles on the level, what extra energy will we gain? (ignore particles interactions) Like electron degeneracy pressure, ...
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67 views

Why is there longitudinal conductance in a partially-filled Landau level?

Suppose I consider an infinite, non-interacting (so no FQHE should happen) 2DEG in the magnetic field $\vec B=B\hat z$ with a non-integer filling factor, say 0.13 or whatever. Suppose I apply an ...
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1answer
60 views

How to implement the form of current density in a Hall Effect related calculation?

Please consider the following; Question. A rectangular plate of semiconducting material has dimensions 10mm x 4mm x 1mm. A current of 3 mA flows along the length and a Hall Voltage of 13.6 mV is ...
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228 views

Hall Effect p-type Germanium holes density

I had to do some experiments with a Hall Effect Apparatus of Leybolds with a p-doped Germanium plate, this is the datasheet (pdf). eq. (1) $U_H=R_H \frac{IB}{d}$ $U_H$ = Hall voltage $R_H$ = Hall ...