What is Quantum hall effect: Definition and 30 Discussions

The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect and which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values at certain level














{\displaystyle R_{xy}={\frac {V_{\text{Hall}}}{I_{\text{channel}}}}={\frac {h}{e^{2}\nu }},}
where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,...) values. Here, ν is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively.
The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization).The fractional quantum Hall effect is more complicated, its existence relies fundamentally on electron–electron interactions. The fractional quantum Hall effect is also understood as an integer quantum Hall effect, although not of electrons but of charge-flux composites known as composite fermions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.

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  1. T

    I Hall Conductivity and Rotational Invariance

    I am reading up on QHE from: https://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf and am confused about the comment: "The action (5.5) has no Hall conductivity because this is ruled out in d = 3+1 dimensions on rotational grounds." Can someone explain why this is the case? My only guess is that...
  2. C

    A Is the Fractional Quantum Hall Effect an emergent property?

    I do not think that true emergent properties -- as defined by behavior of matter that cannot be reduced to fundamental physical law -- exist. Yet I have been told that the Fractional Quantum Hall Effect is an example of an emergent property. What is the consensus?
  3. C

    A Quantum Hall Effect Basics: Topological Insulator & Semi-Metal

    I need them short. I need them so I can understand the basics of topological insulator and semi-metal.
  4. Mr_Allod

    Edge States in Integer Quantum Hall Effect (IQHE)

    Hello there, I am having trouble understanding what parts b-d of the question are asking. By solving the Schrodinger equation I got the following for the Landau Level energies: $$E_{n,k} = \hbar \omega_H(n+\frac 12)+\frac {\hbar^2k^2}{2m}\frac{\omega^2}{\omega_H^2}$$ Where ##\omega_H =...
  5. binbagsss

    Does the quantum Hall effect come under the category condensed matter?

    Title? Thanks. I think it does since these do : - Quasi particles - Collective behaviour of particles - Phase transitions Any others?
  6. J

    A Edge state question for a 2-D material and the quantum Hall effect

    I have read some materials about quantum hall effect and know that at the edge of a 2D material , one can linearize the potential V and the linear dispersion relation represents right/left moving fermion. So , Can I say that for a given hamiltonian , if I can linearizae it at edge, then this...
  7. binbagsss

    A E-writing Action on a different slice of space-time, Quantum Hall Effect

    Hi, I'm looking at QHE notes D.Tong and wondering how he gets from equation 5.46 to 5.48 ( http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf ) ##S_{CS}=\frac{k}{4\pi}\int d^3 x \epsilon^{\mu \nu \rho} tr(a_{\mu}\partial_{\nu}a_{\rho} -\frac{2i}{3}a_{\mu}a_{\nu}a_{\rho})##. manifold ## \bf{R}...
  8. binbagsss

    A Fractional Quantum Hall Effect- degeneracy of ground state (Tong's notes)

    Hi , I'm looking at the argument in David Tongs notes (http://www.damtp.cam.ac.uk/user/tong/qhe/three.pdf) for ground state degeneracy on depending on the topology of the manifold (page 97, section 3.2.4). I follow up to getting equation 3.31 but I'm stuck on the comment after : ' But such an...
  9. hideelo

    Composite Fermion Approach to FQHE

    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 says that a vortex is something around which...
  10. J

    How to find von-Klitzing constant based on graph?

    Hi all, Given that the question: From what i know , I am not sure how this equation can help me estimate the von-klitzing constant? Or is there another way? Thanks!
  11. J

    Solid State Books on the Integer Quantum Hall effect

    Hi, does anybody know of any good sources to learn about the Integer Quantum Hall effect from the perspective of theoretical physics? Any suggestion will be appreciated, thanks.
  12. J

    Solid State Books: Weyl semimetals, Topological Insulators

    Hello! What are some good sources(preferably textbooks) to learn about Weyl semimetals? I also want some sources to learn about topological insulators and anything containing the Integer Quantum Hall effect would be great. As an aside, if you have any good book on theoretical condensed matter...
  13. L

    A Can I find a smooth vector field on the patches of a torus?

    I am looks at problems that use the line integrals ##\frac{i}{{2\pi }}\oint_C A ## over a closed loop to evaluate the Chern number ##\frac{i}{{2\pi }}\int_T F ## of a U(1) bundle on a torus . I am looking at two literatures, in the first one the torus is divided like this then the Chern number...
  14. E

    I Longitudinal resistivity in Integer Quantum Hall Effect

    I have studied the integer quantum hall effect mainly from David Tong's notes and i understand how the ## \rho_{xy}## is quantized in terms of the chern number. What I don't understand is - how the chern numbers relate to the number of filled Landau levels though. - I also don't understand the...
  15. L

    A A question about linear response and conductivity

    I am trying to derive the DC electrical conductivity using the pertubation theory in Interaction picture and linear response theory. If working in a energy eigen basis and using the density matrix, the Fourier transform of the susceptibility can be written as ##\chi {(\omega )_{ij}} =...
  16. P

    A Understanding Orbital Angular Momentum Coupling to Christoffel Connection

    I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953 They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...
  17. S

    A Why the physical meaning of the 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 hall effect is important in graphene transport...
  18. VishalSharma

    I Harper-Hofstader Model: Butterfly & Landau Levels Relationship

    How are Hofstader's Butterfly and Landau Levels in 2-Dimesnions related to each other, if at all ?
  19. C

    Independent study for lab work

    Hi everybody, I'm a second semester physics major who was fortunate enough to get a position in a research group at my school. What I want to do is get a head start on learning the physics that this lab studies. Currently, I'm in the honors section of basic E & M and I do well in class, not...
  20. Benevito

    Current and Quantum Hall Effect

    Why does the presence of an energy gap in QHE guarantee dissipationless current flow?
  21. R

    Quantum Hall Effect resistivity

    I'm having trouble understanding why the resistivity behaves as it does in comparison to the density of states for the quantum hall effect. Take the following two diagrams: (A) (B) I understand that there can be no scattering in (A) because all states are full (i.e. no elastic) and the gap is...
  22. C

    Quantum Hall Effect: Hamiltonian & Finding Solutions

    Hi , I need a good book or lecture on quantum hall effect. my supervisor wants me to find the Hamiltonian for the Qunatum hall effect, he want me to find this from this relation if it looks like a 2nd order differential of harmonic oscillation. can you please guide me doing this? $$H=...
  23. F

    What Causes the Plateaus and Zeros in the Quantum Hall Effect?

    Hi! I'm having trouble understanding the quantum hall effect, that is, the fact that the Hall resistance versus magnetic field curve has regions where it drops to zero, and the longitudinal resistance versus magnetic field curve features plateaus. When the filling factor is an integer, this...
  24. A

    Diophantine equation in the integer quantum hall effect

    Hi everybody! I'm studying the IQHE and I want to understand the rise of the diophantine equation. I read the thouless article but it was no so conclusive. I've also read the kohmoto article (phys rev B 1989) and he says that that property comes from the darboux theorem but i don't...
  25. W

    Quantum hall effect and disorder

    Hello fellow PFers! I have been trying to understand the Integer Quantum Hall Effect for quite a while. Many things seem to be understandable, however, I cannot create a satisfactory explanation of why IQHE (i.e. plateaux in the the Hall resistance R as a function of the magnetic field B)...
  26. L

    Fractional Quantum Hall Effect

    Can someone explain to me as simply as possible why the Laughlin states create energy gaps in the lowest landau level? I am trying to understand for a presentation why the Laughlin states correctly model the QHE effect when the filling factor is a odd fraction (1/3, 1/5, 1/7). As far as I...
  27. S

    Longitudinal resistivity in the Quantum Hall Effect

    My only problem with a basic conceptual understanding of the Quantum Hall Effect is the relation between longitudinal conductivity and resistivity when the magnetic field is such that the filling factor is an integer, and the Hall resistance is quantized. I fully understand the splitting of the...
  28. Y

    What is Spin Hall effect and quantum hall effect

    hi what is Spin Hall effect and quantum hall effect? i can not find a good description on wikipedia.com do you have a good link or description? and another question: why in franck hertz experiment we use MERCURY instead of hydrogen? thanks
  29. E

    Fractional quantum Hall effect, Anyon, Sundance Bilson-Thoompson

    Could Anyons and Fractional quantum Hall effect create 2-D ribbons w/fractional electric charge (e/3) that combine to form fermions or bosons? Sundance Bilson-Thompson proposed a braiding model of 3's which could account for some particles of the standard model (i.e first generation fermions...
  30. M

    Integer quantum hall effect - edge states/bulk effects

    Hi there, I am currently learning about the quantum hall effect and am a bit confused about the edge states picture and how this fits in with the rest of the theory. In most books/review texts the theory is dicussed from the point of view of an infinite 2D system the magneteic field collapses...