Haldane Model: Does edge current exist for a filled band?

In summary, the conversation is about investigating the edge current on a finite strip of Zigzag Haldane model. The speaker measures the current by taking the expectation value of a current operator, which is a function of wavevector k, for each eigenvector of the wavevector-dependent Hamiltonian. When the fermi level is set at the top of the edge mode band, the net current is zero, which confuses the speaker since this should result in a non-zero current for a quantum hall system. The other person asks for more information about the current operator and clarifies the meaning of "the point of the top of the edge mode band". They also mention being confused about the boundary conditions and the expectation of a current without an applied
  • #1
Teek
11
0
Hi all,

I'm currently trying to investigate the edge current on a finite strip of Zigzag Haldane model (spinless, pi/2 phase) and I measure the current (in my code) by taking the expectation value of my current operator which is a function of wavevector k, for each eigenvector of the wavevector-dependent Hamiltonian H(k). The current operator is the net directional hopping matrix when considering only a line across the sample.

When I set the fermi level at the point of the top of the edge mode band, I get zero net current, for a quantum hall system, should this not be a non-zero current? I am confused

Thanks.
 
  • #3
Hello. Can you write down this current operator you speak of?

What exactly do you mean by 'the point of the top of the edge mode band'?

I suppose in general I am confused about a few things: since you talk about k it seems you are doing periodic boundary conditions, but since you mention edge mode band it sounds like you are doing open boundary conditions?
Also, do we expect a current if there is no applied electric field?
Both of these questions might have to do with me not knowing what the current operator is you are using?
 

Related to Haldane Model: Does edge current exist for a filled band?

1. What is the Haldane model and how does it relate to edge current?

The Haldane model is a theoretical model used to study the electronic properties of materials. It is specifically used to understand the behavior of electrons in a magnetic field. The model suggests that a quantum Hall effect can occur even in a system with a filled band, which means that there is no net current in the bulk of the material. However, the model also predicts the existence of edge currents at the boundaries of the material, which can be thought of as a flow of electrons along the edges of the material.

2. How does the Haldane model explain the existence of edge current?

The Haldane model takes into account the topology of the material's band structure, particularly the Berry curvature, which is a measure of how the electronic wave functions change as a function of position. In a magnetic field, the Berry curvature can become non-zero, resulting in a net flow of electrons along the edges of the material. This is known as the quantum anomalous Hall effect and is a manifestation of the edge current predicted by the Haldane model.

3. Is the existence of edge current in a filled band confirmed by experiments?

Yes, the existence of edge current in a filled band has been confirmed through various experiments, including the observation of the quantum anomalous Hall effect in several materials. This has provided strong evidence for the validity of the Haldane model and its predictions of edge currents in materials with filled bands.

4. How does the presence of edge current affect the electronic transport properties of a material?

The presence of edge current can significantly alter the electronic transport properties of a material. This is because the edge current is localized to the boundaries of the material and does not contribute to the bulk electrical conductivity. Therefore, the material may exhibit different transport behaviors, such as a quantized conductance, in the presence of edge currents compared to when they are absent.

5. Can edge currents be controlled or manipulated in materials?

Yes, edge currents can be controlled and manipulated in materials through various methods, including changing the magnetic field strength, modifying the properties of the material's edges, or introducing defects. These techniques can be used to study the behavior of edge currents and potentially harness them for applications in quantum computing and spintronics.

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