Related Experiment Video
Updated: May 22, 2026
10:36
Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
Published on: January 21, 2016
Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term
1Institute for Theoretical Physics, University of Cologne, Cologne, Germany.
Physical Review Letters
|May 1, 2012
Summary
A magnetic field creates one-dimensional edge channels in topological insulators. The Hall effect in these channels remains quantized, even when bulk properties are not, revealing new physics in edge channel coupling.
Area of Science:
- Condensed Matter Physics
- Materials Science
Background:
- Topological insulators possess unique surface states with potential applications.
- Understanding edge states is crucial for harnessing topological properties.
Purpose of the Study:
- Investigate magnetic field-induced edge channels in gapped topological insulator surface states.
- Analyze the quantization of the Hall effect in these one-dimensional channels.
- Explore the interplay of orbital and Zeeman effects on quantum Hall transitions.
Main Methods:
- Utilizing magnetic fields to gap two-dimensional surface states of three-dimensional topological insulators.
- Measuring the Hall effect by contacting induced one-dimensional edge channels.
- Performing model calculations to understand quantum Hall transitions and channel redistribution.
Main Results:
- One-dimensional edge channels are induced by magnetic fields in gapped topological insulator surface states.
- The Hall effect in these edge channels remains quantized despite broken time-reversal symmetry.
- Model calculations reveal quantum Hall transitions driven by orbital and Zeeman effects, redistributing channels along crystal edges.
Conclusions:
- Quantized Hall effect in edge channels persists even when bulk properties are not quantized.
- The change in the θ term around edge channels dictates quantization.
- The edge network offers novel avenues for studying edge channel coupling.
Related Concept Videos
01:30The Hall Effect
Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting material. From a historical perspective, this experiment was the first to demonstrate that the charge carriers in most metals are negative.
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:27Magnetic Fields
A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
A magnetic field is defined by the force that a charged particle experiences...
01:03Atomic Nuclei: Nuclear Spin State Overview
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
01:23Magnetic Field due to Moving Charges
A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
01:26Electric Field at the Surface of a Conductor
Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on its outer surface, regardless of where they originate.
In the 19th century, Michael Faraday conducted the famous ice pail experiment to prove that the charges always reside on the surface of a conductor. The experimental set-up consists of a conducting uncharged container mounted on an insulating stand. The outer surface of the container is...
In the 19th century, Michael Faraday conducted the famous ice pail experiment to prove that the charges always reside on the surface of a conductor. The experimental set-up consists of a conducting uncharged container mounted on an insulating stand. The outer surface of the container is...