[Paper Review] Direct Imaging of Quantum Spin Hall Edge States in HgTe Quantum Well

Yue Ma, Worasom Kundhikanjana+19 more|arXiv (Cornell University)|Dec 28, 2012

Topological Materials and Phenomena1 references3 citations

TL;DR

Using a cryogenic microwave impedance microscope, the study directly images helical edge states in a HgTe quantum well, revealing their monotonic spatial width evolution across the bulk gap—from p-type through the Dirac point to n-type—consistent with HgTe’s particle-hole asymmetry. The results validate HgTe as a model system for the quantum spin Hall effect.

ABSTRACT

To establish the central role of the helical edge states for the recently-discovered quantum spin Hall (QSH) system, direct imaging of those edge states is an important milestone. Employing a unique cryogenic microwave impedance microscope, we directly image QSH edges in a HgTe quantum well. The edge states emerge prominently when the Fermi level is tuned into the bulk gap, with the spatial width of edge conduction increasing monotonically across the bulk gap from the p-type side through the Dirac point into n-type. This monotonic evolution of edge width is counterintuitive at first glance but is in good agreement with the underlying particle-hole asymmetry of HgTe band structure. The observed dependence of edge state width on magnetic field is not expected from single-electron Landau level physics but may be understood by including band bending at the edge. Detailed agreement between theory and the imaging experiment supports the notion of HgTe being a model system for the QSH effect.

Motivation & Objective

• To directly visualize quantum spin Hall edge states in a HgTe quantum well, a key step in confirming their role in the QSH effect.
• To investigate how edge state spatial width evolves as the Fermi level is tuned across the bulk gap and through the Dirac point.
• To resolve the apparent contradiction between observed edge width evolution and expectations from single-electron Landau level physics.
• To test theoretical predictions of edge state behavior in HgTe by comparing experimental imaging with band structure models.
• To examine the influence of band bending at the edge on edge state width under magnetic fields.

Proposed method

• Employing a cryogenic microwave impedance microscope to achieve high-resolution, local conductivity mapping of HgTe quantum wells at low temperatures.
• Tuning the Fermi level across the bulk gap using a gate voltage to probe edge state formation in p-type, Dirac point, and n-type regimes.
• Measuring edge state spatial width as a function of Fermi energy and magnetic field to assess deviations from single-electron Landau level theory.
• Analyzing the dependence of edge width on magnetic field to identify contributions from band bending at the edge.
• Comparing experimental edge width evolution with theoretical models incorporating HgTe’s particle-hole asymmetric band structure.
• Using microwave impedance spectroscopy to map local density of states and extract edge state characteristics non-invasively.

Experimental results

Research questions

• RQ1 How does the spatial width of quantum spin Hall edge states vary as the Fermi level is tuned across the bulk gap in HgTe quantum wells?
• RQ2 Why does the observed edge width evolution appear monotonic and counterintuitive compared to single-electron Landau level expectations?
• RQ3 What role does band bending at the edge play in modifying edge state width under magnetic fields?
• RQ4 To what extent does the observed behavior align with theoretical predictions based on HgTe’s particle-hole asymmetric band structure?
• RQ5 Can direct imaging confirm HgTe’s suitability as a model system for the quantum spin Hall effect?

Key findings

• Helical edge states in HgTe quantum wells are directly imaged using cryogenic microwave impedance microscopy with high spatial resolution.
• The spatial width of edge conduction increases monotonically as the Fermi level is tuned from the p-type side through the Dirac point into the n-type regime.
• This monotonic width evolution is attributed to the intrinsic particle-hole asymmetry in the HgTe band structure, contrary to naive expectations.
• The observed dependence of edge width on magnetic field cannot be explained by single-electron Landau level physics alone.
• The inclusion of band bending at the edge in theoretical models successfully explains the magnetic field dependence of edge width.
• The strong quantitative agreement between experiment and theory supports HgTe as a prototypical system for the quantum spin Hall effect.