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Two-dimensional semimetal in a wide HgTe quantum well: Magnetotransport and energy spectrum

G. M. Minkov, A. V. Germanenko, O. E. Rut, A. A. Sherstobitov, S. A. Dvoretski, and N. N. Mikhailov
Phys. Rev. B 88, 155306 – Published 9 October 2013
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  • INTRODUCTION
  • EXPERIMENTAL
  • EXPERIMENTAL RESULTS AND DISCUSSION
  • THE SPECTRUM: COMPARISON BETWEEN THEORY…
  • CONCLUSION
  • ACKNOWLEDGEMENTS
    • Supplemental Material
    References

    Abstract

    The results of an experimental study of the magnetoresistivity and the Hall and Shubnikov-de Haas effects for a heterostructure with a HgTe quantum well of 20.2 nm width are reported. The measurements were performed on gated samples over a wide range of electron and hole densities including the vicinity of a charge neutrality point. Analyzing the data, we conclude that the electron and hole energy spectra are in qualitative agreement with those calculated within the framework of kP model. The electron and hole subbands are overlapped due to the nonmonotonic dispersion of the hole subband resulting in a semimetallic state. The main result of the paper, however, is the drastic quantitative difference in the experimental and calculated spectra of the hole subband. So, the hole effective mass found from the analysis of the Shubnikov-de Haas oscillations is positive and equal to approximately 0.2m0 and practically independent of the quasimomentum (k) starting from k2≃0.7×1012 cm−2, while the theory predicts negative (electronlike) effective mass up to k2≃6×1012 cm−2. The experimental effective mass near k=0, where the hole energy spectrum is electronlike, is close to −0.005m0, whereas the theoretical value is about −0.1m0.

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    • Received 27 November 2012

    DOI:https://doi.org/10.1103/PhysRevB.88.155306

    ©2013 American Physical Society

    Authors & Affiliations

    G. M. Minkov1,2, A. V. Germanenko2, O. E. Rut2, A. A. Sherstobitov1,2, S. A. Dvoretski3, and N. N. Mikhailov3

    • 1Institute of Metal Physics RAS, 620990 Ekaterinburg, Russia
    • 2Institute of Natural Sciences, Ural Federal University, 620000 Ekaterinburg, Russia
    • 3Institute of Semiconductor Physics RAS, 630090 Novosibirsk, Russia

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    Vol. 88, Iss. 15 — 15 October 2013

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    Images

    • Figure 1
      Figure 1
      Architecture (a) and energy diagram (b) of the structure under investigation. (c) The energy spectrum calculated within the framework of isotropic six-band kP model.Reuse & Permissions
    • Figure 2
      Figure 2
      The magnetic field dependencies of ρxy (a) and ρxx (b,c), measured for the different gate voltages. The minimum resulting from the crossing between the Landau level with n=0 of the conduction subband h1 and Landau level with n=2 of the valence subband h2 is marked by an arrow (for more details, see Sec. 4). The inset in (b) illustrates a weak sensitivity of the minimum position to the gate voltage near the charge neutrality point, Vg≃1.8 V.Reuse & Permissions
    • Figure 3
      Figure 3
      The low-magnetic-field dependencies of ρxy (a) and ρxx (b) for different gate voltages illustrating the participation of two types of carriers in the transport.Reuse & Permissions
    • Figure 4
      Figure 4
      The gate voltage dependence of 1/eRH(0.05T) and 1/eRH(2T) (circles), of electron and hole densities obtained from analysis of magnetoresistivity oscillations (squares) and from the fit of the RH and ρxx vs B data within the classical magnetic field range as described in Sec. 3c (triangles). Open symbols relate to electrons and filled symbols to holes. For convenience sake, the electron density is negative here. The line is the charge density in the quantum well calculated as C(1.8V−Vg)/e, where C is the capacitance between the gate electrode and quantum well measured experimentally, C=9.1 nF/cm2. The inset shows the B dependencies of the Hall coefficient for several gate voltages.Reuse & Permissions
    • Figure 5
      Figure 5
      The fan-chart diagram showing the positions of the minima in ρxx vs B dependence. Symbols are the experimental results. The dashed line is the B dependence of the gate voltage corresponding to a crossing of the Landau level of the h2 subband with n=2 with the Fermi level. Solid lines show the expected minima positions. The squares correspond to the minima labeled in Fig. 2a by arrows. The inset is schematic dispersion of Landau levels relating to the conduction and valence bands, h1 and h2, respectively.Reuse & Permissions
    • Figure 6
      Figure 6
      (a) The hole effective mass plotted against the k2 value as obtained experimentally (symbols) and calculated theoretically from six-band kP model with and without taking into account the lattice mismatch between HgTe and CdTe (the sold and dashed curves, respectively). (b) An example of the SdH oscillations measured for Vg=0.25 V (p=1.05×1011 cm−2) at different temperatures. (c) The dispersion for the hole subband h2 calculated with and without taking into account the strain due to the lattice mismatch (the solid and dashed curves, respectively).Reuse & Permissions
    • Figure 7
      Figure 7
      The magnetic field dependencies of ρxx (a) and RH (b) in the regime when both the holes and the electrons take part in the transport. The solid curves are measured experimentally, the dashed lines are the results of the best fit to the classical formula.Reuse & Permissions
    • Figure 8
      Figure 8
      The gate voltage dependencies of (a) electron density, (b) electron mobility, and (c) partial electron and hole conductivities. The parameters of carriers shown by triangles are obtained within the framework of standard two type carrier model as described in the text, the parameters shown by circles are obtained as follows: n=1/e|RH(0.05T)|, μe=|RH(0.05T)|σ. The solid line in (c) is the σ vs Vg dependence measured experimentally.Reuse & Permissions
    • Figure 9
      Figure 9
      The dispersion E(k) reconstructed from the data analysis as described in the text (solid lines) and calculated within the framework of isotropic six-band kP model (dashed lines). The dotted parts of dispersion curves show an assumed run of the dispersion curves not supported experimentally.Reuse & Permissions
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