^{1,2,a)}, E. B. Olshanetsky

^{1}, D. A. Kozlov

^{1}, E. Novik

^{3}, N. N. Mikhailov

^{1}and S. A. Dvoretsky

^{1}

### Abstract

The first results are reported from a study of a new two-dimensional electron system, a two-dimensional semimetal, that is observed in wide quantum wells based on mercury telluride, which have an inverted band spectrum. Magnetotransport experiments confirm the existence of a semimetal state in quantum wells with (013) and (112) orientations and thicknesses of . These experiments show that the band overlap . A comparison of the experimentally determined with a theoretical calculation of the energy spectrum reveals the fundamental role of strain effects in the formation of the semimetal state. Scattering processes in the two-dimensional semimetal are studied and it is found that the jump in the electron mobility during electronic metal-two-dimensional semimetal transitions is caused by shielding of electron scattering on impurities by holes. The substantial, anomalous rise in the resistivity of the two-dimensional semimetal with increasing temperature is caused by electron-hole scattering. This is the first observation of the direct effect of interparticle scattering (Landau mechanism) on the resistivity of metals. The properties of two-dimensional semimetals in the quantum Hall effect regime are examined. Primary attention is devoted to the observed suppression of strong localization under the conditions of the quantum Hall effect. It is shown that in a strong magnetic field the two-component electron-hole plasma has fundamentally different topological properties from those of an ordinary single-component (electron or hole) plasma. It is proposed that these lead to the appearance of an infinite set of conducting current states and to the suppression of localization.

INTRODUCTION

QUANTUM WELLS BASED ON HgTe. TECHNOLOGY AND STRUCTURE

SAMPLES AND EXPERIMENTAL TECHNIQUE

THE SEMIMETAL STATE IN WIDTH HgTe QUANTUM WELLS WITH AN INVERTED BAND STRUCTURE. THEIR DISCOVERY AND NATURE

SCATTERING PROCESSES IN A TWO-DIMENSIONAL SEMIMETAL

QUANTUM HALL EFFECT

CONCLUSION

### Key Topics

- Magnetic fields
- 28.0
- Quantum wells
- 25.0
- Semimetals
- 23.0
- Electron scattering
- 17.0
- Mercury (element)
- 13.0

## Figures

Schematic cross section of a structure with an undoped HgTe quantum well grown by molecular-beam epitaxy.

Schematic cross section of a structure with an undoped HgTe quantum well grown by molecular-beam epitaxy.

A transistor Hall structure with a field gate. The top figure is a schematic vertical cross section and the bottom, a view from above.

A transistor Hall structure with a field gate. The top figure is a schematic vertical cross section and the bottom, a view from above.

The Hall component of the resistance, for a (013) HgTe quantum well with a thickness of for different values of the gate voltage (a); energy spectra of two-dimensional electron systems in an HgTe well: 2D semimetal, 2D electron gas (2DEG), and 2D hole gas (2DHG) (b).

The Hall component of the resistance, for a (013) HgTe quantum well with a thickness of for different values of the gate voltage (a); energy spectra of two-dimensional electron systems in an HgTe well: 2D semimetal, 2D electron gas (2DEG), and 2D hole gas (2DHG) (b).

The concentrations of electrons and holes as functions of gate voltage for a -thick (013) HgTe quantum well.

The concentrations of electrons and holes as functions of gate voltage for a -thick (013) HgTe quantum well.

for (a), the Hall component of the resistivity for a -thick (112) HgTe quantum well for different gate voltages (b), and the electron and hole concentrations as functions of gate voltage for the same wells (c)

for (a), the Hall component of the resistivity for a -thick (112) HgTe quantum well for different gate voltages (b), and the electron and hole concentrations as functions of gate voltage for the same wells (c)

Calculated dispersion relation for a -thick (112) HgTe quantum well, neglecting the mismatch of the lattice constants of HgTe and CdTe (a). For lattice constants of HgTe equal to and CdTe, (b), the smooth curves and the dashed curves .

Calculated dispersion relation for a -thick (112) HgTe quantum well, neglecting the mismatch of the lattice constants of HgTe and CdTe (a). For lattice constants of HgTe equal to and CdTe, (b), the smooth curves and the dashed curves .

The mobilities of two-dimensional electrons and holes as functions of gate voltage for a two-dimensional semimetal in a -thick (013) HgTe quantum well at .

The mobilities of two-dimensional electrons and holes as functions of gate voltage for a two-dimensional semimetal in a -thick (013) HgTe quantum well at .

curves for and different temperatures in the range (the temperature increases from the bottom to the top curve) (a); for , , and (b). The curves are calculated using Eq. (1); the solid symbols are experimental data. The inset shows the fitting parameter as a function of gate voltage: the curves are calculated using Eqs. (2) and (3) and the points are experimental data.

curves for and different temperatures in the range (the temperature increases from the bottom to the top curve) (a); for , , and (b). The curves are calculated using Eq. (1); the solid symbols are experimental data. The inset shows the fitting parameter as a function of gate voltage: the curves are calculated using Eqs. (2) and (3) and the points are experimental data.

Diagonal and Hall components of the resistivity tensor as a function of gate voltage for a fixed magnetic field of . The Hall component of the resistivity tensor is indicated for two signs of the magnetic field. Inset: a Landau level diagram for the electron and hole subbands. The last Landau levels from the electron and hole subbands intersect at . is the Fermi level at the charge neutrality point (a). The diagonal and Hall conductivities as functions of gate voltage for the fixed magnetic field and . The arrow indicates the position of the charge neutrality point, where (b).

Diagonal and Hall components of the resistivity tensor as a function of gate voltage for a fixed magnetic field of . The Hall component of the resistivity tensor is indicated for two signs of the magnetic field. Inset: a Landau level diagram for the electron and hole subbands. The last Landau levels from the electron and hole subbands intersect at . is the Fermi level at the charge neutrality point (a). The diagonal and Hall conductivities as functions of gate voltage for the fixed magnetic field and . The arrow indicates the position of the charge neutrality point, where (b).

Diagonal and Hall conductivities as functions of gate voltage for a fixed magnetic field and different temperatures : 850, 250, and 90 (a). The diagonal and Hall conductivities as functions of gate voltage for different magnetic fields : 1.5, 2, and 2.5 and . The vertical line indicates the position of the charge neutrality point. (b)

Diagonal and Hall conductivities as functions of gate voltage for a fixed magnetic field and different temperatures : 850, 250, and 90 (a). The diagonal and Hall conductivities as functions of gate voltage for different magnetic fields : 1.5, 2, and 2.5 and . The vertical line indicates the position of the charge neutrality point. (b)

Magnetoresistance at the charge neutrality point for different temperatures. Inset: resistance as a function of 1/T for fixed values of the magnetic field , from bottom to top: 4, 6, and 7. The straight line in the inset is an Arrhenius dependence with (a). Magnetoresistance at the charge neutrality point for temperatures of 90 and . The smooth curves are fits to . The dashed curve is a fit obtained using percolation theory for spiral states in the case of a random quasiclassical magnetic field^{13} (b).

Magnetoresistance at the charge neutrality point for different temperatures. Inset: resistance as a function of 1/T for fixed values of the magnetic field , from bottom to top: 4, 6, and 7. The straight line in the inset is an Arrhenius dependence with (a). Magnetoresistance at the charge neutrality point for temperatures of 90 and . The smooth curves are fits to . The dashed curve is a fit obtained using percolation theory for spiral states in the case of a random quasiclassical magnetic field^{13} (b).

Schematic illustration of electron-hole spiral states propagating along contours at the charge neutrality point in a strong magnetic field and of the geometry of a saddle point between neighboring percolation clusters.

Schematic illustration of electron-hole spiral states propagating along contours at the charge neutrality point in a strong magnetic field and of the geometry of a saddle point between neighboring percolation clusters.

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