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Register a new userWeak antilocalization in HgTe quantum well with inverted energy spectrum
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Alexander Germanenko
Publication date
2012
fields
Physics
and research's language is
English
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The results of experimental study of the magnetoconductivity of 2D electron gas caused by suppression of the interference quantum correction in HgTe single quantum well heterostructure with the inverted energy spectrum are presented. It is shown that only the antilocalization magnetoconductivity is observed at the relatively high conductivity $sigma>(20-30)G_0$, where $G_0= e^2/2pi^2hbar$. The antilocalization correction demonstrates a crossover from $0.5ln{(tau_phi/tau)}$ to $1.0ln{(tau_phi/tau)}$ behavior with the increasing conductivity or decreasing temperature (here $tau_phi$ and $tau$ are the phase relaxation and transport relaxation times, respectively). It is interpreted as a result of crossover to the regime when the two chiral branches of the electron energy spectrum contribute to the weak antilocalization independently. At lower conductivity $sigma<(20-30)G_0$, the magnetoconductivity behaves itself analogously to that in usual 2D systems with the fast spin relaxation: being negative in low magnetic field it becomes positive in higher one. We have found that the temperature dependences of the fitting parameter $tau_phi$ corresponding to the phase relaxation time demonstrate reasonable behavior, close to 1/T, over the whole conductivity range from $5G_0$ up to $130G_0$. However, the $tau_phi$ value remains practically independent of the conductivity in distinction to the conventional 2D systems with the simple energy spectrum, in which $tau_phi$ is enhanced with the conductivity.
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The results of experimental study of interference induced magnetoconductivity in narrow HgTe quantum wells of hole-type conductivity with a normal energy spectrum are presented. Interpretation of the data is performed with taking into account the strong spin-orbit splitting of the energy spectrum of the two-dimensional hole subband. It is shown that the phase relaxation time found from the analysis of the shape of magnetoconductivity curves for the relatively low conductivity when the Fermi level lies in the monotonic part of the energy spectrum of the valence band behaves itself analogously to that observed in narrow HgTe quantum wells of electron-type conductivity. It increases in magnitude with the increasing conductivity and decreasing temperature following the $1/T$ law. Such a behavior corresponds to the inelasticity of electron-electron interaction as the main mechanism of the phase relaxation and agrees well with the theoretical predictions. For the higher conductivity, despite the fact that the dephasing time remains inversely proportional to the temperature, it strongly decreases with the increasing conductivity. It is presumed that a nonmonotonic character of the hole energy spectrum could be the reason for such a peculiarity. An additional channel of the inelastic interaction between the carriers in the main and secondary maxima occurs when the Fermi level arrives the secondary maxima in the depth of the valence.
The results of experimental study of interference induced magnetoconductivity in narrow quantum well HgTe with the normal energy spectrum are presented. Analysis is performed with taking into account the conductivity anisotropy. It is shown that the fitting parameter tau_phi corresponding to the phase relaxation time increases in magnitude with the increasing conductivity (sigma) and decreasing temperature following the 1/T law. Such a behavior is analogous to that observed in usual two-dimensional systems with simple energy spectrum and corresponds to the inelasticity of electron-electron interaction as the main mechanism of the phase relaxation. However, it drastically differs from that observed in the wide HgTe quantum wells with the inverted spectrum, in which tau_phi being obtained by the same way is practically independent of sigma. It is presumed that a different structure of the electron multicomponent wave function for the inverted and normal quantum wells could be reason for such a discrepancy.
The results of the longitudinal and Hall magnetoresistivity measurements in the Shubnikov - de Haas oscillation regime for the HgCdTe/HgTe/HgCdTe heterostructures with a wide (20.3 nm) HgTe quantum well are presented. An anomalous phase shift of magneto-oscillations is detected: in the region of spin-unsplit peaks the longitudinal resistivity maxima are located at even filling factor numbers in contradiction with a conventional situation in 2D systems. It is shown that the observed features are associated with the inverted nature of the spectrum in the investigated quantum well with the electron-type conduction along the size-quantized subband H1 of HgTe band {Gamma}8, for which the spin splitting is comparable to (and even greater than) the orbital one. The results obtained are compared with the phase shift effects of both magneto-oscillations and the plateau of the quantum Hall effect in monolayer graphene.
The energy spectrum of the valence band in HgTe/Cd$_x$Hg$_{1-x}$Te quantum wells with a width $(8-20)$~nm has been studied experimentally by magnetotransport effects and theoretically in framework $4$-bands $kP$-method. Comparison of the Hall density with the density found from period of the Shubnikov-de Haas (SdH) oscillations clearly shows that the degeneracy of states of the top of the valence band is equal to 2 at the hole density $p< 5.5times 10^{11}$~cm$^{-2}$. Such degeneracy does not agree with the calculations of the spectrum performed within the framework of the $4$-bands $kP$-method for symmetric quantum wells. These calculations show that the top of the valence band consists of four spin-degenerate extremes located at $k eq 0$ (valleys) which gives the total degeneracy $K=8$. It is shown that taking into account the mixing of states at the interfaces leads to the removal of the spin degeneracy that reduces the degeneracy to $K=4$. Accounting for any additional asymmetry, for example, due to the difference in the mixing parameters at the interfaces, the different broadening of the boundaries of the well, etc, leads to reduction of the valleys degeneracy, making $K=2$. It is noteworthy that for our case two-fold degeneracy occurs due to degeneracy of two single-spin valleys. The hole effective mass ($m_h$) determined from analysis of the temperature dependence of the amplitude of the SdH oscillations show that $m_h$ is equal to $(0.25pm0.02),m_0$ and weakly increases with the hole density. Such a value of $m_h$ and its dependence on the hole density are in a good agreement with the calculated effective mass.
The anomalous magnetoresistance caused by the weak antilocalization (WAL) effects in 200-nm HgTe films is experimentally studied. The film is a high quality 3D topological insulator with much stronger spatial separation of surface states than in previously studied thinner HgTe structures. However, in contrast to that films, the system under study is characterized by a reduced partial strain resulting in an almost zero bulk energy gap. It has been shown that at all positions of the Fermi level the system exhibits a WAL conductivity correction superimposed on classical parabolic magnetoresistance. Since high mobility of carriers, the analysis of the obtained results was performed using a ballistic WAL theory. The maximum of the WAL conductivity correction amplitude was found at a Fermi level position near the bulk energy gap indicating to full decoupling of the surface carriers in these conditions. The WAL amplitude monotonously decreases when the density of either bulk electrons or holes increases that results from the increasing coupling between surface and bulk carriers.
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