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Register a new userFingerprint of Different Spin-Orbit Terms for Spin Transport in HgTe Quantum Wells
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Using $vec{k}$$cdot$$vec{p}$ theory, we derive an effective four band model describing the physics of the typical two-dimensional topological insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in z-direction inversion breaking and in-plane confining potentials. We find that up to third order in perturbation theory, only the inversion breaking potential generates new elements to the four band Hamiltonian that are off-diagonal in spin space. When this new effective Hamiltonian is folded into an effective two band model for the conduction (electron) or valence (heavy hole) bands, two competing terms appear: (1) a Rashba spin-orbit interaction originating from inversion breaking potential in z-direction and (2) an in-plane Pauli term as a consequence of the in-plane confining potential. Spin transport in the conduction band is further analysed within the Landauer-Buttiker formalism. We find that for asymmetrically doped HgTe quantum wells, the behaviour of the spin-Hall conductance is dominated by the Rashba term.
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We analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Greens function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signature of the gap of the edge states due to their finite overlap from opposite sample boundaries -- both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst signal is related to the spin Hall conductance by a Mott-like relation which is exact to all orders in the temperature difference between the warm and the cold reservoir.
We present a microscopic theory for transport of the spin polarized charge density wave with both electrons and holes in the $(111)$ GaAs quantum wells. We analytically show that, contradicting to the commonly accepted belief, the spin and charge motions are bound together only in the fully polarized system but can be separated in the case of low spin polarization or short spin lifetime even when the spatial profiles of spin density wave and charge density wave overlap with each other. We further show that, the Coulomb drag between electrons and holes can markedly enhance the hole spin diffusion if the hole spin motion can be separated from the charge motion. In the high spin polarized system, the Coulomb drag can boost the hole spin diffusion coefficient by more than one order of magnitude.
We study the depolarization of optically oriented electrons in quantum wells subjected to an in-plane magnetic field and show that the Hanle curve drastically depends on the carrier mobility. In low-mobility structures, the Hanle curve is described by a Lorentzian with the width determined by the effective g-factor and the spin lifetime. In contrast, the magnetic field dependence of spin polarization in high-mobility quantum wells is nonmonotonic: The spin polarization rises with the magnetic field induction at small fields, reaches maximum and then decreases. We show that the position of the Hanle curve maximum can be used to directly measure the spin-orbit Rashba/Dresselhaus magnetic field.
Spin-orbit splitting of conduction band in HgTe quantum wells was studied experimentally. In order to recognize the role of different mechanisms, we carried out detailed measurements of the Shubnikov-de Haas oscillations in gated structures with a quantum well widths from $8$ to $18$ nm over a wide range of electron density. With increasing electron density controlled by the gate voltage, splitting of the maximum of the Fourier spectrum $f_0$ into two components $f_1$ and $f_2$ and the appearance of the low-frequency component $f_3$ was observed. Analysis of these results shows that the components $f_1$ and $f_2$ give the electron densities $n_1$ and $n_2$ in spin-orbit split subbands while the $f_3$ component results from magneto-intersubband oscillations so that $f_3=f_1 - f_2$. Comparison of these data with results of self-consistent calculations carried out within the framework of four-band emph{kP}-model shows that a main contribution to spin-orbit splitting comes from the Bychkov-Rashba effect. Contribution of the interface inversion asymmetry to the splitting of the conduction band turns out to be four-to-five times less than that for the valence band in the same structures.
Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We have fabricated such sample structures with low density and high mobility in which we can tune, through an external gate voltage, the carrier conduction from n-type to the p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e^2/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nm, is also independently determined from the magnetic field induced insulator to metal transition. These observations provide experimental evidence of the quantum spin Hall effect.
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