Rashba splitting in<i>n</i>-type modulation-doped HgTe quantum wells with an inverted band structure

Zhang, X. C.; Pfeuffer-Jeschke, A.; Ortner, K.; Hock, V.; Buhmann, H.; Becker, C. R.; Landwehr, G.

doi:10.1103/physrevb.63.245305

Cited by 164 publications

(114 citation statements)

References 26 publications

Supporting

Mentioning

102

Contrasting

Unclassified

Order By: Relevance

“…47 The spin-orbit interaction can also include higher, e.g., cubic terms relevant for the bulk InSb and the HgTe quantum wells with an inverted band structure. 48,49 Here, only linear terms with Rashba symmetry are considered with r so ͑k͒ being disregarded as we expect effect of H so = r so ͑k͒ ١ V͑r͒ on the AHE to be small for wide band semiconductors in which is relatively small. 50 The disorder in the system is modeled by impurity delta scatterers…”

Section: A Calculational Proceduresmentioning

confidence: 99%

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

et al. 2009

View full text Add to dashboard Cite

We present a study of transport in multiple-band noninteracting Fermi metallic systems based on the Keldysh formalism and the self-consistent T-matrix approximation ͑TMA͒ taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba two-dimensional electron-gas ferromagnet and calculate the anomalous Hall effect ͑AHE͒ and anisotropic magnetoresistance ͑AMR͒. The numerical calculations of the AHE reproduce analytical results in the metallic regime revealing the crossover between the skew-scattering mechanism dominating in the clean systems and intrinsic mechanism dominating in the moderately dirty systems. As we increase the disorder further, the AHE starts to diminish due to the spectral broadening of the quasiparticles. Although for certain parameters this reduction of the AHE can be approximated as xy ϳ xx , with varying around 1.6, this is found not to be true in general as xy can go through a change in sign as a function of disorder strength in some cases. Furthermore, the disordered region consistent with the TMA is relatively narrow and a theory with a wider range of applicability in strong disorder limit is called for. By considering the higher order skew-scattering processes, we resolve some discrepancies between the AHE results obtained by using the Keldysh, Kubo, and Boltzmann approaches. We also show that similar higher order processes are important for the AMR when the nonvertex and vertex parts cancel each other. We calculate the AMR in anisotropic systems properly taking into account the anisotropy of the nonequilibrium distribution function. These calculations confirm recent findings on the unreliability of common approximations to the Boltzmann equation.

show abstract

Section: A Calculational Proceduresmentioning

confidence: 99%

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

et al. 2009

View full text Add to dashboard Cite

show abstract

“…In Table I we list the band parameters used in our calculation 10,11 . The Kane parameters of Hg 1−x Cd x Te can be assumed to be x-independent 10 , since the band structure dependence on the Cd composition x caused mainly by the variation of the band gap E g .…”

mentioning

confidence: 99%

Electric field driven quantum phase transition between band insulator and topological insulator

Chang

2009

Applied Physics Letters

View full text Add to dashboard Cite

We demonstrate theoretically that electric field can drive a quantum phase transition between band insulator to topological insulator in CdTe/HgCdTe/CdTe quantum wells. The numerical results suggest that the electric field could be used as a switch to turn on or off the topological insulator phase, and temperature can affect significantly the phase diagram for different gate voltage and compositions. Our theoretical results provide us an efficient way to manipulate the quantum phase of HgTe quantum wells. PACS numbers: 73.43.Nq, 72.25.Rb, 73.61.Ga, Topological insulator (TI) is a very recent discovery and has attracted a rapid growing interests due to its novel transport peoperty 1,2,3,4 . Topological insulators possess a gap in the bulk but a gapless edge states at its boundary, therefore display remarkable transport property due to the presence of the topological edge states, e.g., quantum spin Hall effect (QSHE). The QSHE is protected by the time-reversal symmetry and robust against the local perturbation, e.g., impurity scattering. Searching for new TI becomes a central issue in this rapid growing field. Recently, the HgTe QWs have been demonstrated to be a 2D TI to exhibit the QSHE 3 and BiSb alloys have been proven to be a 3D TI with a conducting surface 5 . A few other materials, such as InAs/GaSb QWs, BiSe, BiTe and SbTe alloys 6 , are also predicted to be TIs and demonstrated experimentally. Besides finding new TI materials, searching the ways to drive a band insulator (BI) into a topological insulator is also important. It has been demonstrated to be possibly realized by tuning the thickness of HgTe QW. However, tuning the thickness of QW is not a convenient way to drive the phase transition. Therefore other efficient ways such as external fields and temperature is highly desirable to drive a BI into a TI. These ways would be very important for both potential device applications and basic physics.In this Letter, we demonstrate theoretically that a BI can be driven into a TI by tuning external electric field in CdTe/Hg 1−x Cd x Te/CdTe QWs based on the self-consistent calculation of the eight-band Kane model and the Poisson equation. We demonstrate electric field can change the interband coupling significantly and consequently leads to strong variations of the band structures, i.e., therefore leads to the quantum phase transition from a BI to a TI. We also show phase diagrams at plenty of parameters and consider the temperature effect on the phase transition. One can see that the critical gate voltage of external phase transition can be reduced at high temperature, small Cd composition and thick thickness of well. Our results could be useful in finding the optimized parameters to realize the phase transition in experiment.We consider a CdTe/Hg 1−x Cd x Te/CdTe QW grown along the [001] direction [see Fig. 1 (a) inside the QW will redistribute due to the effect of the electric field. The charge redistribution induces an internal electric field, which affects the charge density distribution, therefore we n...

show abstract

“…This narrow-gap material exhibits a strong Rashba spin-orbit (SO) splitting [17], which can be modified over a wide range via an exter- nally applied gate voltage [18,19]. The n-type QWs are symmetrically modulation doped and have been epitaxially grown in a MBE system [18,20].…”

mentioning

confidence: 99%

Direct Observation of the Aharonov-Casher Phase

et al. 2006

Self Cite

View full text Add to dashboard Cite

Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study AharonovBohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe non-monotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magneto-conductance for a multichannel ring structure within the Landauer-Büttiker formalism. In the early 1980s it was shown that a quantum mechanical system acquires a geometric phase for a cyclic motion in parameter space. This geometric phase under adiabatic motion is called Berry phase [1], while its later generalization to include non-adiabatic motion is known as Aharonov-Anandan phase [2]. A manifestation of the Berry phase is the well known AharonovBohm (AB) phase [3] of an electrical charge which cycles around a magnetic flux. Aside from the AB effect, the first experimental observation of the Berry phase was reported in 1986 for photons in a wound optical fiber [4]. Another important Berry phase effect is the AharonovCasher (AC) effect [5], which has been proposed to occur when an electron propagates in a ring structure in an external magnetic field perpendicular to the ring plane in the presence of SO interaction [6].This AC effect can be seen when two partial waves move around the ring in different directions. They will acquire a phase difference which depends on the spin orientation with respect to the total magnetic field B tot = B ext + B ef f and the path of each partial wave. B ef f is the effective field induced by the SO interaction. The phase difference is approximately [6] where s =↑ and ↓ denote parallel and anti-parallel orientation to B tot , b = +1 for s =↑ and b = −1 for s =↓, and the superscript −(+) denotes a clockwise (counterclockwise) evolution, respectively. In the above equations, α is the SO parameter, r the ring radius, m * the effective electron mass and θ the angle between the external ( B ext ) and the total magnetic field B tot . For both equations, the first term on the right hand side can be identified with the AB phase and the second term of Eq. (1) with the geometric Berry or Aharonov-Anandan phase. The second term in Eq. (2) represents the dynamic part of the AC phase, i.e. the phase of a particle with a magnetic moment that moves around an electric field. From the expressions above, it can be seen that an increase of the AC phase will lead to a phase change that increases continuously with α, whereas the contribution due to the geometric phase results in a phase shift limited to ∆ϕ geom ≤ π.Both the AC phase [7] and the geometric phase [8, 9] depend on the SO interaction. As a result, one expects a complicated non-monotonic interference pattern as a function of magnetic field and SO interaction strength. So far, to our knowledge, apart from the AB effect no direct observation of phase related effects in solid state systems has been reported. Rec...

show abstract

Rashba splitting inn-type modulation-doped HgTe quantum wells with an inverted band structure

Cited by 164 publications

References 26 publications

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

Electric field driven quantum phase transition between band insulator and topological insulator

Direct Observation of the Aharonov-Casher Phase

Contact Info

Product

Resources

About