Giant spin-orbit splitting in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">HgTe</mml:mi></mml:mrow></mml:math>quantum well

Gui, Y. S.; Becker, C. R.; Dai, Ning; Liu, J.; Qiu, Zhijun; Novik, E. G.; Schäfer, Markus; Shu, Xinyu; Chu, Junhao; Buhmann, H.; Molenkamp, L. W.

doi:10.1103/physrevb.70.115328

Cited by 123 publications

(133 citation statements)

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“…For example the heavy-hole conduction band of HgTe displays SO splitting values ranging between 10 − 17 meV and 30 meV. 5,6 Much stronger SO splittings have been observed in the surface states of metals 7 and semimetals 8,9 , and the corresponding ∆ so may be so large, e.g. ∆ so ≃ 110 meV in Au(111), 7 that the possibility of detecting SO split image states has been recently put forward.…”

Section: Introductionmentioning

confidence: 99%

Electron-phonon effects on spin-orbit split bands of two-dimensional systems

2007

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The electronic self-energy is studied for a two dimensional electron gas coupled to a spin-orbit Rashba field and interacting with dispersionless phonons. For the case of a momentum independent electron-phonon coupling (Holstein model) we solve numerically the self-consistent non-crossing approximation for the self-energy and calculate the electron mass enhancement m * /m and the spectral properties. We find that, even for nominal weak electron-phonon interaction, for strong spin-orbit couplings the electrons behave as effectively strongly coupled to the phonons. We interpret this result by a topological change of the Fermi surface occurring at sufficiently strong spin-orbit coupling, which induces a square-root divergence in the electronic density of states at low energies. We provide results for m * /m and for the density of states of the interacting electrons for several values of the electron filling and of the spin-orbit interaction.

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Section: Introductionmentioning

confidence: 99%

Electron-phonon effects on spin-orbit split bands of two-dimensional systems

2007

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“…As a general rule, the spin-orbit coupling is assumed to be quite small with respect to the other relevant energy scales, in particular with respect to the electronic dispersion, so that the infinite bandwidth limit is often employed. While this assumption is indeed rather reasonable in most of the cases, the natural aim of the current investigations is to search for new materials with stronger spin-orbit couplings, as for instance in HgTe quantum wells [6], or the surface states of metals and semimetals [7,8]. For this reason, experimental evidence of a Rashba SO coupling with energy E 0 (to be defined below) as large as ≃ 220 meV in bismuth/silver alloys [9], or with E 0 ≃ 30 − 200 meV in non-centrosymmetric superconductors CePt 3 Si [10,11], Li 2 Pd 3 B, and Li 2 Pt 3 B [12,13], is certainly an important step towards the investigation of new materials with large SO coupling.…”

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confidence: 99%

Topological Change of the Fermi Surface in Low-Density Rashba Gases: Application to Superconductivity

2007

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Strong spin-orbit coupling can have a profound effect on the electronic structure in a metal or semiconductor, particularly for low electron concentrations. We show how, for small values of the Fermi energy compared to the spin-orbit splitting of Rashba type, a topological change of the Fermi surface leads to an effective reduction of the dimensionality in the electronic density of states. We investigate its consequences on the onset of the superconducting instability. We show, by solving the Eliashberg equations for the critical temperature as a function of spin-orbit coupling and electron density, that the superconducting critical temperature is significantly tuned in this regime by the spin-orbit coupling. We suggest that materials with strong spin-orbit coupling are good candidates for enhanced superconductivity. . As a general rule, the spin-orbit coupling is assumed to be quite small with respect to the other relevant energy scales, in particular with respect to the electronic dispersion, so that the infinite bandwidth limit is often employed. While this assumption is indeed rather reasonable in most of the cases, the natural aim of the current investigations is to search for new materials with stronger spin-orbit couplings, as for instance in HgTe quantum wells [6], or the surface states of metals and semimetals [7,8]. For this reason, experimental evidence of a Rashba SO coupling with energy E 0 (to be defined below) as large as ≃ 220 meV in bismuth/silver alloys [9], or with E 0 ≃ 30 − 200 meV in non-centrosymmetric superconductors CePt 3 Si [10, 11], Li 2 Pd 3 B, and Li 2 Pt 3 B [12,13], is certainly an important step towards the investigation of new materials with large SO coupling. Needless to say, the existence of such materials compels us to carry out a more thorough investigation of the properties of SO systems when E 0 is no longer necessarily the smallest energy scale in the problem.The possibility of having novel interesting features in low density systems with Fermi energy E F of the same order or lower than the SO energy E 0 , in particular, has not been sufficiently investigated to date, in our opinion, and only few studies have been devoted to this problem. In Ref.[14] for instance, it was shown that the vanishing of the spin-Hall current in the low density limit n → 0 of Rashba disordered systems is not related to the vanishing of the vertex function (which applies only in the strict E F /E 0 → ∞ limit) but rather to the cancellation between on-Fermi surface and off-Fermi surface contributions. Another interesting effect was also pointed out in Ref. [15]: there the spin relaxation time τ s for E F ≪ E 0 was shown to be proportional to the electron scattering time τ , in contrast with the standard Dyakonov-Perel behavior, where τ s scales as 1/τ [16]. On the other hand, in spite of the growing interest in the properties of non-centrosymmetric superconductors with strong SO coupling [17,18], no specific investigation to explore the regime where E F /E 0 < ∼ 1 has been pursued, to our knowled...

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“…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].…”

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Direct Observation of the Aharonov-Casher Phase

et al. 2006

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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...

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Giant spin-orbit splitting in aHgTequantum well

Cited by 123 publications

References 17 publications

Electron-phonon effects on spin-orbit split bands of two-dimensional systems

Electron-phonon effects on spin-orbit split bands of two-dimensional systems

Topological Change of the Fermi Surface in Low-Density Rashba Gases: Application to Superconductivity

Direct Observation of the Aharonov-Casher Phase

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