Electrons in elliptical valleys prefer elliptical light – towards bismuth valleytronics



By Pieter J. de Visser and Alexey B. Kuzmenko, Department of Quantum Matter Physics, UNIGE
After an article published in Physical Review Letters

In electronics and photonics there is a continuous quest for novel ways to excite and manipulate electrons in materials due to interaction with light. A recent development is valleytronics, in which the valley degree of freedom of a material (on top of charge and spin) is used for manipulation using polarized light, potentially with little energy loss. Researchers at UNIGE now demonstrate that the electrons living in the valleys of Bismuth, which are strongly stretched due to an anisotropic mass, absorb left and right handed polarized light in almost equal amounts. In other words, they preferentially absorb elliptically polarized light, which therefore opens up a new way to selectively drive electrons in valleys.

Bismuth is a canonical and a very interesting semimetal with a markedly different character of electrons and holes, an extremely long electronic mean free path, a huge effective mass anisotropy and a relatively weak magnetic field required to achieve the extreme quantum limit [1]. When doped with Sb, it becomes a 3D topological insulator with 2D surface states [2]. Recently, it was proposed that bismuth is also a promising material for valleytronics [3] as the carrier population in different valleys is sensitive to magnetic field.

In a recent paper in Physical Review Letters [4], Pieter de Visser, Julien Levallois et al. from UNIGE present accurate measurements of the terahertz magneto-optical conductivity spectra for left- and right-handed circular polarizations in magnetic field up to 7 Tesla [Figure 1].



Figure 1: (a) Measured spectra showing the conductivity for right and left circular polarizations. Clearly the hole transition (open squares) only shows up for one polarization, whereas electron transitions (filled symbols) have almost equal strength in both handedness. (b) A bismuth crystal in a magnetic field is exposed to terahertz radiation. The reflected signal has a different polarization and rotation angle due to the interaction with the electrons in the elliptical pockets. (c) In the plane on which the reflection is measured, hole carriers trace out circular orbits, absorbing only one circular polarization. Because of the strong anisotropy of the effective mass and the elliptical orbits, electrons absorb light of both circular polarizations.

By combining for the first time magneto-reflectivity and magneto-optical Kerr rotation spectra, they solved the technical challenge of generating circular polarization in a broad range of frequencies [5]. The high spectral resolution allows them to separate the intraband Landau level transitions originating from the electron (Dirac-type) and hole (parabolic) Fermi pockets.
The hole transitions exhibit a 100% magnetic circular dichroism, i.e. they absorb only one circular polarization, as generally expected for cyclotron motion. However, the magnetic circular dichroism for electrons is reduced to only 13% (!), i.e. the electrons absorb almost equal amounts of left and right circular polarisations.

In other words, the electrons prefer elliptical light. The scientists demonstrate quantitatively that this counterintuitive observation is explained by the large effective mass anisotropy (>200) of the electron Fermi pockets and can be generally regarded as a manifestation of the mismatch between the spatial metric experienced by the photons (isotropic) and the electrons (anisotropic).

An important consequence of this observation is that the magneto-absorption in bismuth is highly valley sensitive. The team proposes that by shining elliptically polarized light with the same ellipticity as one of the electronic Fermi pockets and the polarization rotation opposite to the cyclotron motion of the electrons, one can modulate magneto-absorption in each of the three valleys between 0 and 100% in a constant magnetic field [Figure 2].


Figure 2: (a) Elliptically polarized light with the same ellipticity as the electron orbits, but with opposite rotation, leads to valley-selective absorption of radiation as a function of polarization angle, enabling valley polarization with elliptical light. (b) Normalized magneto-absorption in each valley as a function of the azimuth angle of the polarization ellipse.

Moreover, different valleys can be selected by simply rotating the main axis of the incident polarization. This is a fundamentally different way of valley selective optical pumping as compared to exciting interband transitions with a circular radiation from spin-split bands [6,7] or by rotating magnetic field around the trigonal axis [3]. These results thus pave the way to future valleytronic applications of bismuth and other materials with a strong effective-mass anisotropy.


[1] M. H. Cohen and E. I. Blount, Phil. Mag. 5, 115 (1960).
[2] D. Hsieh et al., Nature 452, 907 (2008).
[3] Z. Zhu, A. Collaudin, B. Fauqué, W. Kang and K. Behnia, Nature Physics 8, 89 (2012)
[4] P.J. de Visser, J. Levallois, M.K. Tran, J.-M. Poumirol, I.O Nedoliuk, J. Teyssier, C. Uher, D. van der Marel, and A.B. Kuzmenko, Phys. Rev. Lett. 117, 017402 (2016), Editor’s choice
[5] J. Levallois, I. Nedoliuk, I. Crassee and A. Kuzmenko, Review of Scientific Instruments 86, 033906 (2015)
[6] H. Zeng, J. Dai, W. Yao, Di Xiao, and X. Cui, Nature Nanotechnology 7, 490 (2012).
[7] K. F. Mak, K. He, J. Shan, and T. F. Heinz, Nature Nanotechnology 7, 494 (2012).

Contact: Alexey Kuzmenko, (Tél. +41 22 379 3105)


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