Session L48: Invited Session: Light-matter Interaction in Valleytronic Materials and Topological Insulators

(1) Majorana fermions in pinned vortices; (2) Manipulating and probing Majorana fermions using superconducting circuits; and (3) Controlling a nanowire spin-orbit qubit via electric-dipole spin resonance

We study [1,2] a heterostructure which consists of a topological insulator and a superconductor with a hole. This system supports a robust Majorana fermion state bound to the vortex core. We study the possibility of using scanning tunneling spectroscopy (i) to detect the Majorana fermion in this setup and (ii) to study excited states bound to the vortex core. The Majorana fermion manifests itself as an $H$-dependent zero-bias anomaly of the tunneling conductance. The excited states spectrum differs from the spectrum of a typical Abrikosov vortex, providing additional indirect confirmation of the Majorana state observation. We also study [3] how to manipulate and probe Majorana fermions using super-conducting circuits. In [4] we consider a semiconductor nanowire quantum dot with strong spin-orbit coupling (SOC), which can be used to achieve a spin-orbit qubit. In contrast to a spin qubit, the spin-orbit qubit can respond to an external ac electric field, i.e., electric-dipole spin resonance. We develop a theory [4] that can apply in the strong SOC regime. We find that there is an optimal SOC strength $\eta_{\mathrm{opt}}=\surd $2/2, where the Rabi frequency induced by the ac electric field becomes maximal. Also, we show that both the level spacing and the Rabi frequency of the spin-orbit qubit have periodic responses to the direction of the external static magnetic field. These responses can be used to determine the SOC in the nanowire. \\[4pt] [1] A.L. Rakhmanov, A.V. Rozhkov, F. Nori, \textit{Majorana Fermions in Pinned Vortices}, Phys. Rev. B \textbf{84}, 075141 (2011).\\[0pt] [2] R.S. Akzyanov, A.V. Rozhkov, A.L. Rakhmanov, F. Nori, \textit{Tunneling Spectrum of a Pinned Vortex with a Robust Majorana State}, arXiv:1307.0923.\\[0pt] [3] J.Q. You, Z.D. Wang, W. Zhang, F. Nori, \textit{Manipulating and probing Majorana fermions using superconducting circuits }(2011). arXiv:1108.3712\\[0pt] [4] R. Li, J.Q. You, C.P. Sun, F. Nori, \textit{Controlling a Nanowire Spin-Orbit Qubit via Electric-Dipole Spin Resonance}, Phys. Rev. Lett. \textbf{111}, 086805 (2013).   

Engineering vacuum and thermal fluctuations with metamaterials

In 1987, the search for a medium that expels vacuum fluctuations in a prescribed bandwidth and rigorously forbids spontaneous emission led to the concept of the photonic crystal. Here, we argue that the search for the opposite effect: enhancing vacuum and thermal fluctuations inside a medium within a prescribed bandwidth can be accomplished by an artificial medium known as a hyperbolic metamaterial. We will present the fluctuational electrodynamics of such media with hyperbolic dispersion and show that they exhibit broadband super-planckian thermal emission in the near-field. We will also present the quantum nanophotonics of such media where the enhanced vacuum fluctuations within the medium leads to a broadband Purcell effect. Finally, we will present associated effects in such artificial media such as optical topological transitions which make it viable to experimentally detect the signatures of these predicted effects.   

Topological valleytronics in 2D Transition Metal Dichalcogenides Semiconductors

In many crystals the Bloch bands have inequivalent and well separated energy extrema in the momentum space, known as valleys. The valley index constitutes a well-defined discrete degree of freedom for low-energy carriers that may be used to encode information. This has led to the concept of valleytronics, a new type of electronics based on manipulating the valley index of carriers. In the first part of this talk, I will describe a general scheme based on inversion symmetry breaking to control the valley index, using graphene and monolayers of MoS2 as an example. In particular, the valley Hall effect and valley-dependent optical selection will be discussed. In the second part, I will discuss the Berry phase effect on excitons formation and dynamics.   

Polaron-like nature of massive Dirac fermions in valleytronic materials and topological insulators

In this talk I will investigate the interplay of curvature modifications and spin-orbit interaction. As is well known, band curvature modifications can origin from electron-phonon interaction or other distortions, for example, the cubic or even higher in momentum warping term and the quadratic in momentum classical term, both of which modify drastically the transport properties (optical and magneto-optical, for example) of Dirac fermions in a topological insulator. A not so well known fact is that Berry curvature will also be modified by electron-phonon interaction and this may change the topology and dichroism of the system. Strong coupling theory of small polarons will be revisited in the presence of spin-orbit interaction and wave functions obtained there will be useful to construct low energy effective theory from the strong coupling limit. Phonon structures can be identified in many experiments, for example, STM, ARPES, Raman spectra, inelastic neutron scattering and so on. We have provided results from theoretical investigations for the first two experiments. In a recent work we have studied the optical conductivity in the presence of three terms, which are cubic, quadratic and linear in momentum, and find the interband optical conductivity will vanish when a SU(2) symmetry is recovered. This can be verified in both semiconductors and cold atoms, although the energy scale of these two systems differs by at least 1000000 times. \\[4pt] [1] Phys. Rev. B \textbf{87}, 155416 (2013).\\[0pt] [2] Phys. Rev. B \textbf{88}, 045414 (2013).\\[0pt] [3] Phys. Rev. B \textbf{88}, 045417 (2013).\\[0pt] [4] Phys. Rev. B \textbf{88}, 195133 (2013).\\[0pt] [5] Scientific Reports \textbf{3}, 02828 (2013).   

Enhanced Valley Splitting for Quantum Electronics in Silicon

Silicon is a placid environment for quantum degrees of freedom with long spin and valley coherence times [1]. A natural drawback is that the same features that protect the quantum state from its environment also hamper its control with external fields. Indeed, engineered nanostructures typically lead to sub-meV splittings between valley states [2], hindering the implementation of both spin [1] and valley [3] based quantum devices. We will discuss the microscopic theory of valley splitting [2,4], presenting three schemes to control valleys on a scale higher than 1 meV: a) in a quantum well, the adoption of a barrier constituted of a layered heterostructure might lead to constructive reflection if the layer thicknesses match the electron wavelength, in analogy with a Bragg mirror [5]; b) the disparity between the high valley splitting in a impurity donor potential and the low splitting in a Si/Insulator interface may be harnessed controlling the tunneling between these two states, so that the valley splitting may be controlled digitally [6]; c) intrinsic Tamm/Shockley interface states might strongly hybridize with conduction states, leading to a much enhanced valley splitting[4], and its contribution to the 2DEG ground state may be experimentally identified [7]. We argue that this effect is responsible for the enhanced splitting in Si/BOX interfaces [8]. \\[4pt] [1] F. Zwanenburg et al., Rev. Mod. Phys. \textbf{85}, 961 (2013).\\[0pt] [2] A Saraiva, M. J. Calder\'{o}n, Xuedong Hu, S. Das Sarma and Belita Koiller, PRB \textbf{80}, 081305 (2009).\\[0pt] [3] D. Culcer, A. L. Saraiva, Belita Koiller, Xuedong Hu, and S. Das Sarma, PRL \textbf{108}, 126804 (2012).\\[0pt] [4] A. Saraiva, Belita Koiller and M. Friesen, Phys. Rev. B~\textbf{82}, 245314 (2010).\\[0pt] [5] L. Zhang, J.-W. Luo, A Saraiva, Belita Koiller, Alex Zunger, Nature Comm. \textbf{4}, 2396 (2013).\\[0pt] [6] A. Baena, A. L. Saraiva, Belita Koiller, and M. J. Calder\'{o}n, PRB~86, 035317 (2012).\\[0pt] [7] A. Dusko, A. Saraiva and Belita Koiller, arXiv:1310.6878 (2013).\\[0pt] [8] K. Takashina, Y. Ono, A. Fujiwara, Y. Takahashi and Y. Hirayama, \textit{PRL} \textbf{96, }236801 (2006).