The Valley Hall Effect in MoS2 Transistors
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1 Journal Club 2017/6/28 The Valley Hall Effect in MoS2 Transistors Kagimura arxiv: [cond-mat.mes-hall] Kin Fai Mak 1,2, Kathryn L. McGill 2, Jiwoong Park 1,3, and Paul L. McEuen
2 Electronics Spintronics Valleytronics MRAM(Motorola) Prospective 2
3 Outline 1. Anomalous velocity 2. The valley Hall effect 3. Valley-selective circular dichroism of monolayer MoS2 4. The valley Hall effect in MoS2 transistors 3
4 1. Anomalous velocity
5 Berry curvature parameter set : instantaneous eigenstates of Hamiltonian at each value of i.e. 5
6 Hamiltonian and eigenstates Independent electron approximation periodic potential with Bloch s theorem: -dependent Hamiltonian: band index crystal momentum parameter space: Brillouin zone, 6 : basis function
7 Wave function : changes slowly in time time-dependent Scrhodinger equation: instantaneous eigenstates 7
8 First-order wave function We have an initial condition: For Integrate by parts 8
9 The average velocity Apart from the overall phase factor, velocity operator in the q representation : Berry curvature
10 uniform vector potential With electric field q-space gauge invariant crystal momentum: eigenstates: preserve the translational symmetry,
11 Anomalous velocity Berry curvature: anomalous velocity: transverse to the electric field give rise a Hall current
12 2. The valley Hall effect
13 Symmetry consideration time-reversal sym. spatial inversion sym. time-reversal and spatial inversion symmetry
14 (a) 2-valley structure
15 Valley Hall effect valley index: Valley Hall Effect: valley Hall conductivity valley current: time reversal inversion symmetry
16 Berry curvature of graphene In low energy, 1 80 (ev) (a 2 ) (b) kx ~ ~ ~ ~ ( / a)
17 Valley Hall current Anomalous velocity: Valley Hall current!
18 Pathway to valleytronics It provides a new and standard pathway to potential applications of valleytronics in a broad class of semiconductors.
19 3. Valley-selective circular dichroism of monolayer MoS2 [Ting Cao, Ji Feng, Junren Shi, Qian Niu, Enge Wang,(2012)]
20 Graphene? graphene: inversion symmetry Unprecedented control of the lattice structure on the scale of a single atom is required. Valleytronics in graphene is very difficult
21 MoS2 Mo S inversion symmetry
22 MoS2 for valleytronics 1.8eV
23 Degree of circular polarization difference between the absorption of left- and righthanded lights, between the top of the valence bands and the bottom of conduction bands circular polarization: inter-band matrix elements:
24 at in MoS K_ ev 0 K
25 Berry curvature 10 z (k) (Å 2 ) K K+
26 Hall effect
27 4. The valley Hall effect in MoS2 transistors
28 Monolayer MoS2 Hall bar device
29 The valley Hall effect
30 Doping dependence of the anomalous Hall conductivity
31 Open question What does cause the observed quick drop of Hall conductance at laser frequency? Inter-corn scattering? What are the relevant sources of scattering present in MoS 2 2, and what are their relative strengths? What are the next steps towards the long standing goal of valleytronics?
32 Summary 1. Anomalous velocity 2. The valley Hall effect 3. Valley-selective circular dichroism of monolayer MoS2 4. The valley Hall effect in MoS2 transistors
33 Electronics Spintronics Valleytronics MRAM(Motorola) Don t miss it!
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SPIN Vol. 06, No. 1640003 (2016) 1 19 c World Scientific Publishing Company arxiv:1609.06482v2 [cond-mat.mtrl-sci] 3 Nov 2016 Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications
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