Unconventional quasiparticle scattering in disordered 2D TMDs

Kristen Kaasbjerg (kkaa@nanotech.dtu.dk)

Dept. of Micro- and Nanotechnology

Technical University of Denmark

Mathematical Modeling of 2D materials IMA workshop, UMN, 05/2017

Collaboration:

T. Low, UMN A.-P. Jauho, DTU J. Martiny, DTU

Atomic disorder in 2D TMDs

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Komsa et al., PRL 109, 035503 (2012)

(a) Atomic structures of a single-layer MoS2 by aberration-corrected TEM. The SVs are

highlighted by red arrows. Upper inset shows the MoS2 sample edge to confirm the single-

layer nature. Lower inset shows the schematics of the highlighted region. Scale bar, 10 nm. (b)

Intensity profile of along lattices with (red

symbol) and without (black symbol) SV, along with simulations of a single SV (red line). The

corresponding sections are highlighted in a by dashed lines. Inset shows the simulated TEM

image of a single SV. (c) Histogram of SV density. The density was obtained by counting

the number of SVs in 5 × 5 nm2 areas.

Three defect states are generated inside the band gap. Since the V_S has trigonal symmetry [Figs. 6(a) and 6(b)], the defect states can be classified as a singlet a1 state and doubly degenerate e states. Due to the absence of an anion in the single-layer MoS2, in the neutral charge state (V_S^0), two excess electrons occupy the a1 state, and the two e states are empty, as shown in Fig. 6(c), where the Fermi level is located in between the a1 and e states, which agrees with the previous DFT calculation [25] and scanning tunneling spectroscopy [24]. The charge density of the a1 state is shown in Fig. 6(a), and that of the e states are in Fig. 6(b). The Kohn-Sham (KS) level of the a1 state is found to be near the VBM, and that of the empty e degenerate states is located inside the band gap, asshown in Fig. 6(c).

Therefore the V_S is an important (abundant) defect in single-layer MoS2, whereas it acts as an electron trap center with ionized into V_S^-1 in a typical n-type MoS2.

The electronic density of states of V_S^-1 is shown in Fig. 6(d). The V_S-1 state, which is stable in the n-type single-layer MoS2, is spin-polarized having the spin moment of μ = 1/2. The e states are singly occupied, and the Fermi level crosses the doubly degenerate e levels of the majority spin. Whether the spin moments of V_S-1’s in a single-layer MoS2 have a magnetic ordering is not clear yet and beyond our scope.

The V_S^-2 state can have a μ = 1 spin moment, but it is unstable. When the electrons occupy the e states, the strong on-site electron-electron (repulsive) interaction at the V_S site destabilizes the q < −1 charged states, as can be seen from the higher e levels in V_S-1 than those in V_S^0 [Figs. 6(c) and 6(d)].

Qiu et al., Nature Communications 4, 2642 (2013)

Noh et al., PRB 89, 205417 (2014)

The analysis of the electronic structure revealed an occupied bonding type vacancy state close to valence band maximum and an empty antibonding type state in the mid gap, which stabilizes the structure. For the occupied bonding defect state, the electronic charge is localized at the vacancy site, analogous to bulk MoS2, where Mo atoms donate electrons to S atoms. This is true for all of the semiconducting materials: MoX2, WX2, and PtX2. The rest of the considered materials are etals or semimetals, for which the bonding vacancy state may become unoccupied, which is reflected in larger relaxation and lower formation energies.

Noh et al., PRB 89, 205417 (2014)

Lin et al., Nature Communications 6,

6736 (2014)

Noh et al., PRB 89, 205417 (2014)

MoS2

S vacancy

Mo vs S vacancies?

Scanning tunneling spectroscopy (WSe2)

3

Yankowitz et al., PRL 115, 136803 (2015)

Liu et al., Nature Comm. 6, 8180 (2015)

JDOS

They argue that they don’t tunnel into the states at K,K’ and therefore don’t consider scattering between them.

FT of the LDOS:

Single-impurity Green’s function:

JDOS:

FT-STS: Theory

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Schmidt et al.,

Nano Lett. 14, 1909 (2014)

STS at finite q

;

Disorder T matrix

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Schmidt et al.,

Nano Lett. 14, 1909 (2014)

Ingredients:

• band structure:

• disorder matrix elements (next slide)

MoS2

Take-home message

Don’t invert that matrix!

NxN BZ sampling → N2xN2 matrices:

K Q

Atomistic supercell method Scattering due to perturbations in the

crystal potential:

Disorder scattering potential:

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• Disorder potential Vi and

Bloch functions calculated with DFT-LDA (PAW).

• Momentum conservation: k’ → k + q.

Atomic disorder (substitutional, vacancies, etc), impurities, phonons:

Atomic monovacancies (MoS2)

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δ-function disorder:

Mo vacancy:

FT-STS: Mo vacancy

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q1 q1

FT-STS: Mo vacancy

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q1 q1

FT-STS: Mo vacancy

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q=2k k

q

q1 q1

FT-STS: Mo vacancy

11

q5

q5 q1

q1

q2

q6

q6

q2

q3

q3

q4

q7

q4

q7

FT-STS: S vacancy

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FT-STS: S vacancy

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FT-STS: S vacancy

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q1 q1

???

C3 symmetry:

• γi,c = 1 for Mo centered disorder

• γi,c ≠ 1 for S centered disorder

Selection rule: C3 symmetry

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S vacancy

FT-STS: S vacancy

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q5

q5 q1

q1

q2

q6

q6

q2

q3

q3

q4

q7

q4

q7

Midgap states

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Mo vacancy

S vacancy

Gated TMDs

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• FT-STS provides a unique fingerprint of vacancy type and their scattering properties.

• Symmetry-induced suppression (C3) of intervalley scattering in addition to spin-valley coupling.

• Long valley lifetimes even in disordered TMDs.

• FT-STS useful tool for resolving band-structure issues (K vs Q valley ordering) in mono- and multilayer systems.

• Further STS studies on TMD systems.

• Impact of atomic vacancies on transport in TMDs.

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Summary