Odd-Integer Quantum Hall States and Giant Spin Susceptibility in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-Type Few-Layer<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>WSe</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

Coulomb interaction between electrons lies at the heart of magnetism in solids 1, 2 . In contrast to conventional two-dimensional (2D) systems, electrons in monolayer transition metal dichalcogenides (TMDs) possess coupled spin and valley degrees of freedom by the spin-orbit interaction 3, 4 . The electrons are also strongly interacting even in the high-density regime because of the weak dielectric screening in two dimensions and a large band mass 5,6 . The combination of these properties presents a unique platform for exploring spin and valley magnetism in 2D electron liquids. Here we report an observation by magneto-photoluminescence spectroscopy of a nonlinear valley Zeeman effect, correlated with an over fourfold enhancement in the exciton g-factor in monolayer WSe 2 . The effect occurs when the Fermi level crosses the spin-split upper conduction band, corresponding to a change of the spin-valley degeneracy from 2 to 4. The enhancement increases, shows no sign of saturation as the sample temperature decreases. Our result suggests the possibility of rich manybody ground states in monolayer TMDs with multiple internal degrees of freedom.Electrons in monolayer transition metal dichalcogenide (TMD) semiconductors with a honeycomb lattice structure possess a two-fold valley degree of freedom, corresponding to the K and K' point of the Brillouin zone [3][4][5] . Because of the strong spinorbit interaction, the bands are spin split with the valley and spin locked to satisfy the time reversal symmetry 3-5 (Fig. 1a). Similar to the spin, the valley carries a magnetic moment and has been proposed as a new type of information carriers 3,7 . Several new valley dependent phenomena, including the valley contrasting optical selection rules [8][9][10][11][12] , valley Zeeman effect [13][14][15][16][17][18] and valley Hall effect 19,20 , have emerged in the independentparticle picture and provided means to manipulate the valley polarization. In particular, the valley exciton splitting in an out-of-plane magnetic field has been shown to depend linearly on the field up to 65 Tesla 18 and an exciton g-factor between -2 and -4 has been reported for various monolayer TMDs 6, 13-18 . On the other hand, even in the relatively high-density regime (~ 5×10 !" cm -2 ), electrons in monolayer TMDs are strongly interacting with the Coulomb energy (~ 100's meV) dominating all other energy scales (Fermi energy, conduction band spin splitting at K/K' ~ 10's meV for WSe 2 ) 6 . The valley magnetic response of the independent-particle picture is thus expected to be modified by the strong electron-electron interaction and the system may even develop a magnetically ordered ground state [21][22][23][24] . A unique scenario emerges when the Fermi level crosses the spin-split upper conduction band (Fig. 1a), where the spin-valley degeneracy ! ! changes from 2 to 4 ( ! and ! stand for the spin and valley degeneracy, respectively) 6 . We observe a strongly enhanced valley magnetic response, which can be understood as a consequence of a step rise in ...

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“…| ! | in similar material systems but under different conditions have also been reported by recent studies [40][41][42] .…”

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confidence: 80%

Strongly Interaction-Enhanced Valley Magnetic Response in Monolayer WSe2

2018

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“…A similar behavior was observed even for bilayer WSe 2 , suggesting indeed that E Z is insensitive to θ, and in turn, to the parallel component of the B-field (B || ) in both mono-and bilayer WSe 2 . This observation is in stark contrast to the vast majority of 2DESs explored in host semiconductors such as Si [6,18], GaAs [7], AlAs [8], black phosphorus [19], and bulk WSe 2 [11].…”

mentioning

confidence: 72%

Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe2

et al. 2017

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We report a study of the quantum Hall states (QHSs) sequence of holes in mono-and bilayer WSe2. The QHSs sequence transitions between predominantly even and predominantly odd filling factors as the hole density is tuned in the range 1.6 − 12 × 10 12 cm −2 . The QHSs sequence is insensitive to the transverse electric field, and tilted magnetic field measurements reveal an insensitivity of the QHSs sequence to the in-plane magnetic field, evincing that the hole spin is locked perpendicular to the WSe2 plane. These observations imply that the QHSs sequence is controlled by the Zeemanto-cyclotron energy ratio, which remains constant as a function of perpendicular magnetic field at a fixed carrier density, but changes as a function of density due to strong electron-electron interaction.The strong spin-orbit coupling and broken inversion symmetry in 2H transition metal dichalcogenide (TMD) monolayers leads to coupled spin and valley degrees of freedom [1]. Breaking the time reversal symmetry by applying a perpendicular magnetic field further lifts the valley degeneracy, thanks to the spin (valley) Zeeman effect [2,3]. Insights into the Zeeman effect, a fundamental property of TMDs, have been provided by magnetooptical measurements of TMD monolayers, which report the exciton g-factors from luminescence shifts in perpendicular magnetic fields [4,5]. While magnetotransport measurements have been traditionally used to determine the effective g-factor (g * ) in several two-dimensional electron systems (2DESs) [6][7][8], the lack of reliable low temperature Ohmic contacts, combined with a moderate mobility, have hampered a similar progress in TMDs. Recent advances in sample fabrication have now facilitated more detailed studies of the electron physics in TMDs [9][10][11]. Tungsten diselenide (WSe 2 ) is of particular interest because of a large spin-orbit splitting in the valence band [12], high-mobility [10], and low temperature Ohmic contacts [13].In this work, we report on the magnetotransport of holes in mono-and bilayer WSe 2 in the quantum Hall regime. An examination of the Shubnikov-de Haas (SdH) oscillations, and the quantum Hall states (QHSs) sequence reveals interesting carrier density-dependent transitions between predominantly even and predominantly odd filling factors (FFs) as the hole density is tuned. Measurements in tilted magnetic fields reveal an insensitivity of the QHSs sequence to the in-plane magnetic field, indicating that the hole spin is locked perpendicular to the WSe 2 plane. The QHSs sequence is also found to be insensitive to the applied transverse electric field. These observations can be explained by a Zeeman-tocyclotron energy ratio which remains constant as a function of perpendicular magnetic field at a fixed carrier density, but changes as a function of density because of strong electron-electron interaction.Figure 1(a) shows the schematic cross section, and Fig. 1(b) the optical micrograph of an hBN encapsulated WSe 2 sample with bottom Pt contacts, and separate local top-and back-gates. ...

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“…However, unlike those orbitals at ±K points with strong SOC, the orbitals at Γ point are composed of the delocalized out‐of‐plane 5

d_{z^{2}}

orbitals of W atoms, thereby a negligibly weak SOC. As a result, the enhanced g * in 8‐layer WSe 2 is reasonably attributed to the short‐range electron‐electron interactions, rather than the SOC in mono‐ and bilayer cases …”

Section: Quantum Hall Effect and Quantum Oscillationsmentioning

confidence: 94%

“…For multilayer WSe 2 , Xu et al. observed an unconventional QH states sequence with predominantly odd‐integer filling factors at moderate B ‐fields . The SdH and QHE measurements unraveled a giant spin susceptibility χ≈5.65 m 0 and a large hole mass of m * ≈0.8 m 0 in 8‐layer WSe 2 , giving rise to an extremely large g * ≈6.52.…”

Section: Quantum Hall Effect and Quantum Oscillationsmentioning

confidence: 98%

Recent Advances in Quantum Effects of 2D Materials

Chen

et al. 2019

Adv Quantum Tech

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The celebrated discovery of graphene has spurred tremendous research interest in two‐dimensional layered materials (2DLMs) with unique attributes in the quantum regime. In 2DLMs, each layer is composed of a covalently bonded lattice and is weakly coupled to its neighboring layers by van der Waals interactions. There are abundant members in this 2DLM family beyond graphene, such as transition metal dichalcogenides (MX2, M = Mo, W; X = S, Se, Te), semimetal chalcogenide (InSe), black phosphorus, etc. The 2DLMs afford rich and ideal material platforms for studying quantum effects and their corresponding applications in the two‐dimensional (2D) limit. In this review, the emerging quantum effects in 2DLMs are examined with particular focus on their band structure evolvement, valleytronics, and quantum Hall/quantum spin Hall effects. Based on the summary of quantum effects discovered in 2DLMs, the future research directions and prospective applications are also discussed.

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Odd-Integer Quantum Hall States and Giant Spin Susceptibility inp-Type Few-LayerWSe2

Cited by 42 publications

References 41 publications

Strongly Interaction-Enhanced Valley Magnetic Response in Monolayer WSe2

Strongly Interaction-Enhanced Valley Magnetic Response in Monolayer WSe2

Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe2

Recent Advances in Quantum Effects of 2D Materials

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