Experimental Observation of Hidden Berry Curvature in Inversion-Symmetric Bulk 2H−WSe2

Abstract

We investigate the hidden Berry curvature in bulk 2H-WSe2 by utilizing the surface sensitivity of angle resolved photoemission (ARPES). The symmetry in the electronic structure of transition metal dichalcogenides is used to uniquely determine the local orbital angular momentum (OAM) contribution to the circular dichroism (CD) in ARPES. The extracted CD signals for the K and K valleys are almost identical but their signs, which should be determined by the valley index, are opposite. In addition, the sign is found to be the same for the two spin-split bands, indicating that it is independent of spin state. These observed CD behaviors are what are expected from Berry curvature of a monolayer of WSe2. In order to see if CD-ARPES is indeed representative of hidden Berry curvature within a layer, we use tight binding analysis as well as density functional calculation to calculate the Berry curvature and local OAM of a monolayer WSe2. We find that measured CD-ARPES is approximately proportional to the calculated Berry curvature as well as local OAM, further supporting our interpretation. PACS numbers: 79.60.-i, 74.20.Pq, 73.20.-rThe broken inversion symmetry in a monolayer (ML) of transition metal dichalcogenides (TMDCs) 2H-MX 2 , together with strong spin-orbit coupling (SOC), results in inequivalent valleys with spin splitting at K and K in the Brillouin zone (BZ) [1][2][3][4]. These inequivalent valleys at K and K lead to the valley Hall effect which, unlike the ordinary Hall effect, produces not only charge but also spin imbalance at the edges [1,2,[5][6][7][8]. The valley Hall effect has been understood in terms of the Berry curvature [2,[9][10][11][12]16]; the symmetries in 1ML 2H-MX 2 causes sign change in the Berry curvature as one goes from one valley (K) to an inequivalent valley (K ) in the BZ [2,5,13,14,16,17]. This allows us to understand the valley Hall effect in terms of pseudo-spins, and provides possibilities to control the pseudo-spins by an external field [2,[18][19][20][21][22][23][24][25][26].On the other hand, the Berry curvature is expected to vanish in the bulk (so does the valley Hall effect) because the bulk TMDCs have an inversion symmetry [5,24]. However, one can imagine that the valley Hall in each layer could be non-vanishing -only the sum vanishes. This may naturally introduce the concept of "hidden Berry curvature", a non-vanishing Berry curvature localized in each layer. An analogous case can be found in the case of the hidden spin polarization proposed and mea-sured recently [3,5,[27][28][29][30]. Existence of hidden Berry curvature implies that the topology could be determined by local field; the local symmetry determines the physics [28,31,32]. While experimental verification of hidden Berry phase in the Bloch state is highly desired, standard measurements such as quantum oscillation [33][34][35] cannot reveal hidden Berry phase because these measurements represent an averaged quantity, with hidden quantity invisible.However, if we use a external field [25] or surface sensitive techni...

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