Intrinsic bending flexoelectric constants in two-dimensional materials

Zhuang, Xiaoying; He, Bo; Javvaji, Brahmanandam; Park, Harold S.

doi:10.1103/physrevb.99.054105

Cited by 76 publications

(89 citation statements)

References 76 publications

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“…(20) is the average of O in the maximally mixed state of H ⊗k , which does not equal the right-hand side of Eq. (17). If |E i1 , .…”

Section: B Definition Of K-ethmentioning

confidence: 99%

“…, which implies that all the kth moments of ν equal those of the HRU [5][6][7]. The previous studies [12][13][14][15][16][17] revealed the fundamental relationship between unitary k-designs and information scrambling. As discussed below, on the other hand, there is a subtle issue about the relationship between unitary k-designs and Hamiltonian dynamics [12].…”

Section: A Basic Ideamentioning

confidence: 99%

“…(86) holds. For the LTE L, M (k) L equals the set of operators that satisfy the exact k-ETH (17). In other words, the k-ETH is regarded as a specific case of PU k-designs, where pseudo-randomness originates from the randomtime sampling of quantum chaotic dynamics.…”

Section: B Definition Of Pu Designsmentioning

confidence: 99%

“…The second example is the ensemble of random diagonal-unitaries [11,60,61], which includes the LTE L as a special case. We will derive an explicit expression of the set of operators that satisfy the exact k-ETH (17).…”

Section: Random Diagonal-unitariesmentioning

confidence: 99%

“…The HRU requires an exponential number of quantum gates to implement, because it is the most random dynamics with full complexity [8], while unitary k-designs can be approximately implemented by using a polynomial number of quantum gates [9][10][11]. It has been argued that unitary k-designs have the fundamental relationship with information scrambling [12][13][14][15][16][17] quantified by out-of-time-ordered correlators (OTOCs) [18][19][20][21][22][23][24][25], which is originally motivated by the black hole information paradox [26][27][28]. There are also several studies that discussed the relationship between thermalization and information scrambling in quantum chaotic systems [29][30][31][32][33][34][35][36][37][38][39].…”

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confidence: 99%

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Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

2020

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Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order complexity, which is represented by the eigenstate thermalization hypothesis (ETH) stating that individual energy eigenstates are thermal. Here, we propose a higher-order generalization of the ETH, named the k-ETH (k = 1, 2, . . . ), to quantify higher-order complexity of quantum many-body dynamics at the level of individual energy eigenstates, where the lowest order ETH (1-ETH) is the conventional ETH. The explicit condition of the k-ETH is obtained by comparing Hamiltonian dynamics with the Haar random unitary of the k-fold channel. As a non-trivial contribution of the higher-order ETH, we show that the k-ETH with k ≥ 2 implies a universal behavior of the kth Rényi entanglement entropy of individual energy eigenstates. In particular, the Page correction of the entanglement entropy originates from the higher-order ETH, while as is well known, the volume law can be accounted for by the 1-ETH. We numerically verify that the 2-ETH approximately holds for a nonintegrable system, but does not hold in the integrable case. To further investigate the information-theoretic feature behind the k-ETH, we introduce a concept named a partial unitary k-design (PU k-design), which is an approximation of the Haar random unitary up to the kth moment, where partial means that only a limited number of observables are accessible. The k-ETH is a special case of a PU k-design for the ensemble of Hamiltonian dynamics with random-time sampling. In addition, we discuss the relationship between the higher-order ETH and information scrambling quantified by out-of-time-ordered correlators. Our framework provides a unified view on thermalization, entanglement entropy, and unitary k-designs, leading to deeper characterization of higher-order quantum complexity. Contents

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“…(20) is the average of O in the maximally mixed state of H ⊗k , which does not equal the right-hand side of Eq. (17). If |E i1 , .…”

Section: B Definition Of K-ethmentioning

confidence: 99%

Section: A Basic Ideamentioning

confidence: 99%

Section: B Definition Of Pu Designsmentioning

confidence: 99%

Section: Random Diagonal-unitariesmentioning

confidence: 99%

mentioning

confidence: 99%

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Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

2020

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Out‐of‐Plane Polarization in Bent Graphene‐Like Zinc Oxide and Nanogenerator Applications

Tan

Willatzen

Wang

2019

Adv Funct Materials

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Highly efficient piezoelectric nanogenerator operation is demonstrated based on dynamic bending of graphene-like ZnO nanosheets. Energy is harvested by an external resistor by virtue of a strong time-varying piezoelectric polarization component perpendicular to the graphene-like ZnO plane. It is shown analytically and verified numerically using molecular dynamics simulations that the 6m2 point group of flat graphene-like ZnO is reduced to monoclinic m symmetry for bent graphene-like ZnO. The latter symmetry allows for a nonzero and large piezoelectric polarization component perpendicular to the plane of the 2D structure. The numerical results confirm that flexoelectric effects are negligible subject to graphene-like ZnO bending operation.

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Acoustic Gain in Solids due to Piezoelectricity, Flexoelectricity, and Electrostriction

Willatzen

Gao

Christensen

et al. 2020

Adv Funct Materials

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A quantitative discussion of the combined influence of three electro mechanical effects: piezoelectricity, flexoelectricity, and electrostriction in solids is provided for acoustic absorption and gain. While piezoelec tricity occurs in noncentrosymmetric materials only, flexoelectricity and electrostriction exist in all materials. Two important new results are dem onstrated: 1) the possibility to realize acoustic gain in all materials (cen trosymmetric and noncentrosymmetric) when the acoustic Cherenkov condition is fulfilled, and 2) realization of acoustic gain in the presence of a strong dc electric field, even when the Cherenkov condition is not fulfilled, in the case of strong crosscoupling between piezoelectricity, flexoelec tricity, and electrostriction. A simple analytical expression for the acoustic dispersion relation is derived for the combined effect of piezoelectricity, flexoelectricity, and electrostriction. At lower frequencies, the piezoelectric effect dominates for inversionasymmetric materials. At high frequencies (≈>1 MHz) flexoelectricity becomes increasingly important and eventually provides a major mechanism for gain and absorption in barium titanate (BaTiO 3). In the presence of strong electric fields (≈>1 MV m −1), electrostric tion provides a dominant isolated contribution to absorption/gain in BaTiO 3. Strong coupling between the three electromechanical contributions determines the total absorption/gain coefficient.

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Intrinsic bending flexoelectric constants in two-dimensional materials

Cited by 76 publications

References 76 publications

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

Out‐of‐Plane Polarization in Bent Graphene‐Like Zinc Oxide and Nanogenerator Applications

Acoustic Gain in Solids due to Piezoelectricity, Flexoelectricity, and Electrostriction

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