Dynamics of the effective mass and the anomalous velocity in two-dimensional lattices

Fang, Yiqi; Duque-Gomez, Federico; Sipe, J. E.

doi:10.1103/physreva.90.053407

Cited by 6 publications

(9 citation statements)

References 42 publications

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“…This results in the form of the usual effective mass term for electrons and holes in

1 / m_{i j}^{*} (t)

in the long‐time limit, noting that

k (t) = K + {boldk}_{c} (t)

. A similar behavior was recently observed in different systems for ultracold atoms in optical lattices studied in previous studies . As a point of emphasis, we note that the inertial effective mass becomes quite central in studies concerning complex quasiparticle formation and for terahertz electromagnetic field generation .…”

Section: Density Matrix Approachsupporting

confidence: 79%

“…In a later section on the density matrix formulation, we obtain an identical result to Equation , but with density matrix initial conditions; in that context, a detailed analysis of the characteristics for

⟨ v ⟩

and

\frac{d ⟨ v ⟩}{d t}

will then be discussed. This includes a discussion for expressing Equation in the form

\frac{d {⟨ v ⟩}_{i}}{d t} = \sum_{j} \frac{1}{m_{i j}^{*} (k (t))} {boldF}_{j}

where

1 / m_{i j}^{*} (k (t))

is referred to as a dynamical inverse effective mass tensor as it has an implicit dependence on the electric field and time due to the presence of

k (t) = K + {boldk}_{c} (t)

.…”

Section: Transport Properties: Velocity Acceleration and Dynamical mentioning

confidence: 99%

“…The specific behavior of Ψðr, tÞ will depend on the initial conditions. For example, if initially the valence band is populated with a distribution in K so that a vK ðt 0 Þ 6 ¼ 0 and the conduction band is empty, i.e., a cK ðt 0 Þ ¼ 0, then one can see from Equation (34) and the definition of AðtÞ in Equation (31c) that the initial distribution will redistribute in a conserving manner from one instantaneous eigenstate to the other with transition probability jp n c n v ðtÞj 2 . In contrast, if p n c n v ðtÞ ≃ 0 (no transition amplitude) and a cK ðt 0 Þ ¼ 0, then choosing a vK ðt 0 Þ ¼ δ KK 0 gives rise to Ψðr, tÞ ¼ Ψ n v K 0 ðr, tÞe…”

Section: Time-dependent Wave Function: Two-band Modelmentioning

confidence: 99%

“…Detailed analysis of time evolution can be found in previous studies. [31][32][33] In the next section, we will use the wave function of Equation (34) to calculate key expectation values of the electron velocity and acceleration and determine their associated response to the electric field.…”

Section: Time-dependent Wave Function: Two-band Modelmentioning

confidence: 99%

“…where 1=m Ã ij ðkðtÞÞ is referred to as a dynamical inverse effective mass tensor [34] as it has an implicit dependence on the electric field and time due to the presence of kðtÞ ¼ K þ k c ðtÞ.…”

Section: Transport Properties: Velocity Acceleration and Dynamical Effective Massmentioning

confidence: 99%

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The Bloch Electron Response to Electric Fields: Application to Graphene

Iafrate

Sokolov

2020

Physica Status Solidi (b)

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The theory of Bloch electron dynamics for carriers in homogeneous electric fields of arbitrary time dependence is developed in consideration of the electronic transport properties in graphene. The general approach is to use the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including Zener tunneling, is treated exactly; also, the electric field is described in the vector potential gauge. Within the ABR, the instantaneous eigenstates for the central Hamiltonian are described and utilized to develop both the time‐dependent wave functions and the single‐particle density matrix pictures with explicit application to intrinsic graphene. The Bloch electron analysis for graphene in a constant electric field reveals the explicit manifestation of electron–hole pair creation, Bloch oscillations, and Wannier–Stark localization. The average velocity and acceleration are established as an explicit function of the electric field, and their behavior is characterized on short and long time scales. Further, it is shown that the average acceleration in a nonvanishing electric field gives rise to an electric field induced dynamical effective mass tensor in the direction of the field.

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“…This results in the form of the usual effective mass term for electrons and holes in

1 / m_{i j}^{*} (t)

in the long‐time limit, noting that

k (t) = K + {boldk}_{c} (t)

Section: Density Matrix Approachsupporting

confidence: 79%

⟨ v ⟩

and

\frac{d ⟨ v ⟩}{d t}

will then be discussed. This includes a discussion for expressing Equation in the form

\frac{d {⟨ v ⟩}_{i}}{d t} = \sum_{j} \frac{1}{m_{i j}^{*} (k (t))} {boldF}_{j}

where

1 / m_{i j}^{*} (k (t))

is referred to as a dynamical inverse effective mass tensor as it has an implicit dependence on the electric field and time due to the presence of

k (t) = K + {boldk}_{c} (t)

.…”

Section: Transport Properties: Velocity Acceleration and Dynamical mentioning

confidence: 99%

Section: Time-dependent Wave Function: Two-band Modelmentioning

confidence: 99%

Section: Time-dependent Wave Function: Two-band Modelmentioning

confidence: 99%

Section: Transport Properties: Velocity Acceleration and Dynamical Effective Massmentioning

confidence: 99%

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The Bloch Electron Response to Electric Fields: Application to Graphene

Iafrate

Sokolov

2020

Physica Status Solidi (b)

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Experimental Study of Effective Mass and Spin–Orbital Energy of the Al₂O₃/NiO Nanoheterostructure Material

et al. 2019

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The effective mass of the materials relies on exciton dynamics which is greatly dominated by energy gap of the materials. We examined the effective mass for the Al 2 O 3 /NiO nanoheterostructure material through polarization in the dielectric study. The mean optical effective mass was calculated to be m opt * = 5.69645 × 10 −20 m op /m 0 in the UV−visible region (1 × 10 6 to 5.4 × 10 6 Hz). From the group and phase velocity values, we observed that Al 2 O 3 /NiO is an anisotropic material. The electron spin−orbit energy splitting associated to electron in the valence band was identified using the Gaussianconfining 3D potential under normalized angular momentum (n, l = 0, 1, 2, 3). The 1S ( 1 S 1/2 ) and 2S ( 2 S 1/2 ) orbital ionization energies were calculated to be −6.08 and −5.99 eV for AlO 3 /NiO. The orbital ionization energies were established from the Bohr radius a B = 5.29 × 10 −11 m and donor Rydberg constant R y = 1.097 × 10 7 m −1 of the identical hydrogen atom. Our study gives insights into the exciton dynamics and calculation of orbital energy for the nanoheterostructure materials.

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Wigner transport in linear electromagnetic fields

Etl,

Ballicchia,

Nedjalkov

et al. 2024

J. Phys. A: Math. Theor.

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The widespread Wigner formulation of quantum mechanics is obtained with the help of the Weyl transform of the density matrix and the corresponding von Neumann equation formulated in terms of scalar potentials only. To obtain a gauge-invariant Wigner theory in an electromagnetic field, one can apply a Weyl-Stratonovich transform to remove the vector potential from the evolution equation of the Wigner function. This corresponds to a variable transform replacing the canonical momentum with the kinetic momentum, which, being a physical quantity, is gauge-invariant. The obtained multidimensional equation is, however, numerically very challenging. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and enables to gain first experience with a gauge-invariant Wigner equation. In the latter, the Liouville operator interplays with a term containing high-order mixed derivatives on position and momentum, which replaces the Wigner potential of the electrostatic Wigner theory. We present an equation analysis and show that a finite difference approach to the high-order derivatives allows for reformulation into a Fredholm integral equation. The resolvent expansion of the latter contains consecutive integrals, which is favorable for Monte Carlo solution approaches. To that end, we present two stochastic (Monte Carlo) algorithms that evaluate averages of generic physical quantities or directly the Wigner function. The algorithms give rise to a quantum particle model, which interprets quantum transport in heuristic terms.

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Dynamics of the effective mass and the anomalous velocity in two-dimensional lattices

Cited by 6 publications

References 42 publications

The Bloch Electron Response to Electric Fields: Application to Graphene

The Bloch Electron Response to Electric Fields: Application to Graphene

Experimental Study of Effective Mass and Spin–Orbital Energy of the Al₂O₃/NiO Nanoheterostructure Material

Wigner transport in linear electromagnetic fields

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Dynamics of the effective mass and the anomalous velocity in two-dimensional lattices

Cited by 6 publications

References 42 publications

The Bloch Electron Response to Electric Fields: Application to Graphene

The Bloch Electron Response to Electric Fields: Application to Graphene

Experimental Study of Effective Mass and Spin–Orbital Energy of the Al2O3/NiO Nanoheterostructure Material

Wigner transport in linear electromagnetic fields

Contact Info

Product

Resources

About

Experimental Study of Effective Mass and Spin–Orbital Energy of the Al₂O₃/NiO Nanoheterostructure Material