Scientific Sources — Case38
References
Daniel Moos, Hannah Jürß and Dieter Bauer, Intense-laser-driven electron dynamics and high-order harmonic generation in solids including topological effects, Physical Review A 102, 053112 (2020).
Two-band dynamics, radiation observables, valley-resolved response, coherent occupied-band integration, and polarization interpretation.
Relevant locations
Eqs. (25)-(28), p. 053112-3
Eq. (54), p. 053112-4; Eq. (57), p. 053112-5
Eq. (67), p. 053112-6
Eqs. (68)-(71), Fig. 2 and model cases, p. 053112-7
Eq. (72), Fig. 3(a,b): fixed K; Fig. 3(c,d): fixed K-prime; Fig. 4(a-d): velocity-plane trajectories; discussion, p. 053112-8
Integrated-response discussion, p. 053112-8; Fig. 5(a,b) and conclusions, p. 053112-9
Appendix B, Eqs. (B1)-(B8), p. 053112-11; coupling continuation, p. 053112-12
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Moos, Jürß and Bauer, Phys. Rev. A 102, 053112 (2020), p. 053112-7, Eqs. (68)-(71) and Fig. 2; p. 053112-11, Appendix B, Eqs. (B1)-(B8); pulse Eq. (67), p. 053112-6. |
| F2 | Moos, Jürß and Bauer (2020), p. 053112-3, Eqs. (25)-(28); Eq. (54), p. 053112-4; Eq. (57), p. 053112-5. |
| F3, O3, M4 | Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9. |
| F4 | Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window. Moos, Jürß and Bauer (2020), p. 053112-3, Eqs. (25)-(28); Eq. (54), p. 053112-4; Eq. (57), p. 053112-5. |
| O1, I1 | Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7. |
| O2, I2, M2 | Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7. |
| O4, I3, M5 | Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9. Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window. |
| M1 | Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7. Moos, Jürß and Bauer, Phys. Rev. A 102, 053112 (2020), p. 053112-7, Eqs. (68)-(71) and Fig. 2; p. 053112-11, Appendix B, Eqs. (B1)-(B8); pulse Eq. (67), p. 053112-6. |
| M3 | Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7. Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7. |
| M6 | Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9. Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7. Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7. |
| M7 | Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window. |
| V1 | Moos, Jürß and Bauer (2020), assumptions, p. 053112-1; occupied-band and interference discussion, p. 053112-5; conclusions, p. 053112-9. Risk and scope requirements implement the stated research commission, not a prescribed source-specific validation test. Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window. |
| V2 | Moos, Jürß and Bauer (2020), assumptions, p. 053112-1; occupied-band and interference discussion, p. 053112-5; conclusions, p. 053112-9. Risk and scope requirements implement the stated research commission, not a prescribed source-specific validation test. |
Formula and convention notes
The geometry is fixed by $\mathbf a_1=\boldsymbol\delta_1-\boldsymbol\delta_3=\frac a2(3,\sqrt3)$ and $\mathbf a_2=\boldsymbol\delta_2-\boldsymbol\delta_3=\frac a2(3,-\sqrt3)$, hence $\mathbf g_1=(0,\sqrt3a)$, $\mathbf g_2=-\frac a2(3,\sqrt3)$ and $\mathbf g_3=\frac a2(3,-\sqrt3)$. A compatible reciprocal basis is $\mathbf b_1=\frac{2\pi}{a}(\frac13,\frac1{\sqrt3})$, $\mathbf b_2=\frac{2\pi}{a}(\frac13,-\frac1{\sqrt3})$. In this convention $K=(2\mathbf b_1+\mathbf b_2)/3=(0.78061688498,0.45068936868)$ and $K'=(\mathbf b_1+2\mathbf b_2)/3=(0.78061688498,-0.45068936868)$ for $a=2.683$. Other coordinates require a complete physical equivalence mapping, not arbitrary valley relabelling with the drive kept incompatible.
The model has $H=\mathbf d\cdot\boldsymbol\sigma$ and energies $E_\pm=\pm|\mathbf d|$. The stated lattice, signs, two imaginary hoppings and finite pulse define one physical comparison; replacing their identity with a different model is material even if one spectral feature agrees.
The common calculation chain is $\mathbf k(t)=\mathbf k+\mathbf A(t)$, $i\dot C=H[\mathbf k(t)]C$, $C(\mathbf k,0)=C_-(\mathbf k)$, and $v_j=C^\dagger\partial_{k_j}H[\mathbf k(t)]C$. Fixed valleys use their single-point velocities. The filled band uses $v_j^{\mathrm{BZ}}(t)=\frac{V_{\mathrm{cell}}}{(2\pi)^2}\int_{\mathrm{BZ}}v_j(\mathbf k,t),d^2k$, with $V_{\mathrm{cell}}=3\sqrt3a^2/2$, before constructing radiation; an incoherent intensity sum is not equivalent.
An accepted acceleration convention is $\mathcal A_j(\Omega)=\mathcal F\dot v_j$, $Y_j(\Omega)\propto|\mathcal A_j(\Omega)|^2$ and $\Delta\phi=\arg\mathcal A_\parallel-\arg\mathcal A_\perp$. Equivalent velocity/current/Fourier routes must include the appropriate derivative-frequency/phase mapping and common normalization. Relative phase, together with magnitudes, determines polarization; helicity is interpretable only when both channels are resolved. A different overall phase-sign convention is accepted only with the helicity mapping transformed consistently.
At fixed $K$, the reference broad pattern is a change from about $-\pi/2$ in the trivial case to about $+\pi/2$ in the nontrivial case for most resolved harmonics, including the fundamental. Perpendicular even harmonics appear; the resolved trivial second harmonic has opposite helicity to the usual trivial family. These are robust family-level scientific anchors, not an every-harmonic sequence mandate.
At fixed $K'$, the trivial response is near $+\pi/2$ and the nontrivial response has harmonic-dependent/alternating changes. The source's low-order example has no fundamental flip, a second-harmonic flip, no third-to-fifth flip and a sixth-harmonic flip. The nontrivial spectrum has a gap-related dip near H13, rolloff to its left and plateau onset to its right. These explain the valley distinction; exact sequence coverage, dip depth and the detailed weak $K'$ envelope are not mandatory or pointwise scoring targets.
Similar minimum gaps at $K$ but changed trajectory chirality/complex-channel phase support the topology-sensitive broad reversal. Larger case-dependent gap differences and weaker perpendicular velocity at $K'$ support a different envelope and nonuniform phase response. Coherent occupied-band integration can preserve robust polarization while cancellation makes individual harmonics window-sensitive. Equivalent band-gap, trajectory, velocity-decomposition or equally discriminating mechanisms are accepted.
Numerical choices belong to the candidate: BZ grid, time step, solver, differentiation, Fourier window, weak-signal threshold and plot range. The $1500\times1500$ reference grid is not a duty. Missing a routine convergence checklist is neither a separate deduction nor an automatic RC3 trigger. Reliability matters only through actual affected evidence, claims or a fairly triggered material risk.
Scope of the source anchors
Two-band dynamics, radiation observables, valley-resolved response, coherent occupied-band integration, and polarization interpretation.