Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
Bibliographic record
Abstract
Lifshitz transition is a kind of topological phase transition in which the Fermi surface is reconstructed. It can occur in the two-dimensional (2D) tilted Dirac materials when the energy bands change between the type-I phase ($0<t<1$) and the type-II phase ($t>1$) through the type-III phase ($t=1$), where different tilts are parametrized by the values of $t$. In order to characterize the Lifshitz transition therein, we theoretically investigate the longitudinal optical conductivities (LOCs) in type-I, type-II, and type-III Dirac materials within linear response theory. In the undoped case, the LOCs are constants either independent of the tilt parameter in both type-I and type-III phases or determined by the tilt parameter in the type-II phase. In the doped case, the LOCs are anisotropic and possess two critical frequencies determined by $\ensuremath{\omega}={\ensuremath{\omega}}_{1}(t)$ and $\ensuremath{\omega}={\ensuremath{\omega}}_{2}(t)$, which are also confirmed by the joint density of state. The tilt parameter and chemical potential can be extracted from optical experiments by measuring the positions of these two critical boundaries and their separation $\mathrm{\ensuremath{\Delta}}\ensuremath{\omega}(t)={\ensuremath{\omega}}_{2}(t)\ensuremath{-}{\ensuremath{\omega}}_{1}(t)$. With increasing the tilting, the separation becomes larger in the type-I phase whereas smaller in the type-II phase. The LOCs in the regime of large photon energy are exactly the same as that in the undoped case. The type of 2D tilted Dirac bands can be determined by the asymptotic background values, critical boundaries, and their separation in the LOCs. These can therefore be taken as signatures of Lifshitz transition therein. The results of this work are expected to be qualitatively valid for a large number of 2D tilted Dirac materials, such as 8-Pmmn borophene monolayer, $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SnS}}_{2}, {\mathrm{TaCoTe}}_{2}, {\mathrm{TaIrTe}}_{4}$, and $1{T}^{\ensuremath{'}}$ transition metal dichalcogenides, due to the underlying intrinsic similarities of 2D tilted Dirac bands.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".