An efficient algorithm to calculate intrinsic thermoelectric parameters based on Landauer approach

The Landauer approach provides a conceptually simple way to calculate the intrinsic thermoelectric (TE) parameters of materials from the ballistic to the diffusive transport regime. This method relies on the calculation of the number of propagating modes and the scattering rate for each mode. The modes are calculated from the energy dispersion (E(k)) of the materials which require heavy computation and often supply energy relation on sparse momentum (k) grids. Here an efficient method to calculate the distribution of modes (DOM) from a given E(k) relationship is presented. The main features of this algorithm are, (i) its ability to work on sparse dispersion data, and (ii) creation of an energy grid for the DOM that is almost independent of the dispersion data therefore allowing for efficient and fast calculation of TE parameters. The inclusion of scattering effects is also straight forward. The effect of k-grid sparsity on the compute time for DOM and on the sensitivity of the calculated TE results are provided. The algorithm calculates the TE parameters within 5% accuracy when the K-grid sparsity is increased up to 60% for all the dimensions (3D, 2D and 1D). The time taken for the DOM calculation is strongly influenced by the transverse K density (K perpendicular to transport direction) but is almost independent of the transport K density (along the transport direction). The DOM and TE results from the algorithm are bench-marked with, (i) analytical calculations for parabolic bands, and (ii) realistic electronic and phonon results for $Bi_{2}Te_{3}$.Comment: 16 Figures, 3 Tables, submitted to Journal of Computational electronic

Emergence of coherence in the charge-density wave state of 2H-NbSe₂

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T$_{CDW}$. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe$_{2}$ intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T$_{CDW}$ marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states

GdCo1-xGa3Ge: Charge density wave in a Ga square net

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Orbital selectivity causing anisotropy and particle-hole asymmetry in the charge density wave gap of 2H−TaS2

We report an in-depth angle-resolved photoemission spectroscopy study on 2H-TaS2, a canonical incommensurate charge density wave (CDW) system. This study demonstrates that just as in related incommensurate CDW systems, 2H-TaSe2 and 2H-NbSe2, the energy gap (ΔCDW) of 2H-TaS2 is localized along the K-centered Fermi surface barrels and is particle-hole asymmetric. The persistence of ΔCDW even at temperatures higher than the CDW transition temperature TCDW in 2H-TaS2, reflects the similar pseudogap behavior observed previously in 2H-TaSe2 and 2H-NbSe2. However, in sharp contrast to 2H-NbSe2, where ΔCDW is nonzero only in the vicinity of a few "hot spots" on the inner K-centered Fermi surface barrels, ΔCDW in 2H-TaS2 is nonzero along the entirety of both K-centered Fermi surface barrels. Based on a tight-binding model, we attribute this dichotomy in the momentum dependence and the Fermi surface specificity of ΔCDW between otherwise similar CDW compounds to the different orbital orientations of their electronic states that participate in the CDW pairing. Our results suggest that the orbital selectivity plays a critical role in the description of incommensurate CDW materials

Orbital selectivity causing anisotropy and particle-hole asymmetry in the charge density wave gap of 2H−TaS2

We report an in-depth angle-resolved photoemission spectroscopy study on 2H-TaS2, a canonical incommensurate charge density wave (CDW) system. This study demonstrates that just as in related incommensurate CDW systems, 2H-TaSe2 and 2H-NbSe2, the energy gap (ΔCDW) of 2H-TaS2 is localized along the K-centered Fermi surface barrels and is particle-hole asymmetric. The persistence of ΔCDW even at temperatures higher than the CDW transition temperature TCDW in 2H-TaS2, reflects the similar pseudogap behavior observed previously in 2H-TaSe2 and 2H-NbSe2. However, in sharp contrast to 2H-NbSe2, where ΔCDW is nonzero only in the vicinity of a few "hot spots" on the inner K-centered Fermi surface barrels, ΔCDW in 2H-TaS2 is nonzero along the entirety of both K-centered Fermi surface barrels. Based on a tight-binding model, we attribute this dichotomy in the momentum dependence and the Fermi surface specificity of ΔCDW between otherwise similar CDW compounds to the different orbital orientations of their electronic states that participate in the CDW pairing. Our results suggest that the orbital selectivity plays a critical role in the description of incommensurate CDW materials