Multi-orbital physics in lithium-molybdenum purple-bronze: going beyond paradigm

Abstract

Abstract.We investigate the role of inter-orbital fluctuations in the low energy physics of a quasi-1D material -lithium molybdenum purple bronze (LMO). It is an exceptional material that may provide us a long sought realization of a Tomonaga-Luttinger liquid (TLL) physics, but its behaviour at temperatures of the order of T * ≈ 30 K remains puzzling despite numerous efforts. Here we make a conjecture that the physics around T * is dominated by multi-orbital excitations. Their properties can be captured using an excitonic picture. Using this relatively simple model we compute fermionic Green's function in the presence of excitons. We find that the spectral function is broadened with a Gaussian and its temperature dependence acquires an extra T 1 factor. Both effects are in perfect agreement with experimental findings. We also compute the resistivity for temperatures above and below critical temperature T0. We explain an upturn of the resistivity at 28 K and interpret the suppression of this extra component of resistivity when a magnetic field is applied along the conducting axis. Furthermore, in the framework of our model, we qualitatively discuss and consistently explain other experimentally detected peculiarities of purple bronze: the breaking of Wiedmann-Franz law and the magnetochromatic behaviour. Our model consistently explains all these.

ARPES and NMTO Wannier Orbital Theory of LiMo$_{6}$O$_{17}$ - Implications for Unusually Robust Quasi-One Dimensional Behavior

“…What we must do is to k c -average the first expression (36) with k F (k c ) being the ∆-gapped FS. This is essentially what was done leading to Table (35), but only for the three characteristic values of k c . We may of course split up the k c -integral (although that is not done in standard computations).…”

“…The quarter filled ladder model has been used for a number of theoretical discussion of the properties of LiPB [31][32][33][34][35]. Ref.…”

“…In contrast to early theory which took rather generic quasi-1D TB models to discuss the possibility of triplet SC in LiPB [36,37], three somewhat later papers [32][33][34] employed the quarter-filled ladder model for theorizing about possible symmetries of the SC order parameter. The most recent work [35] with the quarter-filled ladder model introduces additionally the orbitals that produce the filled bands below E F , and their antibonding partner bands above E F , and considers the implications of the possibility that these bands enable a gas of exceptionally long lived excitons that interacts with the electrons in the 1D chain bands to produce the surprising low temperature properties of LiPB described above, including its power-law resistivity upturn, its associated negative magnetoresistance, an interesting magneto-chromatic effect [38], and the low-T departures of the ARPES lineshapes from those of the TL model.…”

Emergence of a real-space symmetry axis in the magnetoresistance of the one-dimensional conductor Li 0.9 Mo 6 O 17

“…In previous theoretical treatments of the TLL physics of LMO, only the pure d xy orbitals were considered as a key starting ingredient (an assumption justified by the fact that only these cross E F ) ( 30 , 34 ). Recently however, other orbital degrees of freedom, in particular the interorbital interactions of the d xz and d yz orbitals, were incorporated into the many-body formalism and shown to affect the low-energy physics ( 26 ) (further details of the model are expounded in section S4). In particular, the specific arrangement of the d iz -derived bands provides favorable conditions for the formation of excitons along the P-K line (highlighted in green in the lower panel of Fig.…”

“…S8 (and section S3), which ensures that there is always a residual component of the B -field that is orthogonal to the quantization axis and, thus, the condition for perfect alignment is never satisfied. When the magnetic field is rotated within the ab or bc plane, the angle between the B -field and the quantization axis is always maximized when B // b , and so is the negative MR ( 17 , 26 ). In addition, B // a and B // c have a higher positive MR than B // b due to the enhanced Lorentz force as well as a propensity for field-induced one-dimensionalization whenever the B -field is perpendicular to the atomic chains ( 36 ).…”