Thermoelectric properties of the bismuth telluride nanowires in the constant-relaxation-time approximation

Electronic structure of bismuth telluride nanowires with the growth directions [110] and [015] is studied in the framework of anisotropic effective mass method using the parabolic band approximation. The components of the electron and hole effective mass tensor for six valleys are calculated for both growth directions. For a square nanowire, in the temperature range from 77 K to 500 K, the dependence of the Seebeck coefficient, the electron thermal and electrical conductivity as well as the figure of merit ZT on the nanowire thickness and on the excess hole concentration are investigated in the constant-relaxation-time approximation. The carrier confinement is shown to play essential role for square nanowires with thickness less than 30 nm. The confinement decreases both the carrier concentration and the thermal conductivity but increases the maximum value of Seebeck coefficient in contrast to the excess holes (impurities). The confinement effect is stronger for the direction [015] than for the direction [110] due to the carrier mass difference for these directions. The carrier confinement increases maximum value of ZT and shifts it towards high temperatures. For the p-type bismuth telluride nanowires with growth direction [110], the maximum value of the figure of merit is equal to 1.3, 1.6, and 2.8, correspondingly, at temperatures 310 K, 390 K, 480 K and the nanowire thicknesses 30 nm, 15 nm, and 7 nm. At the room temperature, the figure of merit equals 1.2, 1.3, and 1.7, respectively.Comment: 13 pages, 7 figures, 2 tables, typos added, added references for sections 2-

Emptying Dirac valleys in bismuth using high magnetic fields

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here, we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, $B_{\rm{empty}}$, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across $B_{\rm{empty}}$ to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results. Coulomb interaction may play a role in shaping the fine details.Comment: 19 pages, 5 figures, Supplemental Material available upon reques

Resonant plasmon-phonon coupling and its role in magneto-thermoelectricity in bismuth

Using diagrammatic methods we derive an effective interaction between a low energy collective movement of fermionic liquid (acoustic plasmon) and acoustic phonon. We show that the coupling between the plasmon and the lattice has a very non-trivial, resonant structure. When real and imaginary parts of the acoustic plasmon's velocity are of the same order as the phonon's velocity, the resonance qualitatively changes the nature of phonon-drag. In the following we study how magneto-thermoelectric properties are affected. Our result suggests that the novel mechanism of energy transfer between electron liquid and crystal lattice can be behind the huge Nernst effect in bismuth.Comment: accepted in EPJB, to appear with a highligh

Collective excitations and low temperature transport properties of bismuth

We examine the influence of collective excitations on the transport properties (resistivity, magneto- optical conductivity) for semimetals, focusing on the case of bismuth. We show, using an RPA approximation, that the properties of the system are drastically affected by the presence of an acoustic plasmon mode, consequence of the presence of two types of carriers (electrons and holes) in this system. We found a crossover temperature T* separating two different regimes of transport. At high temperatures T > T* we show that Baber scattering explains quantitatively the DC resistivity experiments, while at low temperatures T < T* interactions of the carriers with this collective mode lead to a T^5 behavior of the resistivity. We examine other consequences of the presence of this mode, and in particular predict a two plasmon edge feature in the magneto-optical conductivity. We compare our results with the experimental findings on bismuth. We discuss the limitations and extensions of our results beyond the RPA approximation, and examine the case of other semimetals such as graphite or 1T-TiSe_2

Signatures of Electron Fractionalization in Ultraquantum Bismuth

Because of the long Fermi wavelength of itinerant electrons, the quantum limit of elemental bismuth (unlike most metals) can be attained with a moderate magnetic field. The quantized orbits of electrons shrink with increasing magnetic field. Beyond the quantum limit, the circumference of these orbits becomes shorter than the Fermi wavelength. We studied transport coefficients of a single crystal of bismuth up to 33 tesla, which is deep in this ultraquantum limit. The Nernst coefficient presents three unexpected maxima that are concomitant with quasi-plateaus in the Hall coefficient. The results suggest that this bulk element may host an exotic quantum fluid reminiscent of the one associated with the fractional quantum Hall effect and raise the issue of electron fractionalization in a three-dimensional metal.Comment: 9 pages, four figures and supposrting online materia