Breakdown of the Wiedemann-Franz law in strongly-coupled electron-phonon system, application to the cuprates

Abstract

With the superconducting cuprates in mind, a set of unitary transformations was used to decouple electrons and phonons in the strong-coupling limit. While phonons remain almost unrenormalised, electrons are transformed into itinerent singlet and triplet bipolarons and thermally excited polarons. The triplet/singlet exchange energy and the binding energy of the bipolarons are thought to account for the spin and charge pseudogaps in the cuprates, respectively. We calculated the Hall Lorenz number of the system to show that the Wiedemann-Franz law breaks down due to the interference of the polaron and bipolaron contributions to heat flow. The model provides a quantitative fit to magnetotransport data in the cuprates. Furthermore we are able to extract the phonon component of the thermal conductivity with the use of experimental data and the model. Our results further validate the use of a charged Bose gas model to describe normal and superconducting properties of unconventional superconductors.

Study of thermal material properties for Ta- and Al-substituted Li7La3Zr2O12 (LLZO) solid-state electrolyte in dependency of temperature and grain size

“…As a general conclusion, the Wiedemann-Franz law can only account for a small part of the overall thermal conductivity in complex oxide systems. [82][83][84] Another contribution to the thermal conductivity could be related to a radiative heat transfer, which means that a certain amount of energy is transmitted by radiation through the material. 75 The comparison of the detector signals from the LFA measurements, which represent the time-dependent temperature prole at the sample rear surface, reveals rst a steplike signal increase followed by the typical time-dependent temperature evolution in LFA measurements (see Fig.…”

Low thermal conductivity of SrTiO3−LaTiO3 and SrTiO3−SrNbO3 thermoelectric oxide solid solutions

“…Furthermore, as a large polaron system, lightly electron-doped SrTiO 3 possesses stronger electron-phonon coupling which may be another origin of the low Lorenz number. 45 However, further experimental and theoretical insight is required to gain a deeper understanding of WF law violation. In this study, even though there is an overestimation of κ ele , charge carriers (electrons) should play an important role in the different heat transfers of SLTO and STNO, since κ displays a consistent behavior with electron transport properties (summarized in Figure S3 of Supplementary).…”

“…In addition, it has been reported that chemically doped or electrostatically controlled SrTiO 3 shows non‐Fermi liquid behavior despite of its T 2 ‐dependent resistance, 44 which may be a possible origin of the WF law violation. Furthermore, as a large polaron system, lightly electron‐doped SrTiO 3 possesses stronger electron‐phonon coupling which may be another origin of the low Lorenz number 45 . However, further experimental and theoretical insight is required to gain a deeper understanding of WF law violation.…”

On the Lorenz number of multiband materials

“…confined dimensions 12,13 such as nano-wires, [14][15][16] quasi-1D systems, [17][18][19] and effective 0-D systems such as quantum dots, [20][21][22] , single molecule [23][24][25] and single atom 26 systems; under conditions of quantum criticality; [27][28][29][30][31] in superconductors; 16,[32][33][34][35][36][37][38] in superlattices and granular metals; [39][40][41][42][43] and in the presence of disorder.…”

“…Therefore, there is no reason to expect that the Sommerfeld value holds for them, nor that the Lorenz number's value can only fall intermediately between the two limiting values. 3 In fact, deviations in the Lorenz number are nothing new and occur in various cases: confined dimensions 12,13 such as nano-wires, [14][15][16] quasi-1D systems, [17][18][19] and effective 0-D systems such as quantum dots, [20][21][22] , single molecule [23][24][25] and single atom 26 systems; under conditions of quantum criticality; [27][28][29][30][31] in superconductors; 16,[32][33][34][35][36][37][38] in superlattices and granular metals; [39][40][41][42][43] and in the presence of disorder. 44,45 However, here we consider a far more common, but yet to be explored, situation -the case of multi-band semiconductors, which are the most relevant case for next generation thermoelectric materials with complex bandstructures.…”