Wiedemann-Franz law in the underdoped cuprate superconductor YBa2Cu3Oy
G. Grissonnanche, F. Laliberte, S. Dufour-Beausejour, M. Matusiak, S. Badoux, F. F. Tafti, B. Michon, A. Riopel, O. Cyr-Choiniere, J. C. Baglo, B. J. Ramshaw, R… 展开作者
G. Grissonnanche, F. Laliberte, S. Dufour-Beausejour, M. Matusiak, S. Badoux, F. F. Tafti, B. Michon, A. Riopel, O. Cyr-Choiniere, J. C. Baglo, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy, S. Kramer, D. LeBoeuf, D. Graf, N. Doiron-Leyraud, L. Taillefer
备注：
8 pages, includes main text and supplementary information
The recent detection of charge-density modulations in YBa2Cu3Oy and other cuprate superconductors raises new questions about the normal state of underdoped cuprates. In one class of theories, the modulations are intertwined with pairing in a dual state, expected to persist up to high magnetic fields as a vortex liquid. In support of such a state, specific heat and magnetisation data on YBa2Cu3Oy have been interpreted in terms of a vortex liquid persisting above the vortex-melting field Hvs at T = 0. Here we report high-field measurements of the electrical and thermal Hall conductivities in YBa2Cu3O6.54 that allow us to probe the Wiedemann-Franz law, a sensitive test of the presence of superconductivity in a metal. In the T = 0 limit, we find that the law is satisfied for fields immediately above Hvs. This rules out the existence of a vortex liquid and it places strict constraints on the nature of the normal state in underdoped cuprates.
We show that the Wiedemann-Franz law is violated in the vortex state of a d-wave superconductor at zero temperature. We use a semiclassical approach, which includes the Doppler shift on the quasiparticles as well as the Andreev scattering from a random distribution of vortices. We also show that the vertex corrections to the electrical conductivity due to the anisotropy of impurity scattering become unimportant in the presence of a sufficiently large magnetic field.
Measurements of longitudinal and transverse transport coefficients were performed in the normal state of a high-quality single crystal of optimally-doped superconductor YBa2Cu3O6.95. We found the Hall-Lorenz number (Lxy) depends only weakly on temperature, thus no appreciable violation of the Wiedemann-Franz law has been observed. However, Lxy is about two times larger than the Sommerfeld's value of the Lorenz number. Our results can be interpreted consistently if we assume that the electronic system of YBa2Cu3O6.95 behaves like a Fermi-liquid with a pseudo-gap that opens at the Fermi level.
The Wiedemann-Franz (WF) ratio compares the thermal and electrical conductivities in a metal. We describe a new way to determine its value, based on the thermal Hall conductivity. The technique is applied to copper and to untwinned YBaCuO. In the latter, we uncover a T-linear dependence and suppression of the Hall-channel WF ratio. We discuss the implications of this suppressions. The general suppression of the WF ratio in systems with predominant electron-electron scattering is discussed.
We study the Wiedemann-Franz (WF) law in the d-density wave (DDW) model. Even though the opening of the DDW gap $(W_{0})$ profoundly modifies the electronic density of states and makes it dependent on energy, the value of the WF ratio at zero temperature (T=0) remains unchanged. However, neither electrical nor thermal conductivity display universal behavior. For finite temperature, with T greater than the value of the impurity scattering rate at zero frequency $γ(0)$ i.e. $γ(0)<T\ll W_{0}$, the usual WF ratio is obtained only in the weak scattering limit. For strong scattering there are large …
We show that the Wiedemann-Franz law is violated at zero temperature in the vortex state of a d-wave BCS superconductor with isotropic impurity scattering. We use a semiclassical approach to include the Doppler shift experienced by the quasiparticles due to the circulating supercurrents and consider as well the Andreev scattering from an array of vortices assumed to be randomly distributed. We also show that the vertex corrections to the electric conductivity, which can be large when there is significant anisotropy in the impurity scattering, become unimportant as the magnetic field is increas…
We propose that the recently observed violation of the Wiedemann-Franz law in the normal state of underdoped cuprates is caused by spin-charge separation and dynamical chiral symmetry breaking in a (2+1)-dimensional system consisting of massless Dirac fermions, charged bosons and a gauge field. While the d-wave spinon gap vanishes at the Fermi points, the nodal fermions acquire a finite mass due to strong gauge fluctuations. This mass provides a gap below which no free fermions can be excited. This implies that there is not a residual linear term for the thermal conductivity, in good agreement…
Longitudinal and transverse transport coefficients of the Ba(Fe1-xCox)2As2 single crystals with x = 0, 0.045, 0.06 and 0.244 were measured in the temperature range 1.4 - 300 K and in magnetic fields up to 12.5 T. The resulting data were used to determine the temperature dependence of the Hall Lorenz number (Lxy) and its evolution with doping. Lxy is defined by the electronic contributions to the thermal and electrical conductivities and it is found to differ from its canonical behavior. This shows the emergence of a pseudogap in samples at intermediate doping.
We show that the Wiedemann-Franz law, which holds for Landau Fermi liquids, breaks down in a large-n treatment of the t-J model. The calculated ratio of the in-plane thermal and electrical conductivities agrees quantitatively with experiments on the normal state of the electron-doped Pr_{2-x}Ce_xCuO_4 (x = 0.15) cuprate superconductor. The violation of the Wiedemann-Franz law in the uniform phase contrasts with other properties of the phase that are Fermi liquid like.
We report data on the thermal conductivity K(T,H) along the basal plane of the hexagonal crystal structure of superconducting Mg{1-y}Al{y}B2 with y=0.02 and 0.07 at temperatures between 0.5 and 50 K and in external magnetic fields between 0 and 70 kOe. The substitution of Al for Mg leads to a substantial reduction of the heat transport via electronic quasiparticles. The analysis of the K(T,H) data implies that the Al impurities provoke an enhancement of the intraband scattering rate, almost equal in magnitude for both the sigma- and the pi band of electronic excitations. This is in contrast wi…
Due to the node structure of the gap in a d-wave superconductor, the presence of impurities generates a finite density of quasiparticle excitations at zero temperature. Since these impurity-induced quasiparticles are both generated and scattered by impurities, prior calculations indicate a universal limit (Ω-> 0, T -> 0) where the transport coefficients obtain scattering-independent values, depending only on the velocity anisotropy v_f/v_2. We improve upon prior results, including the contributions of vertex corrections and Fermi liquid corrections in our calculations of universal limit electr…
We present a study of heat and charge transport in Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+δ}$ focused on the size of the low-temperature linear term of the thermal conductivity at optimal doping level. In the superconducting state, the magnitude of this term implies a d-wave gap with an amplitude close to what has been reported. In the normal state, recovered by the application of a magnetic field, measurement of this term and residual resistivity yields a Lorenz number $L = κ_{N}ρ_{0}/T = 1.3 \pm 0.2 L_{0}$. The departure from the value expected by the Wiedemann-Franz law is thus slightly larger than ou…
We derive the electrical and thermal conductivities of the $d$-density-wave state in an external magnetic field $B$ in the low-temperature regime and in the presence of impurities. We show that in the zero-temperature limit, $T \to 0$, the Wiedemann-Franz (WF) law remains intact irrespectively of the value of the applied field and chemical potential $μ$ as soon as there is a scattering from impurities. For finite $T \lesssim |μ|$ the WF law violation is possible and it is enhanced by the external field. Depending on the relative values of $B$ and $T$ the electrical conduction may dominate the …
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 polaro…
To investigate the validity of the Wiedemann-Franz (WF) law in disordered but metallic cuprates, the low-temperature charge and heat transport properties are carefully studied for a series of impurity-substituted and carrier-overdoped La_{1.8}Sr_{0.2}Cu_{1-z}M_zO_4 (M = Zn or Mg) single crystals. With moderate impurity substitution concentrations of z = 0.049 and 0.082 (M = Zn), the resistivity shows a clear metallic behavior at low temperature and the WF law is confirmed to be valid. With increasing impurity concentration to z = 0.13 (M = Zn) or 0.15 (M = Mg), the resistivity shows a low-T up…
We present a study of heat transport in the cuprate superconductor Bi_{2+x}Sr_{2-x}CuO_{6+δ} at subkelvin temperatures and in magnetic fields as high as 25T. In several samples with different doping levels close to optimal, the linear-temperature term of thermal conductivity was measured both at zero-field and in presence of a magnetic field strong enough to quench superconductivity. The zero-field data yields a superconducting gap of reasonable magnitude displaying a doping dependence similar to the one reported in other families of cuprate. The normal-state data together with the results of …
The in-plane thermal conductivity kappa(T) and electrical resistivity rho(T) of the heavy-fermion metal YbRh2Si2 were measured down to 50 mK for magnetic fields H parallel and perpendicular to the tetragonal c axis, through the field-tuned quantum critical point, Hc, at which antiferromagnetic order ends. The thermal and electrical resistivities, w(T) and rho(T), show a linear temperature dependence below 1 K, typical of the non-Fermi liquid behavior found near antiferromagnetic quantum critical points, but this dependence does not persist down to T = 0. Below a characteristic temperature T* ~…
We compare the thermal conductance $G_{\rm thermal}$ (at temperature $T$) and the electrical shot noise power $P_{\rm shot}$ (at bias voltage $V\gg k_{\rm B}T/e$) of Majorana fermions on the two-dimensional surface of a three-dimensional topological superconductor. We present analytical and numerical calculations to demonstrate that, for a local coupling between the superconductor and metal contacts, $G_{\rm thermal}/P_{\rm shot}= {\cal L}T/eV$ (with ${\cal L}$ the Lorenz number). This relation is ensured by the combination of electron-hole and time-reversal symmetries, irrespective of the mic…
The thermal conductivity $κ$ of the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured down to 50 mK in seven crystals with doping from $p=0.12$ to $p=0.24$, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term $κ_0/T$ as $T \to 0$ across the pseudogap critical point $p^{\star}= 0.23$. In the normal state, we observe an abrupt drop in $κ_0/T$ upon crossing below $p^{\star}$, consistent with a drop in carrier density $n$ from $1 + p$ to $p$, the signature of the pseudogap phase inferred from the Hall…
The thermal conductivity $κ$ of underdoped \Y was measured in the $T \to 0$ limit as a function of hole concentration $p$ across the superconducting critical point at $p_{SC}$ = 5.0%. ``Time doping'' was used to resolve the evolution of bosonic and fermionic contributions with high accuracy. For $p \leqslant p_{SC}$, we observe an additional $T^3$ contribution to $κ$ which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, manifest as a linear term in $κ$, is seen to persist unaltered through $p_{SC}$, showing that the state just below $…
I discuss thermoelectric properties of a quantum dot coupled to one normal and one superconducting lead in the presence of Kondo effect and Andreev scattering. I will focus on conductance, thermal conductance, thermopower and related quantities like thermoelectric figure of merit which is a direct measure of the usefulness of the system for applications and Wiedemann-Franz ratio which indicates if the system is in the Fermi liquid state. I will show that the superconductivity strongly modifies the thermal properties of the system. In particular, the thermopower is strongly enhanced near the su…
We consider the behavior of strongly correlated electron liquid in high-temperature superconductors within the framework of the fermion condensation model. We show that at low temperatures the normal state recovered by the application of a magnetic field larger than the critical field can be viewed as the Landau Fermi liquid induced by the magnetic field. In this state, the Wiedemann-Franz law and the Korringa law are held and the elementary excitations are the Landau Fermi Liquid quasiparticles. Contrary to what might be expected from the Landau theory, the effective mass of quasiparticles de…
The behaviour of electrons in solids is remarkably well described by Landau's Fermi-liquid theory, which says that even though electrons in a metal interact they can still be treated as well-defined fermions, called ``quasiparticles''. At low temperature, the ability of quasiparticles to transport heat is strictly given by their ability to transport charge, via a universal relation known as the Wiedemann-Franz law, which no material in nature has been known to violate. High-temperature superconductors have long been thought to fall outside the realm of Fermi-liquid theory, as suggested by seve…
The transport of heat and charge in the overdoped cuprate superconductor Tl_2Ba_2CuO_(6+delta) was measured down to low temperature. In the normal state, obtained by applying a magnetic field greater than the upper critical field, the Wiedemann-Franz law is verified to hold perfectly. In the superconducting state, a large residual linear term is observed in the thermal conductivity, in quantitative agreement with BCS theory for a d-wave superconductor. This is compelling evidence that the electrons in overdoped cuprates form a Fermi liquid, with no indication of spin-charge separation.
Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778] and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys. Rev. B 93:064513] point to a Fermi liquid regime at low temperature in…
We present a study of the electrical and thermal conductivities of the $d$-density wave (DDW) state in an external magnetic field $B$ in the low temperature regime and in the presence of impurities. We show that in the zero temperature limit, $T \to 0$, the Wiedemann-Franz (WF) law remains intact. For finite $T$ the WF law violation is possible and it is enhanced by the external field.
Strong electron-phonon interaction in cuprates has gathered support over the last decade in a number of experiments. While phonons remain almost unrenormalised, electrons are transformed into itinerent bipolarons and thermally excited polarons when the electron-phonon interaction is strong. We calculate the Lorenz number of the system to show that the Wiedemann-Franz law breaks down because of the interference of polaron and bipolaron contributions in the heat flow. The model fits numerically the experimental Hall Lorenz number, which provides a direct evidence for bipolarons in the cuprates.
