Many complex oxides (including titanates, nickelates and cuprates) show a regime in which resistivity follows a power law in temperature ($ρ\propto T^2$). By analogy to a similar phenomenon observed in some metals at low temperature, this has often been attributed to electron-electron (Baber) scattering. We show that Baber scattering results in a $T^2$ power law only under several crucial assumptions which may not hold for complex oxides. We illustrate this with sodium metal ($ρ_\text{el-el}\propto T^2$) and strontium titanate ($ρ_\text{el-el}\not\propto T^2$). We conclude that an observation of $ρ\propto T^2$ is not sufficient evidence for electron-electron scattering.
The electrical resistivity of Fermi liquids (FLs) displays a quadratic temperature ($T$) dependence because of electron-electron (e-e) scattering. For such collisions to decay the charge current, there are two known mechanisms: inter-band scattering (identified by Baber) and Umklapp events. However, dilute metallic strontium titanate (STO) was found to display $T^2$ resistivity in absence of either of these two mechanisms. The presence of soft phonons and their possible role as scattering centers raised the suspicion that $T$-square resistivity in STO is not due to e-e scattering. Here, we pre…
The quadratic low-temperature dependence of resistance in ordinary metals is determined by the momentum relaxation due to electron-electron scattering in the presence Umklapp processes and scattering on impurities. In metals without inversion center spin-orbit interaction of electrons with crystal lattice lifts spin degeneracy of electron states and splits each band on two bands. The temperature dependence of electron-electron collisions scattering rate is found using the matrix kinetic equation including the electron-impurity and electron-electron intra and inter band scattering. It is shown …
Electron-phonon origins of unconventional resistivity in moderately correlated perovskite oxides
Center for Computational Quantum Physics, Flatiron Institute（Flatiron研究所计算量子物理中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Collège de France（法兰西公学院）；CPHT, CNRS, École Polytechnique, IP Paris（巴黎综合理工学院CNRS CPHT中心）；DQMP, Université de Genève（日内瓦大学DQMP）；Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文学系）
Comment on "Charged impurity scattering limited low temperature resistivity of low density silicon inversion layers" (Das Sarma and Hwang, cond-mat/9812216)
In this work we carry out a theoretical study of the phonon-induced resistivity in twisted double bilayer graphene (TDBG), in which two Bernal-stacked bilayer graphene devices are rotated relative to each other by a small angle $θ$. We show that at small twist angles ($θ\sim 1^\circ$) the effective mass of the TDBG system is greatly enhanced, leading to a drastically increased phonon-induced resistivity in the high-temperature limit where phonon scattering leads to a linearly increasing resistivity with increasing temperature. We also discuss possible implications of our theory on superconduct…
We consider the transport properties of a model of fermions scattered by a critical bosonic mode. The mode is overdamped and scattering is mainly in the forward direction. Such a mode appears at the quantum critical point for a electronic nematic phase transition, and in gauge theories for a U(1) spin liquid. It leads to a short fermion life-time, violating Landau's criterion for a Fermi liquid. In spite of this, transport can be described by a Boltzmann equation. We include momentum relaxation by umklapp scattering, supplemented by weak impurity scattering. We find that above a very low tempe…
A variety of "strange metals" exhibit resistivity that decreases linearly with temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $\hbar/τ=αk_{\rm B} T$, where $α$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the "Planckian limit"---but little is known about the underlying origins of this l…
Fermi-Liquid $T^2$ Resistivity: Dynamical Mean-Field Theory Meets Experiment
Flatiron Institute（平顿研究所）；University of Cologne（科隆大学）；Stony Brook University（石溪大学）；Massachusetts Institute of Technology（麻省理工学院）；Collège de France（法兰西学院）；École Polytechnique（巴黎综合理工学院）；CNRS（法国国家科学研究中心）
Anisotropy of the in-plane resistivity of underdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ superconductors induced by impurity scattering in the antiferromagnetic orthorhombic phase
研究了低掺杂Ba（Fe $_{1-x}$ Co $_x$）$_2$ As $_2$单晶的面内电阻率各向异性。我们表明，在磁结构有序相的电阻率的各向异性产生的各向异性的剩余成分中的Co浓度$x$成比例增加。这证明了各向异性起源于Co原子取代Fe位的杂质散射，而不是迄今为止提出的机制，如重建的费米表面口袋的费米速度的各向异性。随着掺杂进行到顺磁-四极相，Co杂质转变为弱的和各向同性的散射中心。
We study the resistivity of three-dimensional semimetals with linear dispersion in the presence of on-site electron-electron interaction. The well-known quadratic temperature dependence of the resistivity of conventional metals is turned into an unusual $T^6$-behavior. An analogous change affects the thermal transport, preserving the linearity in $T$ of the ratio between thermal and electrical conductivities. These results hold from weak coupling up to the non-perturbative region of the Mott transition. Our findings yield a natural explanation for the hitherto not understood large exponents ch…
We consider a short-range deformation potential scattering model of electron-acoustic phonon interaction to calculate the resistivity of an ideal metal as a function of temperature (T) and electron density (n). We consider both 3D metals and 2D metals, and focus on the dilute limit, i.e., low effective metallic carrier density of the system. The main findings are: (1) a phonon scattering induced linear-in-T resistivity could persist to arbitrarily low T in the dilute limit independent of the Debye temperature ($T_D$) although eventually the low-T resistivity turns over to the expected Bloch-Gr…
Effect of disorder on the resistivity anisotropy near the electronic nematic phase transition in pure and electron-doped BaFe$_2$As$_2$
我们表明，在四重态的代表性欠掺杂的铁砷化物BaFe $_2$作为$_2$，Ba（Fe $_{1-x}$ Co $_x$）$_2$作为$_2$和Ba（Fe $_{1-x}$ Ni $_x$）$_2$作为$_2$的应变诱导电阻率各向异性是独立的无序在很宽的缺陷和杂质浓度范围内。这一结果表明，在顺磁正交状态的平面电阻率的各向异性，这种材料是不是由于弹性散射各向异性缺陷，是最容易理解的电子结构中的固有各向异性。
We address two long-standing questions regarding the hidden order in URu2Si2: Is it associated with the hybridization process, and what are the distinct roles played by the localized and itinerant electrons? Our quasiparticle scattering spectroscopy reveals a hybridization gap ubiquitous in the entire phase space spanned by P and Fe substitutions in URu2Si2, including the no-order and antiferromagnetic regions, with minimal change upon crossing the phase boundary. This indicates its opening isn't associated with the ordering, and thus localized electrons must be the major player. Towards a con…
We report the observation of resistivity saturation in lightly doped ($x\sim 0.10)$ as-grown samples of the electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_4$ (LCCO). The saturation occurs at resistivity values roughly consistent with the phenomenological Mott-Ioffe-Regel criterion once the low effective carrier density of these materials is included in the analysis. These results imply that, at least for light doping, the high-temperature metallic phase of these materials is not necessarily strange and may be understood as simply a low-density metal.
Fe3GeTe2 is a 2-dimensional van der Waals material exhibiting itinerant ferromagnetism upto 230 K. Here, we study aspects of scattering mechanism in Fe3Ge2Te2 single crystals via resistivity, magneto-transport and Hall effect measurements. The quadratic temperature dependence of electrical resistivity below the Curie temperature hints towards the dominance of electron-magnon scattering. A non-saturating positive magnetoresistance (MR) is observed at low temperatures when the magnetic field is applied parallel to the sample plane. The linear negative MR at high fields for T < TC corroborates to…
We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion $U\leq D$ and to first order in (dimensionless) electron-phonon coupling strength $λ\leq0.5$, where $D$ is the half-bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasi-particles as a positive slope i…
In 1937, Baber, Landau and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T$^2$ temperature dependence. The amplitude of this term is small in common metals, but dominant in metals hosting either heavy carriers or a low concentration of them. The link between the temperature dependence and the size of the scattering phase space is straightforward, but not the microscopic source of dissipation. To explain how electron-electron collisions lead to momentum leak, Umklapp events or multiple electron reservoirs …
Resistivity studies under hydrostatic pressure on a low-resistance variant of the quasi-2D organic superconductor kappa-(BEDT-TTF)2Cu[N(CN)2]Br: quest for intrinsic scattering contributions
The increase in the resistivity with decreasing temperature followed by a drop by more than one order of magnitude is observed on the metallic side near the zero-magnetic-field metal-insulator transition in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells. We find that the temperature $T_{\text{max}}$, at which the resistivity exhibits a maximum, is close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value $T_{\text{max}}$ decreases appreciably for spinless electrons in spin-polarizin…
We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT).…
Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
分析了金属在波梅兰丘克量子相变（QPT）附近电子-电子相互作用对电阻率的影响。我们表明，Umklapp过程是不有效的QPT附近，必须考虑相互作用和无序获得有限的和T依赖的电阻率。通过功率计数，在Z=3 QPT附近，在低T下对剩余电阻率的校正标度为Δ T ^{（D+2）/3}。然而，我们表明，A=0的简单连接，凸费米面在2D中，由于隐藏的可积性的电子运动。我们认为，在一个两带（s-d）模型中，A >0，并提出这个模型作为所观察到的T^{（D+2）/3}行为的解释。
Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy-fermions, Fe-chalogenides and pnictides, twisted bi-layer graphene and WSe$_2$, is linear in temperature $T$ as well as in a magnetic field $H$. Scattering of fermions by the excitations of a time-reversal odd polar vector field ${\bf Ω}$ characterizing loop-current fluctuations has been shown to give a linear in T resistivity and other anomalous properties in the cuprates. An extension of this theory to an applied magnetic field is presented. Magnetic field is shown to generate…
