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 present the case of Bi$_2$O$_2$Se, a layered semiconductor with hard phonons, which becomes a dilute metal with a small single-component Fermi surface upon doping. It displays $T$-square resistivity well below the degeneracy temperature where neither Umklapp nor interband scattering is conceivable. We observe a universal scaling between the prefactor of $T^2$ resistivity and the Fermi energy, which is an extension of the Kadowaki-Woods plot to dilute metals. Our results imply the absence of a satisfactory theoretical basis for the ubiquity of e-e driven $T$-square resistivity in Fermi liquids.
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…
We consider clean metals, at finite temperature, in which the inelastic rate, $\hbar/ τ_{ee}$, can become of the order of, or larger, than the band splitting energy. We show that in suchsystems, contrary to the common knowledge, the umklapp scattering rate becomes independent of both $τ_{ee}$ and the temperature $T,$ in three dimensional systems. We discuss the relation of this phenomenon to the saturation of resistivity at high temperature.
Recent conductivity measurements performed on the hole-doped two-leg ladder material $\mathrm{Sr_{14-x}Ca_xCu_{24}O_{41}}$ reveal an approximately linear power law regime in the c-axis DC resistivity as a function of temperature for $x=11$. In this work, we employ a bosonic model to argue that umklapp processes are responsible for this feature and for the high spectral weight in the optical conductivity which occurs beyond the finite frequency Drude-like peak. Including quenched disorder in our model allows us to reproduce experimental conductivity and resistivity curves over a wide range of e…
We study the temperature dependence of the electrical resistivity of interacting two-dimensional metallic systems. We perform a numerical simulation of the nonequilibrium state based on semiclassical Boltzmann transport theory. Through our simulation, we demonstrate that deviations from the predictions of standard Fermi-liquid theory can arise due to the special scattering geometry of umklapp processes, in special cases even in the ultra-low-temperature limit. Umklapp scattering is required to relax the total momentum of the quasiparticle distribution function. We investigate the transport pro…
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…
Thin films of silver containing 0.3 - 1.5 at % Fe have been prepared by vapor co-deposition. Depending on substrate temperature and iron concentration we could systematically follow the formation of nanometer size clusters of iron from initially dilute iron monomers. samples were characterized via X-ray diffraction, resistivity and Mössbauer spectroscopic measurements. The magnetic behavior derived from Mössbauer data can be best described with an ensemble of ferromagnetic mono-domain particles. The magnetic freezing observed at low temperatures, is controlled via the inter-particle interactio…
We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum phase transition (QPT). We show that Umklapp processes are not effective near a QPT, and one must consider both interactions and disorder to obtain finite and T dependent resistivity. By power counting, the correction to the residual resistivity at low T scales as AT^{(D+2)/3} near a Z=3 QPT. We show, however, that A=0 for a simply connected, convex Fermi surface in 2D, due to hidden integrability of the electron motion. We argue that A >0 in a two-band (s-d) model and propose th…
Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature d.c. resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface structure, leading to the well-known relaxation rate Gamma ~ T^2. We observe that local criticality, in which energies scale but momenta do not, provides a distinct route to efficient umklapp scattering. We show that umklapp scattering by an ionic lattice in a locally critical theory leads to Gamma ~ T^(2Δ(k_L)). Here Δ(k_L) \geq 0 is the dimension of the (irrelevant…
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 …
We report measurements of the resistance of silicon MOSFETs as a function of temperature in high parallel magnetic fields where the 2D system of electrons has been shown to be fully spin-polarized. A magnetic field suppresses the metallic behavior observed in the absence of a magnetic field. In a field of 10.8 T, insulating behavior is found for densities up to n_s approximately 1.35 x 10^{11} cm^{-2} or 1.5 n_c; above this density the resistance is a very weak function of temperature, varying less than 10% between 0.25 K and 1.90 K. At low densities the resistance goes to infinity more rapidl…
We report resistivity measurements from 0.03 K to 10 K in a dilute high mobility 2D electron system. Using an undoped GaAs/AlGaAs heterojunction in a gated field-effect transistor geometry, a wide range of densities, $0.16 \times 10^{10} {cm}^{-2}$ to $7.5 \times 10^{10} {cm}^{-2}$, are explored. For high densities, the results are quantitatively shown to be due to scattering by acoustic phonons and impurities. In an intermediate range of densities, a peak in the resistivity is observed for temperatures below 1 K. This non-monotonic resistivity can be understood by considering the known scatte…
We study phenomena driven by electron-electron interactions in the minimally twisted bilayer graphene (mTBLG) with a perpendicular electric field. The low-energy degrees of freedom in mTBLG are governed by a network of one-dimensional domain-wall states, described by two channels of one-dimensional linearly dispersing spin-1/2 fermions. We show that the interaction can realize a spin-gapped inter-channel charge density wave (CDW) state at low temperatures, forming a "Coulomb drag" between the channels and leaving only one charge conducting mode. For sufficiently high temperatures, power-law-in…
The resistivity for an extended two channel Anderson model is calculated. When the temperature decreases, it decreases logarithmically, and has T^1/2 anomaly at very low temperatures, as seen in some dilute U alloys. The single-particle and the spin excitation spectra are also calculated.
Single crystals of the dilute, rare earth bearing, pseudo-ternary series, Gd_xY_{1-x}Fe_2Zn_{20} were grown out of Zn-rich solution. Measurements of magnetization, resistivity and heat capacity on Gd_xY_{1-x}Fe_2Zn_{20} samples reveal ferromagnetic order of Gd^{3+} local moments across virtually the whole series ($x \geq 0.02$). The magnetic properties of this series, including the ferromagnetic ordering, the reduced saturated moments at base temperature, the deviation of the susceptibilities from Curie-Weiss law and the anomalies in the resistivity, are understood within the frame work of dil…
Correlation between the strength of low-temperature T-linear normal-state resistivity and $T_{\rm c}$ in overdoped electron-doped cuprate superconductors
本文在动能驱动超导框架内，揭示了过掺杂电子掺杂型铜氧化物超导体中由自旋激发同时介导的电子umklapp散射与电子配对，自然导致了低温T线性正常态电阻率强度与超导转变温度$T_{\ m c}$之间的内在关联。
In a recent preprint cond-mat/9812216, Das Sarma and Hwang propose an explanation of the sharp decrease in resistivity at low temperatures which has been attributed to a transition to an unexpected conducting phase in dilute high-mobility two-dimensional systems at B=0. In this Comment, we examine whether their model is supported by the available experimental data.
We report measurements of the zero-field resistivity in dilute 2D electron system in silicon at temperatures down to 35 mK. This extends the previously explored range of temperatures by almost an order of magnitude. On the metallic side, the resistivity near the metal-insulator transition continues to decrease with decreasing temperature and shows no low-temperature up-turn. At the critical electron density, the resistivity is found to be temperature-independent in the entire temperature range 35 mK to 1 K.
Resistivity minima are commonly seen in itinerant magnets and they are often attributed to the Kondo effect. However, recent experiments are revealing an increasing number of materials showing resistivity minima in the absence of indications of Kondo singlet formation. In a previous work [Z. Wang, K. Barros, G.-W. Chern, D. L. Maslov, and C. D. Batista, Phys. Rev. Lett. 117, 206601 (2016)], we demonstrated that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction can produce a classical spin liquid state at finite temperature, whose resistivity increases with decreasing temperature. The classi…
Electrical transport properties near an electronic Ising-nematic quantum critical point in two dimensions are of both theoretical and experimental interest. In this work, we derive a kinetic equation valid in a broad regime near the quantum critical point using the memory matrix approach. The formalism is applied to study the effect of the critical fluctuations on the dc resistivity through different scattering mechanisms, including umklapp, impurity scattering, and electron-hole scattering in a compensated metal. We show that electrical transport in the quantum critical regime exhibits a rich…
We theoretically consider the temperature and density dependent transport properties of semiconductor-based 2D carrier systems within the RPA-Boltzmann transport theory, taking into account realistic screened charged impurity scattering in the semiconductor. We derive a leading behavior in the transport property, which is exact in the strict 2D approximation and provides a zeroth order explanation for the strength of metallicity in various 2D carrier systems. By carefully comparing the calculated full nonlinear temperature dependence of electronic resistivity at low temperatures with the corre…
Scattering among electrons generates a distinct contribution to electrical resistivity that follows a quadratic temperature dependence. In strongly-correlated electron systems, the prefactor A of this T$^2$ resistivity scales with the magnitude of the electronic specific heat. Here, we show that one can change the magnitude of A by four orders of magnitude in metallic SrTiO3 by tuning the concentration of the carriers and consequently, the Fermi energy. The T$^2$ behavior persists in the single-band dilute limit despite the absence of two known mechanisms for T$^2$ behavior, distinct electron …
We study the quantum phase transitions in the nickel pnctides, CeNi$_{2-δ}$(As$_{1-x}$P$_{x}$)$_{2}$ ($δ$ $\approx$ 0.07-0.22). This series displays the distinct heavy fermion behavior in the rarely studied parameter regime of dilute carrier limit. We systematically investigate the magnetization, specific heat and electrical transport down to low temperatures. Upon increasing the P-content, the antiferromagnetic order of the Ce-4$f$ moment is suppressed continuously and vanishes at $x_c \sim$ 0.55. At this doping, the temperature dependences of the specific heat and longitudinal resistivity di…
While it is well-known that the electron-electron (\emph{ee}) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T^2 term can result only from a combined--but distinct from quantum-interference corrections-- eff…
We have studied the metallic behaviour in low density GaAs hole systems, and Si electron systems, close to the apparent two-dimensional metal-insulator transition. Two observations suggest a semi-classical origin for the metallic-like behaviour. Firstly the strength of the metallic behaviour is almost independent of the symmetry of the confining potential, and is predominantly determined by the low temperature resistivity (i.e. by k_F*l). Secondly the fractional decrease in conductivity with increasing temperature depends only on T/T_F, independent of the carrier density, in both systems.
Multipolar Fermi Surface Deformations in Sr$_2$RuO$_4$ Probed by Resistivity and Sound Attenuation: A Window into Electron Viscosity and the Collision Operator
An exhaustive investigation of metallic electronic transport and superconductivity of organic superconductors (TMTSF)_2PF_6 and (TMTSF)_2ClO_4 in the Pressure-Temperature phase diagram between T=0 and 20 K and a theoretical description based on the weak coupling renormalization group method are reported. The analysis of the data reveals a high temperature domain (T\approx 20 K) in which a regular T^2 electron-electron Umklapp scattering obeys a Kadowaki-Woods law and a low temperature regime (T< 8 K) where the resistivity is dominated by a linear-in temperature component. In both compounds a c…
We have studied the low-temperature properties of Pr$_{x}$La$_{1-x}$Pb$_{3}$ with non-Kramers $Γ_{3}$ quadrupolar moments of the crystal-electric-field ground state, for a wide concentration range of Pr ions. For $x$$\le$0.05, the specific heat $C/T$ increases monotonically below $T$=1.5 K, which can be scaled with a characteristic temperature $T^{*}$ defined at each concentration $x$. The electrical resistivity $ρ$$(T)$ in the corresponding temperature region shows a marked decrease deviating from a Fermi-liquid behavior $ρ$$(T)$$\propto$$T^{2}$. The Kondo effect arising from the correlation …
The resistivities of the dilute, strongly-interacting 2D electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $ρ(T) = ρ_0 \mbox{exp}[(T_{ES}/T)^{1/2}]$, with $T_{ES}$ and $1/ρ_0$ mapping onto each other if one applies a shift of the critical density $n_c$ reported earlier. With and withoug magnetic field, the parameters $T_{ES}$ and $1/ρ_0 = σ_0$ …
In recent years systematic experimental studies of the temperature dependence of the resistivity in a variety of dilute, ultra clean two dimensional electron/hole systems have revived the fundamental question of localization or, alternatively, the existence of a metal-insulator transition in the presence of strong electron-electron interactions in two dimensions. We argue that under the extreme conditions of ultra clean systems not only is the electron-electron interaction very strong but the role of other system specific properties are also enhanced. In particular, we emphasize the role of va…
It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to or higher than the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time ($τ_p=\hbar/k_BT$). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, a…
Dilute impurities and growth conditions can drastically affect the transport properties of TiSe$_2$, especially below the charge density wave transition. In this paper, we discuss the effects of cooling rate, annealing time and annealing temperature on the transport properties of TiSe$_2$: slow cooling of polycrystalline TiSe$_2$ post-synthesis drastically increases the low temperature resistivity, which is in contrast to the metallic behavior of single-crystalline TiSe$_2$ due to charge doping from the residual iodine transport agent. A logarithmic increase of resistivity upon cooling and neg…
The electrical resistivity including the Kondo resistivity increase at low temperature is calculated for thin films of dilute magnetic alloys. Assuming that in the non-magnetic host the spin-orbit interaction is strong like in Au and Cu, the magnetic impurities have a surface anisotropy calculated in part I. That anisotropy hinders the motion of the spin. Including that anisotropy the effective electron-impurity coupling is calculated by using the second order renormalization group equations. The amplitude of the Kondo resistivity contribution is reduced as the position of the impurity approac…
Electrical resistivity $ρ(T)$ and specific heat $C(T)$ measurements have been made on the diluted 4$f^2$ system Y(Pr)Ir$_2$Zn$_{20}$. Both data of $ρ$ and magnetic specific heat $C_{\rm m}$ per Pr ion are well scaled as a function of $T/T_{\rm 0}$, where $T_{\rm 0}$ is a characteristic temperature of non-Fermi liquid (NFL) behaviors. Furthermore, the temperature dependences of $ρ$ and $C_{\mathrm{m}}/T$ agree with the NFL behaviors predicted by the two-channel Kondo model for the strong coupling limit. Therefore, we infer that the observed NFL behaviors result from the single-site quadrupole K…
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 …
The Fermi-liquid-like (FL) resistivity recently observed in clean HgBa2CuO4 below the pseudogap temperature was related to carriers at the nodal points on the Fermi surface [4]. We show that this necessitates important implications for the electronic spectrum of underdoped (UD) cuprates in whole. Photoemission experiments picture the spectrum as of metallic arcs separated from each other by regions with large energy gaps. We solved the kinetic equation in such model rigorously. The Fermi arcs carriers contribute to FL resistivity, if scattering between the opposite nodal points admits the Umkl…
We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f$^2$ configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the $- \ln T$ divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a po…
Stoichiometric Sr2IrO4 is a ferromagnetic Jeff = 1/2 Mott insulator driven by strong spin-orbit coupling. Introduction of very dilute oxygen vacancies into single-crystal Sr2IrO4-delta with delta < 0.04 leads to significant changes in lattice parameters and an insulator-to-metal transition at TMI = 105 K. The highly anisotropic electrical resistivity of the low-temperature metallic state for delta ~ 0.04 exhibits anomalous properties characterized by non-Ohmic behavior and an abrupt current-induced transition in the resistivity at T* = 52 K, which separates two regimes of resisitive switching …
Electron-electron scattering usually dominates the transport in strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum $ρ_{max}$ increases. Here we show that, in this regime, the entire family of resistivity curves displays a c…
We present the thermopower S(T) and the resistivity rho(T) of Lu(1-x)Yb(x)Rh2Si2 in the temperature range 3 K < T < 300 K. S(T) is found to change from two minima for dilute systems (x < 0.5) to a single large minimum in pure YbRh2Si2. A similar behavior has also been found for the magnetic contribution to the resistivity rho_mag(T). The appearance of the low-T extrema in S(T) and rho_mag(T) is attributed to the lowering of the Kondo scale with decreasing x. The evolution of the characteristic energy scales for both the Kondo effect and the crystal electric field splitting are deduced. An extr…
We observe that an in-plane magnetic field ($B_{||}$) can induce an order of magnitude enhancement in the low temperature ($T$) resistivity ($ρ$) of metallic 2D holes in a narrow (10nm) GaAs quantum well. Moreover, we show the first observation of saturating behavior of $ρ(B_{||})$ at high $B_{||}$ in GaAs system, which suggests our large positive $ρ(B_{||})$ is due to the spin polarization effect alone. We find that this tenfold increase in $ρ(B_{||})$ even persists deeply into the 2D metallic state with the high $B_{||}$ saturating values of $ρ$ lower than 0.1$\times$h/e$^2$. The dramatic ef…
We report the temperature($T$) and perpendicular magnetic field($B$) dependence of the Hall resistivity $ρ_{xy}(B)$ of dilute metallic two-dimensional(2D) holes in GaAs over a broad range of temperature(0.02-1.25K). The low $B$ Hall coefficient, $R_H$, is found to be enhanced when $T$ decreases. Strong magnetic fields further enhance the slope of $ρ_{xy}(B)$ at all temperatures studied. Coulomb interaction corrections of a Fermi liquid(FL) in the ballistic regime can not explain the enhancement of $ρ_{xy}$ which occurs in the same regime as the anomalous metallic longitudinal conductivity. In …
A new reentrant insulating phase (RIP) in low magnetic fields has been reported in the literature in strongly interacting 2D carrier systems and was suggested to be related to the formation of a Wigner crystal [e.g. Qiu et al, PRL 108, 106404 (2012)]. We have studied the transformation between the metallic liquid phase and the low field RIP in a dilute 2D hole system with large interaction parameter $r_s$ (~20-30) in GaAs quantum wells. Instead of a sharp transition, increasing density (or lowering $r_s$) drives the RIP into a state where an incipient RIP coexists with the metallic 2D hole liq…
We present measurements of the Joule heating of a 2D hole gas (2DHG) formed in a 30nm GaAs quantum well. The hole density is in the range (4.6-18.9)*10^9cm^-2 and exhibits an apparent metal-to-insulator transition (MIT) with a critical density 6*10^9 cm^-2. In the limit of zero heating power density P, the GaAs lattice is within 2 mK of the 6 mK base temperature of our dilution refrigerator determined by He-3 melting curve thermometry. Throughout the range of heating power densities used (1 to 10^6 fW/cm^2), the temperature rise of the lattice is estimated to be negligible compared to the temp…
Sr3Ir2O7 exhibits a novel Jeff=1/2 insulating state that features a splitting between Jeff=1/2 and 3/2 bands due to spin-orbit interaction. We report a metal-insulator transition in Sr3Ir2O7 via either dilute electron doping (La3+ for Sr2+) or application of high pressure up to 35 GPa. Our study of single-crystal Sr3Ir2O7 and (Sr1-xLax)3Ir2O7 reveals that application of high hydrostatic pressure P leads to a drastic reduction in the electrical resistivity by as much as six orders of magnitude at a critical pressure, PC = 13.2 GPa, manifesting a closing of the gap; but further increasing P up t…
We report on a study of electronic transport in semi-metallic Bi$_{0.96}$Sb$_{0.04}$. At zero field, the system is a very dilute Fermi liquid displaying a T$^{2}$ resistivity with an enhanced prefactor. Quantum oscillations in resistivity as well as in Hall, Nernst and Seebeck responses of the system are detectable and their period quantifies the shrinking of the Fermi surface with antimony doping. For a field along the trigonal axis, the quantum limit was found to occur at a field as low as 3T. An ultraquantum anomaly at twice this field was detected in both charge transport and Nernst respon…
Single crystals of Cu$_{13}$Ba were successfully grown out of Ba-Cu self flux. Temperature dependent magnetization, $M(T)$, electrical resistivity, $ρ(T)$, and specific heat, $C_p(T)$, data are reported. Isothermal magnetization measurements, $M(H)$, show clear de Haas-van Alphen oscillations at $T$ = 2 K for applied fields as low as $μ_0H$ = 1T. An anomalous behavior of the magnetic susceptibility is observed up to $T$ ~ 50K reflecting the effect of de Haas-van Alphen oscillations at fairly high temperatures. The field- and temperature-dependencies of the magnetization indicate the presence o…
We find that the temperature dependence of the drag resistivity ($ρ_{D}$) between two dilute two-dimensional hole systems exhibits an unusual dependence upon spin polarization. Near the apparent metal-insulator transition, the temperature dependence of the drag, given by $T^α$, weakens with the application of a parallel magnetic field ($B_{||}$), with $α$ saturating at half its zero field value for $B_{||} > B^{*}$, where $B^{*}$ is the polarization field. Furthermore, we find that $α$ is roughly 2 at the parallel field induced metal-insulator transition, and that the temperature dependence of…
