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Phase diagram of cuprate superconductors. Schematic phase diagram of cuprate superconductors as a function of hole concentration (doping) p . The Mott insulator at p = 0 shows antiferromagnetic (AF) order below T N , which vanishes rapidly with doping. At high doping, the metallic state shows all the signs of a conventional Fermi liquid. At the critical doping p c , two events happen simultaneously: superconductivity appears (below a critical temperature T c ) and the resistivity deviates from its Fermi-liquid behaviour, acquiring a linear temperature dependence. The simultaneous onset of T c and linear resistivity is the starting point for our exploration of cuprates. The evolution from metal to insulator is interrupted by the onset of the “pseudogap
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The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation...
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... the QCP in Nd-LSCO marks the onset of a finite- Q modulation of the spin and charge densities at T = 0 which breaks the translational symmetry of the lattice and hence causes a reconstruction of the Fermi surface. (It is possible that spin and charge order set in at somewhat different dopings and temperatures.) The critical doping at which this symmetry-breaking and Fermi- surface reconstruction onset was pinpointed by tracking the upturn in the c -axis resistivity of Nd-LSCO [47], giving p * = 0.235 ± 0.005. A similar study performed on Bi 2 Sr 2 CaCu 2 O 8+ δ gave a comparable value of p * [48]. Calculations [49] show that stripe order does cause the Fermi surface to break up into small electron and hole pockets (plus some quasi-1D sheets), and these can give rise to positive and negative swings in R ( T → 0) as the SDW potential grows with underdoping [50]. This establishes the existence of a QCP inside the superconducting dome, at which stripe order (a form of SDW order) ends, much as in the organic and pnictide superconductors. The analogy then suggests that fluctuations of the stripe order are responsible for the linear resistivity and, given the correlation with T c , the pairing. In support of this connection, the strength of antiferromagnetic fluctuations in overdoped LSCO measured by inelastic neutron scattering has been shown to scale with T c [51]. Two important questions now arise: Is stripe order a generic property of hole-doped cuprates? Is the pseudogap phase related to stripe order? We address the first question in the remainder of this section, and explore the second question in section 6. Scanning tunneling microscopy (STM) studies have revealed real-space modulations of the charge density in three different hole-doped cuprates [52, 53, 54, 80, 94]: Bi 2 Sr 2 CaCu 2 O 8+ δ , Ca 2-x Na x CuO 2 Cl 2 and Bi 2 Sr 2 CuO 6+x . These have stripe-like unidirectional character on the nanometer scale [55, 80]. The modulations persist into the overdoped regime and their real-space period appears to lengthen with doping [54], which points to a charge-density-wave order driven by Fermi-surface nesting. Neutron scattering studies have revealed stripe-like SDW order in LSCO for dopings below p S ≈ 1/8 [56]. This critical doping moves up in a magnetic field [56, 57], such that the QCP is expected to be roughly at p * ≈ 0.2 once superconductivity has been fully suppressed. The fact that the QCP moves up with field, from p S in the superconducting state up to p * in the normal state ( Figure 1 ) is attributed to a competition between SDW and superconducting phases [58, 59, 95]. In Nd-LSCO, where stripe order is stronger, the presence of a weakened superconductivity has little effect on p *, and hence p S ≈ p * = 0.235. In LSCO, superconductivity is stronger and its presence does shift the QCP down significantly. Taken together, STM, neutron and X-ray studies on several different materials make a strong case that stripe order is a generic tendency of hole-doped cuprates at low temperature (for reviews on stripe order and fluctuations, see [60, ...
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... of its high maximal T c and low level of disorder, the case of YBa 2 Cu 3 O y (YBCO) deserves special attention; any phenomenon deemed generic should be seen in YBCO. Muon spin relaxation has shown that magnetism is present in YBCO below p ≈ 0.08 [61], and neutron diffraction has revealed spin-stripe SDW order in YBCO, but again only up to p ≈ 0.08 [62]. Although it is quite conceivable that in zero field the SDW phase is confined to such low doping because of a particularly strong competition from superconductivity (see [63]), it is important to establish whether SDW order persists up to higher doping in the absence of such competition. A number of recent studies in high magnetic fields provide compelling evidence that it does. The observation of quantum oscillations in YBCO at p = 0.10-0.11 [64, 65] revealed the existence of a small closed pocket in the Fermi surface of an underdoped cuprate at T → 0 (see Figure 9 ), whose k -space area is some 30 times smaller than the area enclosed by the large hole-like cylinder characteristic of the overdoped regime [11]. Similar oscillations were also observed in YBa 2 Cu 4 O 8 , for which p ≈ 0.14 [66, 67]. The fact that the Hall coefficient of both materials is large and negative at T → 0 (see Figure 10 ) indicates that this small closed Fermi pocket is in fact electron-like [68]. The normal-state Seebeck coefficient reaches a negative value of S / T as T → 0 which is quantitatively consistent with the frequency and cyclotron mass of the quantum oscillations only if those come from an electron Fermi pocket [41]. The very existence of an electron pocket in a hole-doped cuprate is compelling evidence of broken translational symmetry, the result of a Fermi-surface reconstruction caused by the onset of some new periodicity [69]. In YBCO at p = 0.12, R H ( T ) starts its descent to negative values upon cooling in precisely the same way as it does in Eu-LSCO at p = 0.125 [42], where this drop is associated unambiguously with the onset of stripe order (see Figure 7 ). The same striking similarity between YBCO and Eu-LSCO is observed in the way that S / T falls to negative values [41], pointing again to the same underlying mechanism, the onset of stripe order. In YBCO, this mechanism is still present at p ≈ 0.14 and extrapolation suggests that p * > 0.2. Taken together, these high-field data support the case that the normal-state QCP identified in Nd-LSCO at p * = 0.235 is also present in YBCO and is therefore a generic property of hole-doped cuprates, once the competing superconducting phase has been removed. Note that the temperature below which Fermi-surface reconstruction in YBCO begins ( i . e . where R H and S / T start to fall) is maximal at p = 1/8 [68], the doping where T c is most strongly suppressed relative to its ideal parabolic dependence on doping [70]. The fact that peak (in R H maximum) and dip (in T c ) coincide is consistent with a scenario of competing stripe and superconducting orders, the former being stabilized by commensurate locking with the lattice at p = 1/8, as in the La 2 CuO 4 -based cuprates. Note also that the electron-pocket state is not induced by the magnetic field: at p = 1/8, the drop in R H ( T ) is observed in the limit of zero field and is independent of field [68, 71]. The field simply serves to remove superconductivity and allow transport measurements to be extended to the T → 0 limit. Above we focused on the T → 0 limit and argued that there is a generic normal-state QCP in the overdoped regime of hole-doped cuprates below which translational symmetry is broken and the large hole-like Fermi surface is reconstructed. Now we examine this same process as a function of temperature. In other words, after having investigated a p -cut at T = 0 in the phase diagram ( Figure 1 ), across the QCP at p *, we now look at a T -cut at p < p *, across the pseudogap temperature T *. We begin by defining T * as the temperature T ρ below which the in-plane resistivity ρ ( T ) deviates from its linear temperature dependence at high temperature – a standard definition of T * in YBCO [8, 72]. In Nd-LSCO, T ρ marks the onset of an upward deviation in ρ ( T ), which eventually leads to an upturn at low temperature ( Figure 2 ). In Figure 8 , T ρ is plotted as a function of doping; it goes to zero at p *. Note that T CO , the onset of long-range stripe order, which also vanishes roughly at p *, lies well below T ρ , so that T ρ ≈ 2 T CO . This suggests that T ρ marks the onset of stripe fluctuations and that the pseudogap phase below T * is initially just a short-range / fluctuating precursor of the order that eventually develops fully at lower temperature [42, 73]. As a probe of electronic transformations and phase transitions, the Nernst effect is in general vastly more sensitive than resistivity [74], in essence because changes in carrier density and scattering rate tend to combine in the former whereas they tend to cancel in the latter. Nernst measurements have been used only recently to study the onset of the pseudogap phase in cuprates [46, 75, 76]. A pseudogap temperature T ν can be defined from the Nernst coefficient ν ( T ) in much the same way as for ρ ( T ), namely as the temperature below which ν / T deviates from its linear temperature dependence at high temperature [46, 76, 77]. The resulting phase diagram is shown in Figure 11a for LSCO, Eu- LSCO and Nd-LSCO and in Figure 11b for YBCO. First, we see that T ν = T ρ , within error bars. This shows that both ρ and ν detect the same pseudogap temperature T *, which is not surprising since ν involves the energy derivative of the conductivity [74]. Second, T ν is the same in LSCO and Eu/Nd- LSCO. This shows that the onset of the pseudogap phase is independent of the detailed crystal structure and the relative strength of stripe order and superconductivity. It also strongly suggests that the elusive normal-state QCP in LSCO [20] is located at the same doping p * as it is in Nd-LSCO (namely at p ≈ 0.24), or close to it. Thirdly, T ν in YBCO can be tracked all the way up to p = 0.18 [76], the highest doping achievable in pure YBCO (at full oxygen content [70]). Comparison with the LSCO phase diagram suggests that T ν in YBCO will extrapolate to zero at much the same p *. This is further support for a generic normal-state QCP in hole-doped cuprates at p * ≈ ...
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... suggestion that T * marks the onset of stripe fluctuations (or short-range order) has recently received strong support from a study of the Nernst effect in untwinned crystals of YBCO [76]. Measurements with the temperature gradient applied along the a axis and then the b axis of the orthorhombic lattice reveal a pronounced anisotropy that grows with decreasing temperature starting precisely at T * throughout the phase diagram and reaching values as high as ν b / ν a = 7 before superconductivity intervenes [76] (see Figure 12 ). These findings are consistent with prior evidence of in-plane anisotropy in the resistivity [78] and in the spin fluctuation spectrum [62], detected below p ≈ 0.08. The Nernst data now provide the missing link to the pseudogap phase by showing that T * marks the onset of broken rotational symmetry in the electronic properties of the CuO 2 planes. This unidirectional character is one of the defining signatures of stripe order [60, 73, 96]. Microwave and STM studies have provided complementary evidence of broken rotational symmetry, observed at low temperature in the superconducting state. The microwave conductivity of YBCO exhibits a strong in- plane anisotropy at p = 0.1 which is not present at p = 0.18 [79], suggesting that the zero-field QCP in YBCO lies between those two dopings, i . e . 0.1 < p S < 0.18 (see Figure 1 ). STM revealed that rotational symmetry is broken on the local scale at the surface of two cuprates [55, 80], in the simultaneous presence of broken translational symmetry [55]. This glassy nanostripe order was recently linked to the pseudogap energy scale ...
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... doping phase diagram of hole-doped cuprates is sketched in Figure 1 . With increased hole concentration (doping) p , the materials go from being antiferromagnetic insulators at zero doping to metals at high doping. Given their density of one electron per Cu in the undoped state, they should be metals even at p = 0, with a Fermi surface volume containing 1 + p holes, but strong on-site repulsion prevents electron motion and turns the material into a Mott insulator at low doping. At intermediate doping, between the insulator and the metal, there is a central region of superconductivity, delineated by a critical temperature T c , which can rise to values of order 100 K – higher than in any other family of materials. Near optimal doping, the normal state above T c is referred to as a “strange metal”, characterized by a resistivity that is linear in temperature. In the midst of this strange-metal region, the pseudogap phase sets in, below a crossover temperature T * at which most physical properties undergo a significant change [8]. The question is whether the pseudogap phase is a precursor to some “hidden” ordered state with broken symmetry or a precursor to the Mott insulator, with no broken symmetry. To explore this landscape, we shall start from the far right side of Figure 1 , in the overdoped metallic state. This state is characterized by a large Fermi surface whose volume contains 1 + p holes per Cu atom, as determined by angle-dependent magneto-resistance (ADMR) [9], angle-resolved photoemission spectroscopy (ARPES) [10] and quantum oscillations [11], all performed on the single- layer cuprate Tl 2 Ba 2 CuO 6+ δ (Tl-2201). The low-temperature Hall coefficient R H of overdoped Tl-2201 is positive and equal to 1 / e (1 + p ) [12], as expected for a single-band metal with a hole density n = 1 + p . Conduction in the normal state obeys the Wiedemann-Franz law [13], a hallmark of Fermi- liquid theory. At the highest doping, beyond the superconducting phase ( Figure 1 ), the electrical resistivity ρ ( T ) of Tl-2201 exhibits the standard T 2 temperature dependence of a Fermi liquid [14], also observed in La Sr CuO (LSCO) ...
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... doping phase diagram of hole-doped cuprates is sketched in Figure 1 . With increased hole concentration (doping) p , the materials go from being antiferromagnetic insulators at zero doping to metals at high doping. Given their density of one electron per Cu in the undoped state, they should be metals even at p = 0, with a Fermi surface volume containing 1 + p holes, but strong on-site repulsion prevents electron motion and turns the material into a Mott insulator at low doping. At intermediate doping, between the insulator and the metal, there is a central region of superconductivity, delineated by a critical temperature T c , which can rise to values of order 100 K – higher than in any other family of materials. Near optimal doping, the normal state above T c is referred to as a “strange metal”, characterized by a resistivity that is linear in temperature. In the midst of this strange-metal region, the pseudogap phase sets in, below a crossover temperature T * at which most physical properties undergo a significant change [8]. The question is whether the pseudogap phase is a precursor to some “hidden” ordered state with broken symmetry or a precursor to the Mott insulator, with no broken symmetry. To explore this landscape, we shall start from the far right side of Figure 1 , in the overdoped metallic state. This state is characterized by a large Fermi surface whose volume contains 1 + p holes per Cu atom, as determined by angle-dependent magneto-resistance (ADMR) [9], angle-resolved photoemission spectroscopy (ARPES) [10] and quantum oscillations [11], all performed on the single- layer cuprate Tl 2 Ba 2 CuO 6+ δ (Tl-2201). The low-temperature Hall coefficient R H of overdoped Tl-2201 is positive and equal to 1 / e (1 + p ) [12], as expected for a single-band metal with a hole density n = 1 + p . Conduction in the normal state obeys the Wiedemann-Franz law [13], a hallmark of Fermi- liquid theory. At the highest doping, beyond the superconducting phase ( Figure 1 ), the electrical resistivity ρ ( T ) of Tl-2201 exhibits the standard T 2 temperature dependence of a Fermi liquid [14], also observed in La Sr CuO (LSCO) ...
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... doping phase diagram of hole-doped cuprates is sketched in Figure 1 . With increased hole concentration (doping) p , the materials go from being antiferromagnetic insulators at zero doping to metals at high doping. Given their density of one electron per Cu in the undoped state, they should be metals even at p = 0, with a Fermi surface volume containing 1 + p holes, but strong on-site repulsion prevents electron motion and turns the material into a Mott insulator at low doping. At intermediate doping, between the insulator and the metal, there is a central region of superconductivity, delineated by a critical temperature T c , which can rise to values of order 100 K – higher than in any other family of materials. Near optimal doping, the normal state above T c is referred to as a “strange metal”, characterized by a resistivity that is linear in temperature. In the midst of this strange-metal region, the pseudogap phase sets in, below a crossover temperature T * at which most physical properties undergo a significant change [8]. The question is whether the pseudogap phase is a precursor to some “hidden” ordered state with broken symmetry or a precursor to the Mott insulator, with no broken symmetry. To explore this landscape, we shall start from the far right side of Figure 1 , in the overdoped metallic state. This state is characterized by a large Fermi surface whose volume contains 1 + p holes per Cu atom, as determined by angle-dependent magneto-resistance (ADMR) [9], angle-resolved photoemission spectroscopy (ARPES) [10] and quantum oscillations [11], all performed on the single- layer cuprate Tl 2 Ba 2 CuO 6+ δ (Tl-2201). The low-temperature Hall coefficient R H of overdoped Tl-2201 is positive and equal to 1 / e (1 + p ) [12], as expected for a single-band metal with a hole density n = 1 + p . Conduction in the normal state obeys the Wiedemann-Franz law [13], a hallmark of Fermi- liquid theory. At the highest doping, beyond the superconducting phase ( Figure 1 ), the electrical resistivity ρ ( T ) of Tl-2201 exhibits the standard T 2 temperature dependence of a Fermi liquid [14], also observed in La Sr CuO (LSCO) ...
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... It is expected that in the vicinity of a QCP, the resistivity temperature dependence deviates strongly from the conventional T 2 Fermi liquid behavior towards T−linear variation [42,43]. This was demonstrated in pressure-tuned Ca 3 Ir 4 Sn 13 [14] and in the study of a combination of Ca-Sr alloying and pressure [15]. ...
... A T c (x) increase towards x ∼ 0.5 reflects the competition between CDW and superconductivity, although the absolute variation in T c is not large, from 7 K to 8.3 K. The observation of a plateau in T c (x) dependence rather than of a 'dome shape' is different from the behavior of high−T c cuprates [43], heavy fermions [42] and in phosphorus doped 122 iron-based superconductors [44]. It may suggest that the competition between CDW and superconductivity for the states at Fermi energy, leading to a decrease of T c , is stronger than the effect of quantum fluctuations. ...
Single crystals of the quasi-skutterudite compounds Ca3(Ir1-xRhx)4Sn13 (3–4–13) were synthesized by flux growth and characterized by x-ray diffraction, energy dispersive x-ray spectroscopy, magnetization, resistivity, and radio frequency magnetic susceptibility techniques. The coexistence and competition between the charge density wave (CDW) and superconductivity was studied by varying the Rh/Ir ratio. The superconducting transition temperature, Tc , varies from 7 K in pure Ir (x = 0) to 8.3 K in pure Rh (x = 1). Temperature-dependent electrical resistivity reveals monotonic suppression of the CDW transition temperature, T CDW(x). The CDW starts in pure Ir, x = 0, at T CDW ≈ 40 K and extrapolates roughly linearly to zero at xc≈ 0.53–0.58 under the superconducting dome. Magnetization and transport measurements show a significant influence of CDW on superconducting and normal states. Meissner expulsion is substantially reduced in the CDW region, indicating competition between the CDW and superconductivity. The low-temperature resistivity is higher in the CDW part of the phase diagram, consistent with the reduced density of states due to CDW gapping. Its temperature dependence just above Tc shows signs of non-Fermi liquid behavior in a cone-like composition pattern. We conclude that the Ca3(Ir1-xRhx)4Sn13 alloy is a good candidate for a composition-driven quantum critical point at ambient pressure.
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We derive selection rules in optical absorption and Raman scattering spectra, that can determine the parity of pairing order parameters under inversion symmetry in two classes of \emph{clean} superconductors: (i) chiral superconductors with strong spin-orbit couplings, (ii) singlet superconductors with negligible spin-orbit couplings. Experimentally, the inversion parity of pair wave functions can be determined by comparing the "optical gap" $\Delta_\text{op}$ in Raman and optical spectroscopy and the "thermodynamic gap" $2\Delta$ in specific heat measurements, and the selection rules apply when $\Delta_\text{op}>2\Delta$. We demonstrate the selection rules in superconductivity in models of (i) doped Weyl semimetals and (ii) doped graphene. Our derivation is based on the relation between pairing symmetry and fermion projective symmetry group of a superconductor. We further derive similar selection rules for two-dimensional superconductors with 2-fold rotational symmetry, and discuss how they apply to the superconducting state in magic-angle twisted bilayer graphene.
... The dc resistivity of the high-T c cuprate superconductors is found to exhibit perfect linear-in-T behavior from very high temperature all the way down to zero temperature around the pseudogap endpoint [1][2][3][4][5] . Such an anomalous behavior is hard to reconcile with the fermi liquid transport picture in which the dc resistivity is determined by the quasiparticle scattering rate on the fermi energy. ...
The perfect linear-in-$T$ dc resistivity in the strange metal phase of the high-$T_{c}$ cuprate superconductors is probably the most prominent manifestation of their non-Fermi liquid nature. A major puzzle about the strange metal behavior is that there is no discernible change in the trend of the dc resistivity at a temperature when we expect the electron-phonon coupling to play an essential role. The empirical Matthiessen's rule of summation of the resistivity from different scattering channels seems to be simply violated. On the other hand, the electron-phonon coupling has long been proposed to be responsible for the various spectral anomalies observed in the cuprate superconductors. In particular, the $B_{1g}$ buckling mode of the oxygen ion in the $CuO_{2}$ plane is proposed to be responsible for the peak-dip-hump spectral shape around the anti-nodal point. Here we show that the coupling to the $B_{1g}$ buckling mode is strongly suppressed by the vertex correction from the antiferromagnetic spin fluctuation in the system as a result of the destructive interference between electron-phonon matrix element at momentum differ by the antiferromagnetic wave vector. In the real space scenario, such a destructive interference effect simply amounts to the fact that the electron hopping between nearest-neighboring sites is suppressed by the antiferromagnetic spin correlation between the electrons. More generally, we argue that the electron-phonon coupling strength in the cuprate superconductors should diminish with the proximity of the Mott insulating phase as a result of similar vertex correction from the electron correlation effect. We think that this offers an interpretation for the violation of the Matthiessen's rule in the dc resistivity of the strange metal phase of the cuprate superconductors.
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... Regions I and II seem to be located in one quantum critical region associated with p * , but they exhibit different α 1 (p) relations. This suggests a switch of scattering mechanism upon doping, which contrasts with the scenario that the funnel-shaped region in Fig. 1 is dominated by quantum critical fluctuations [14,39,40]. Interestingly, for region I, the recent resonant inelastic x-ray scattering experiment shows a clear correlation between the charge order and the T -linear resistivity [41]; for region II, the scattering of electrons by classical phonons has been detected by the thermal transport [29]. ...
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The origin of the linear-in-temperature ( T -linear) resistivity in cuprate superconductors remains a profound mystery in condensed matter physics. Here, we investigate the dependence of the T -linear resistivity coefficient on doping, i.e., A 1 ( p ) , for three typical regions in the temperature versus doping phase diagram of hole-doped cuprates, from which the doping dependence of the scattering rate, i.e., α 1 ( p ) , is further derived. It is found that for region I ( p < p * and T > T * ), α 1 ( p ) is almost a constant; for region II ( p > p * and T > T coh ), α 1 ( p ) ∝ p ; for region III ( p > p * and T < T coh ), α 1 ( p ) ∝ p ( p c − p ) , where T * is the onset temperature of the pseudogap phase, p * indicates the doping at which T * goes to zero, T coh marks the onset of antinodal quasiparticle coherence, and p c is the doping where the low-temperature linear behavior in the overdoped regime vanishes. Moreover, the deduced α 1 ( p ) relations are verified with the experimental data from previous reports. The discovered scattering rate versus doping relationship will shed light on the scattering mechanism underlying the T -linear resistivity in cuprate superconductors.
Published by the American Physical Society 2024
... There are a variety of normal-state properties of holedoped cuprate superconductor compounds that deviate from expectations of Fermi liquid theory. For example, there are the anomalous temperature dependences of properties such as magnetic susceptibility, in-plane resistivity ρ ab , the Hall effect, and various spectroscopic features observed especially in underdoped cuprates that have been discussed commonly in terms of pseudogap phenomena [1][2][3][4][5][6][7][8][9]. The crossover temperature T * associated with the pseudogap behaviors decreases as the doped-hole concentration p increases, extrapolating to zero at p * ∼ 0.19 [3]. ...
... In response, Laughlin argued [30] that adiabatic continuity should apply from the overdoped metallic phase through the full doping range where superconducting order exists, so that if there is a Mott insulator phase at p = 0, there should be a first order transition at a p between the antiferromagnetic state and the onset of superconductivity. From his perspective, the pseudogap behavior could be attributed to a competing order that is compatible with conventional band theory (d-densitywave order in his case), with p * corresponding to a quantum critical point (QCP) and strange-metal behavior resulting from critical scattering [31]; others have considered a QCP due to spin-density-wave (SDW) [7,32], charge-densitywave (CDW) [24][25][26]33,34], or pair-density-wave [27] orders. ...
... It is important to note here that, while these correlations can be described as intertwined spin density wave (SDW) and charge density wave (CDW) orders, they are a consequence of competition between antiferromagnetism driven by superexchange [28,29] and the frustrated kinetic energy of the doped holes [51]. They are distinct from the individual SDW or CDW orders that can develop in conventional metals and that have been considered by some [7,[24][25][26]33]. ...
The nature of the normal state of cuprate superconductors continues to stimulate considerable speculation. Of particular interest has been the linear temperature dependence of the in-plane resistivity in the low-temperature limit, which violates the prediction for a Fermi liquid. We present measurements of anisotropic resistivity in La2−xSrxCuO4 that confirm the strange-metal behavior for crystals with doped-hole concentration p=x>p*∼0.19 and contrast with the nonmetallic behavior for p<p*. We propose that the changes at p* are associated with a first-order transition from doped Mott insulator to conventional metal; the transition appears as a crossover due to intrinsic dopant disorder. We consider results from the literature that support this picture; in particular, we present a simulation of the impact of the disorder on the first-order transition and the doping dependence of stripe correlations. Below p*, the strong electronic interactions result in charge and spin stripe correlations that percolate across the CuO2 planes; above p*, residual stripe correlations are restricted to isolated puddles. We suggest that the T-linear resistivity results from scattering of quasiparticles from antiferromagnetic spin fluctuations within the correlated puddles. This is a modest effect compared to the case at p<p*, where the data suggest that there are no coherent quasiparticles in the normal state.
... The ability to easily manipulate the parameters of the system, such as the twist angle or the carrier density, provides a rich experimental platform to test and understand the nature of the correlated phases [6,7,12]. Such understanding may prove to be not only relevant for the phenomena observed in moiré heterostructures, but also for elucidating the mechanisms responsible for unconventional superconductivity in more complex systems, such as in cuprates [13,14]. ...
... Figs. 3 and 4. Due to the strong coupling of the moiré potential at low twist angles, and the nonnegligible contribution of interband transitions, one generally needs to consider many irreducible diagrams in order to achieve a convergence of the selfenergy. A valuable guide to visualize the relevant scattering events can be obtained by giving a diagrammatic representation to Eq. (13). For conciseness, throughout this section we will focus on the self-energy for the top layer, so that γ = (+, k, s). ...
We develop a many-body perturbation theory to account for the emergence of moiré bands in the continuum model of twisted bilayer graphene. Our framework is build upon treating the moiré potential as a perturbation that transfers electrons from one layer to another through the exchange of the three wave vectors that define the moiré Brillouin zone. By working in the two-band basis of each monolayer, we analyze the one-particle Green's function and introduce a diagrammatic representation for the scattering processes. We then identify the moiré-induced self-energy, relate it to the quasiparticle weight and velocity of the moiré bands, and show how it can be obtained by summing irreducible diagrams. We also connect the emergence of flat bands to the behavior of the static self-energy at the magic angle. In particular, we show that a vanishing Dirac velocity is a direct consequence of the relative orientation of the momentum transfer vectors, suggesting that the origin of magic angles in twisted bilayer graphene is intrinsically connected to its geometrical properties. Our approach provides a many-body diagrammatic framework that highlights the physical properties of the moiré bands.
... The phase diagram of the cuprates has become more complicated as the research goes on [4]. However, the generic phase diagram of cuprates is well known [5,6]. The undoped parent copper oxides are antiferromagnetic (AFM) insulators. ...
... There is the peculiar pseudogap phase, which shows a partial suppression of the density of states near the Fermi level and is not completely understood yet. The pseudogap phase is suppressed as the doping increases and, eventually, disappears at a certain doping level on the overdoped side of the phase diagram, which is called the pseudogap critical point (p*) [6]. Recently, an optical study on La 2− x Sr x CuO 4 (LSCO at x = 0.24) at the p* demonstrated that the LSCO at p* showed the Planckian behavior [7]: the normalized optical scattering rate and effective mass as functions of the normalized energy with respect to the temperature (ℏω/ k B T) fall into universal curves. ...
Planckian behavior has been recently observed in La1·76Sr0·24CuO4 at the pseudogap critical point. The Planckian behavior takes place in an intriguing quantum metallic state at a quantum critical point. Here, the Planckian behavior was simulated with an energy-independent (or flat) and weakly temperature-dependent electron-boson spectral density (EBSD) function by using a generalized Allen's (Shulga's) formula. We obtained various optical quantities from the flat EBSD function, such as the optical scattering rate, the optical effective mass, and the optical conductivity. These quantities are well fitted with the recently observed Planckian behavior. Fermi-liquid behavior was also simulated with an energy-linear and temperature-independent EBSD function. The EBSD functions agree well with the overall doping- and temperature-dependent trends of the EBSD function obtained from the optically measured spectra of cuprate systems, which can be crucial for understanding the microscopic electron-pairing mechanism for high-Tc superconductivity in cuprates.
... Another example is the observation of quantum criticality −a scaling between TC and the Tlinear scattering rate [29], which furthermore exhibits the same anisotropy as the d-wave gap [30,31]− pointing to a common origin for anisotropic scattering and pairing [32]. Because illumination modifies both and TC, the question is whether a causal relationship exists and whether the mechanisms behind PPS go beyond the photodoping scenario. ...
... We find instead that PPS is observed only in YBCO films in which illumination produces a significant carrier mobility enhancement, and particularly that the size of PPS scales with the photoinduced mobility enhancement. This unearths an interesting facet of the link between scattering and pairing in the superconducting cuprates [32], i.e. that it is controllable by light. These results call for examining the effect of VIS-UV light on other phenomena that emerge in the underdoped region of the cuprate's phase diagram. ...
The normal-state conductivity and superconducting critical temperature of oxygen-deficient YBa2Cu3O7−δ can be persistently enhanced by illumination. Strongly debated for years, the origin of those effects—termed persistent photoconductivity and photosuperconductivity (PPS)—has remained an unsolved critical problem, whose comprehension may provide key insights to harness the origin of high-temperature superconductivity itself. Here, we make essential steps toward understanding PPS. While the models proposed so far assume that it is caused by a carrier-density increase (photodoping) observed concomitantly, our experiments contradict such conventional belief: we demonstrate that it is instead linked to a photo-induced decrease of the electronic scattering rate. Furthermore, we find that the latter effect and photodoping are completely disconnected and originate from different microscopic mechanisms, since they present different wavelength and oxygen-content dependences as well as strikingly different relaxation dynamics. Besides helping disentangle photodoping, persistent photoconductivity, and PPS, our results provide new evidence for the intimate relation between critical temperature and scattering rate, a key ingredient in modern theories on high-temperature superconductivity.
