Pseudogap Behavior Research Articles

Unusual spin pseudogap behavior in the spin web lattice Cu3TeO6 probed by Te125 nuclear magnetic resonance

We present a $^{125}\mathrm{Te}$ nuclear magnetic resonance (NMR) study in the three-dimensional spin web lattice ${\mathrm{Cu}}_{3}\mathrm{Te}{\mathrm{O}}_{6}$ which harbors topological magnons. The $^{125}\mathrm{Te}$ NMR spectra and the Knight-shift $\mathcal{K}$ as a function of temperature show a drastic change at ${T}_{\mathrm{S}}\ensuremath{\sim}40\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ much lower than the N\'eel ordering temperature ${T}_{\mathrm{N}}\ensuremath{\sim}61\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, providing evidence for the first-order structural phase transition within the magnetically ordered state. Most remarkably, the temperature dependence of the spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ unravels spin-gap-like magnetic excitations, which sharply sets in at ${T}^{*}\ensuremath{\sim}75\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, the temperature well above ${T}_{\mathrm{N}}$. The spin-gap behavior may be understood by weakly dispersive optical magnon branches of high-energy spin excitations originating from the unique corner-sharing Cu hexagon spin-1/2 network with low coordination number.

Experimental evidence for a valence-bond glass in the 5d1 double perovskite Ba2YWO6

We report the magnetic susceptibility, specific heat, and muon spin relaxation results of the $5{d}^{1}$ double perovskite ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$. The dc magnetic susceptibility shows two distinct Curie-Weiss regimes and a sub-Curie-Weiss increase ${T}^{\ensuremath{-}n}$ with $n=0.75(1)$ for $T=3\text{--}100$ K, alluding to the presence of random magnetism. The ac magnetic susceptibility reveals a spin freezing at ${T}_{f}\ensuremath{\sim}0.3$ K with the activation energy of $\mathrm{\ensuremath{\Delta}}/{k}_{B}=27.6$ K. The specific heat data exhibit the pseudogap behavior at 25 K and the subsequent power-law dependence with decreasing temperature, indicating the gradual spin freezing with the quenching of orbital fluctuations. However, the muon spin relaxation data display only a weak muon spin depolarization with lacking long-range magnetic ordering down to 26 mK. Taken together, our results suggest that ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$ is the proximate realization of a random spin-orbit dimer state.

Effect of doping on the pseudogap behaviour and the related terahertz modes in the hybrid chain-ladder compound, Sr14Cu24O41

Using Terahertz (THz) spectroscopy, we report the observation of a pseudogap behaviour in the hybrid chain-ladder compound Sr14Cu24O41 (SCO). This is possibly due to the ordered arrangement of hole pairs in SCO's ladder plane, below the transition temperature, Tco. Several optical modes in the THz frequency range between 60 cm−1 and 90 cm−1, similar to those reported earlier, was also observed. We find that the pseudogap behaviour and the THz-active modes are strongly affected by doping with 5% Co and 0.25% Al, but the effect of 1% Co is not as much. These differences are discussed in terms of the location of these dopants in the chain and ladder substructures.

Interplay between superconductivity and non-Fermi liquid behavior at a quantum-critical point in a metal. V. The γ model and its phase diagram: The case γ=2

This paper is a continuation and a partial summary of our analysis of the pairing at a quantum-critical point (QCP) in a metal for a set of quantum-critical systems, whose low-energy physics is described by an effective model with dynamical electron-electron interaction $V({\mathrm{\ensuremath{\Omega}}}_{m})=(\overline{g}/|{\mathrm{\ensuremath{\Omega}}}_{m}{|)}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). Examples include pairing at the onset of various spin and charge-density-wave and nematic orders and pairing in SYK-type models. In previous papers, we analyzed the physics for $\ensuremath{\gamma}<2$. We have shown that the onset temperature for the pairing ${T}_{p}$ is finite, of order $\overline{g}$, yet the gap equation at $T=0$ has an infinite set of solutions within the same spatial symmetry. As the consequence, the condensation energy ${E}_{c}$ has an infinite number of minima. The spectrum of ${E}_{c}$ is discrete, but becomes more dense as $\ensuremath{\gamma}$ increases. Here we consider the case $\ensuremath{\gamma}=2$. The $\ensuremath{\gamma}=2$ model attracted special interest in the past as it describes the pairing by an Einstein phonon in the limit when the dressed phonon mass ${\ensuremath{\omega}}_{D}$ vanishes. We show that for $\ensuremath{\gamma}=2$, the spectrum of ${E}_{c}$ becomes continuous. We argue that the associated gapless ``longitudinal'' fluctuations destroy superconducting phase coherence at a finite $T$, such that at $0<T<{T}_{p}$, the system displays pseudogap behavior of preformed pairs. We show that for each gap function from the continuum spectrum, there is an infinite array of dynamical vortices in the upper half-plane of frequency. For the electron-phonon case, our results show that ${T}_{p}=0.1827\overline{g}$, obtained in earlier studies, marks the onset of the pseudogap behavior, while the actual superconducting ${T}_{c}$ vanishes at ${\ensuremath{\omega}}_{D}\ensuremath{\rightarrow}0$.

Metal-to-insulator transition in Pt-doped TiSe2 driven by emergent network of narrow transport channels

Metal-to-insulator transitions (MIT) can be driven by a number of different mechanisms, each resulting in a different type of insulator—Change in chemical potential can induce a transition from a metal to a band insulator; strong correlations can drive a metal into a Mott insulator with an energy gap; an Anderson transition, on the other hand, due to disorder leads to a localized insulator without a gap in the spectrum. Here, we report the discovery of an alternative route for MIT driven by the creation of a network of narrow channels. Transport data on Pt substituted for Ti in 1T-TiSe2 shows a dramatic increase of resistivity by five orders of magnitude for few % of Pt substitution, with a power-law dependence of the temperature-dependent resistivity ρ(T). Our scanning tunneling microscopy data show that Pt induces an irregular network of nanometer-thick domain walls (DWs) of charge density wave (CDW) order, which pull charge carriers out of the bulk and into the DWs. While the CDW domains are gapped, the charges confined to the narrow DWs interact strongly, with pseudogap-like suppression in the local density of states, even when they were weakly interacting in the bulk, and scatter at the DW network interconnects thereby generating the highly resistive state. Angle-resolved photoemission spectroscopy spectra exhibit pseudogap behavior corroborating the spatial coexistence of gapped domains and narrow domain walls with excess charge carriers.

Fate of a multiple-band Fermi liquid that is coupled with critical ϕ4 bosons

Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behaviour in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into a same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudo-gap behaviour with a logarithmic energy dependence at the QCP.

Field-dependent specific heat of the canonical underdoped cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8

The cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8, in comparison with most other cuprates, has a stable stoichiometry, is largely free of defects and may be regarded as the canonical underdoped cuprate, displaying marked pseudogap behaviour and an associated distinct weakening of superconducting properties. This cuprate ‘pseudogap’ manifests as a partial gap in the electronic density of states at the Fermi level and is observed in most spectroscopic properties. After several decades of intensive study it is widely believed that the pseudogap closes, mean-field like, near a characteristic temperature, T^*, which rises with decreasing hole concentration, p. Here, we report extensive field-dependent electronic specific heat studies on hbox {YBa}_2hbox {Cu}_4hbox {O}_8 up to an unprecedented 400 K and show unequivocally that the pseudogap never closes, remaining open to at least 400 K where T^* is typically presumed to be about 150 K. We show from the NMR Knight shift and the electronic entropy that the Wilson ratio is numerically consistent with a weakly-interacting Fermion system for the near-nodal states. And, from the field-dependent specific heat, we characterise the impact of fluctuations and impurity scattering on the thermodynamic properties.

Preformed Cooper Pairs in Layered FeSe-Based Superconductors.

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60 K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.

Mott and pseudogap localization in pressurized NbO2

We present a detailed study of correlation-induced electronic reconstruction in baddeleyite-type ${\mathrm{NbO}}_{2}$, a distorted ${\mathrm{ZrO}}_{2}$-type structure that is found at pressures above 8.0 GPa. Based on density-functional plus dynamical mean-field theory (DFT$+$DMFT), we stress the importance of multiorbital Coulomb interactions in concert with first-principles band-structure calculations for a consistent understanding of emergent Mottness and pseudogap behavior in pressurized ${\mathrm{NbO}}_{2}$ and related ${d}^{1}$ systems. After a proper treatment of multiorbital electron-electron interactions, we find a nearly universal Mott behavior for the peak position of the lower Hubbard band that is independent of crystal- and band-structure details. We explain the nature of the metal-pseudogap-insulator transition to be seen in experiment, showing a first-order transition between two metallic states: a correlated metal and a pseudogap state with a deep density of states at the Fermi level. This emergent pseudogap phenomena is expected to play a central role toward quantum criticality in pressurized ${\mathrm{NbO}}_{2}$.

Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model

We show that antiferromagnetic spin-density wave order in the two-dimensional Hubbard model yields a drop of the charge carrier density as observed in recent transport measurements for cuprate superconductors in high magnetic fields upon entering the pseudogap regime. The amplitude and the (generally incommensurate) wave vector of the spin-density wave is obtained from dynamical mean-field theory (DMFT). An extrapolation of the finite temperature results to zero temperature yields an approximately linear doping dependence of the magnetic gap $\Delta(p) \propto p^*-p$ in a broad doping range below the critical doping $p^*$. The magnetic order leads to a Fermi surface reconstruction with electron and hole pockets, where electron pockets exist only in a restricted doping range below $p^*$. DC charge transport properties are computed by combining the renormalized band structure as obtained from the DMFT with a doping-independent phenomenological scattering rate. A pronounced drop of the longitudinal conductivity and the Hall number in a narrow doping range below $p^*$ is obtained.

Truncated unity parquet solver

We present an implementation of a truncated unity parquet solver (TUPS) which solves the parquet equations using a truncated form-factor basis for the fermionic momenta. This way fluctuations from different scattering channels are treated on an equal footing. The essentially linear scaling of computational costs in the number of untruncated bosonic momenta allows us to treat system sizes of up to 76x76 discrete lattice momenta, unprecedented by previous unbiased methods that include the frequency dependence of the vertex. With TUPS, we provide the first numerical evidence that the parquet approximation might indeed respect the Mermin-Wagner theorem and further systematically analyze the convergence with respect to the number of form factors. Using a single form factor seems to qualitatively describe the physics of the half-filled Hubbard model correctly, including the pseudogap behaviour. Quantitatively, using a single or a few form factors only is not sufficient at lower temperatures or stronger coupling.

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

Near a quantum-critical point, a metal reveals two competing tendencies: destruction of fermionic coherence and attraction in one or more pairing channels. We analyze the competition within Eliashberg theory for a class of quantum-critical models with an effective dynamical electron–electron interaction V(Ωm)∝1∕|Ωm|γ (the γ-model) for 0<γ<1. We argue that the two tendencies are comparable in strength, yet the one towards pairing is stronger, and the ground state is a superconductor. We show, however, that there exist two distinct regimes of system behavior below the onset temperature of the pairing Tp. In the range Tcross<T<Tp fermions remain incoherent and the spectral function A(k,ω) and the density of states N(ω) both display “gap filling” behavior in which, i.e., the position of the maximum in N(ω) is set by temperature rather than the pairing gap. At lower T<Tcross, fermions acquire coherence, and A(k,ω) and N(ω) display conventional ”gap closing” behavior, when the peak position in N(ω) scales with the gap and shifts to a smaller value as T increases. We argue that the existence of the two regimes comes about because of special behavior of fermions with frequencies ω=±πT along the Matsubara axis. Specifically, for these fermions, the component of the self-energy, which competes with the pairing, vanishes in the normal state. We further argue that the crossover at T∼Tcross comes about because Eliashberg equations allow an infinite number of topologically distinct solutions for the onset temperature of the pairing within the same gap symmetry. Only one solution, with the highest Tp, actually emerges, but other solutions are generated and modify the form of the gap function at T≤Tcross. Finally, we argue that the actual Tc is comparable to Tcross, while at Tcross<T<Tp phase fluctuations destroy superconducting long-range order, and the system displays a pseudogap behavior.

Non-Fermi-liquid behavior and doping asymmetry in an organic Mott insulator interface

High-${T}_{\mathrm{C}}$ superconductors show anomalous transport properties in their normal states, such as the bad-metal and pseudogap behaviors. To discuss their origins, it is important to speculate whether these behaviors are material-dependent or universal phenomena in the proximity of the Mott transition by investigating similar but different material systems. An organic Mott transistor is suitable for this purpose owing to the adjacency between the two-dimensional Mott insulating and superconducting states, simple electronic properties, and high doping/bandwidth tunability in the same sample. Here we report the temperature dependence of the transport properties under electron and hole doping in an organic Mott electric-double-layer transistor. At high temperatures, the bad-metal behavior widely appears except at half filling, regardless of the doping polarity. At lower temperatures, the pseudogap behavior is observed only under hole doping, while the Fermi-liquid-like behavior is observed under electron doping. The bad-metal behavior seems a universal high-energy-scale phenomenon, while the pseudogap behavior is based on lower-energy-scale physics that can be influenced by details of the band structure.

Hubbard model on a triangular lattice: Pseudogap due to spin density wave fluctuations

We calculate the fermionic spectral function $A_k (\omega)$ in the spiral spin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature $T$. The spiral SDW order $\Delta (T)$ develops below $T = T_N$ and has momentum ${ \bf K} = (4\pi/3,0)$. We pay special attention to fermions with momenta ${\bf k}$, for which ${\bf k}$ and ${\bf k} + {\bf K}$ are close to Fermi surface in the absence of SDW. At the mean field level, $A_k (\omega)$ for such fermions has peaks at $\omega = \pm \Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at $T > T_N$. We show that this behavior changes qualitatively beyond mean-field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a non-perturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that $A_k (\omega)$ shows peak/dip/hump features at $T < T_N$, with the peak position at $\Delta (T)$ and hump position at $\Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p > T_N$, and in between $T_N$ and $T_p$ the spectral function displays the pseudogap behavior. We show that the difference between $T_p$ and $T_N$ is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, $T_p = T_N$, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.

Anomalous electron transport in epitaxial NdNiO3 films

The origin of simultaneous electronic, structural and magnetic transitions in bulk rare-earth nickelates ($RE$NiO$_3$) remains puzzling with multiple conflicting reports on the nature of these entangled phase transitions. Heterostructure engineering of these materials offers unique opportunity to decouple metal-insulator transition (MIT) from the magnetic transition. However, the evolution of underlying electronic properties across these decoupled transitions remains largely unexplored. In order to address this, we have measured Hall effect on a series of epitaxial NdNiO$_3$ films, spanning a variety of electronic and magnetic phases. We find that the MIT results in only partially gapped Fermi surface, whereas full insulating phase forms below the magnetic transition. In addition, we also find a systematic reduction of the Hall coefficient ($R_H$) in the metallic phase of these films with epitaxial strain and also a surprising transition to negative value at large compressive strain. Partially gapped weakly insulating, paramagnetic phase is reminiscence of pseudogap behavior of high $T_c$ cuprates. The precursor metallic phase, which undergoes transition to insulating phase is a non-Fermi liquid with the temperature exponent ($n$) of resistivity of 1, whereas the exponent increases to 4/3 in the non-insulating samples. Such nickelate phase diagram with sign-reversal of $R_H$, pseudo-gap phase and non Fermi liquid behavior are intriguingly similar to high $T_c$ cuprates, giving important guideline to engineer unconventional superconductivity in oxide heterostructure.

Properties of the Electronic Fluid of Superconducting Cuprates from 63Cu NMR Shift and Relaxation

Nuclear magnetic resonance (NMR) provides local, bulk information about the electronic properties of materials, and it has been influential for theories of high-temperature superconducting cuprates. NMR reported early that nuclear relaxation is much faster than what one expects from coupling to fermionic excitations above the critical temperature for superconductivity (Tc), i.e., what one estimates from the Knight shift with the Korringa law. As a consequence, special electronic spin fluctuations have been invoked. Here, based on literature relaxation data, it is shown that the electronic excitations, to which the nuclei couple with a material and doping-dependent anisotropy, are rather ubiquitous and Fermi liquid-like, i.e., they are only affected by Tc not the pseudogap. A suppressed NMR spin shift rather than an enhanced relaxation leads to the failure of the Korringa law for most materials. Shift and relaxation below Tc support the view of suppressed shifts, as well. A simple model of two coupled electronic spin components, one with 3d(x2 − y2) orbital symmetry and the other with an isotropic s-like interaction, can explain the data. The coupling between the two components is found to be negative, and it must be related to the pseudogap behavior of the cuprates. We can also explain the negative shift conundrum and the long-standing orbital shift discrepancy for NMR in the cuprates.

Superconductivity above a quantum critical point in a metal: Gap closing versus gap filling, Fermi arcs, and pseudogap behavior

We consider a quantum-critical metal with interaction mediated by fluctuations of a critical order parameter. This interaction gives rise to two competing tendencies -- pairing and non-Fermi liquid behavior. Due to competition, the pairing develops below a finite $T_p $, however its prominent feedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At $T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor -- the density of states (DOS) and the spectral function (SF) have sharp gaps which close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip, which {\it fills in} with increasing $T$. The SF in this region shows either the same behavior as the DOS, or has a peak at $\omega =0$ (the Fermi arc), depending on the position on the Fermi surface. We argue that phase fluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$, while $T_p$ marks the onset of pseugogap behavior. We compare our theory with the behavior of optimally doped cuprates.

Temperature-dependent valence state within the metallic phase of BaV10O15 probed by hard x-ray photoelectron spectroscopy

We have studied electronic properties of ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ in the intermediate-temperature phase as well as in the high-temperature metallic phase by using hard x-ray photoemission spectroscopy (HAXPES). The V $2p$ HAXPES show a shift in the high-temperature phase between 300 and 245 K which is similar to the shift of spectral weight near the Fermi edge. The binding energy of the O $1\mathit{s}$ HAXPES peak does not change except a slight shift of the lower binding energy edge in the opposite direction between 300 and 180 K across the transition to the intermediate-temperature phase. This behavior is in sharp contrast to the transition to the low-temperature insulating phase where V $2p$ and O $1s$ HAXPES show dramatic shifts in the same direction. This indicates that the charge-orbital change in the intermediate-temperature phase is driven by the correlated V $3d$ electrons and is electronic. The ${\mathrm{V}}^{2.5+}\text{\ensuremath{-}}{\mathrm{V}}^{2.5+}$ bond ordering is related to the metallic contribution and gradually decreases with cooling from 300 K. The valence-band HAXPES show the metallic features of the pseudogap behavior near the Fermi edge in and above the intermediate-temperature phase due to ${\mathrm{V}}^{2.5+}\text{\ensuremath{-}}{\mathrm{V}}^{3+}$ charge fluctuation. The magnitude of the pseudogap increases from 300 to 180 K in parallel with the gradual breaking of the ${\mathrm{V}}^{2.5+}\text{\ensuremath{-}}{\mathrm{V}}^{2.5+}$ bond and formation of trimers.

Thermal transitions, pseudogap behavior, and BCS-BEC crossover in Fermi-Fermi mixtures

We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species dependent quasiparticle behavior we map out the finite temperature phase diagram of this system and show that unlike the balanced Fermi superfluid there are now two different pseudogap regimes as PG-I and PG-II. While within the PG-I regime both the fermionic species are pseudogapped, PG-II corresponds to the regime where pseudogap feature survives only in the light species. We believe that the single particle spectral features that we discuss in this paper are observable through the species resolved radio frequency spectroscopy and momentum resolved photo emission spectroscopy measurements on systems such as, 6$_{Li}$-40$_{K}$ mixture. We further investigate the interplay between the population and mass imbalances and report that at a fixed population imbalance the BCS-BEC crossover in a Fermi-Fermi mixture would require a critical interaction (U$_{c}$), for the realization of the uniform superfluid state. The effect of imbalance in mass on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase has been probed in detail in terms of the thermodynamic and quasiparticle behavior of this phase. It has been observed that in spite of the s-wave symmetry of the pairing field a nodal superfluid gap is realized in the LO regime. Our results on the various thermal scales and regimes are expected to serve as benchmarks for the experimental observations on 6$_{Li}$-40$_{K}$ mixture.

Pseudogap Behavior of the Nuclear Spin–Lattice Relaxation Rate in FeSe Probed by 77Se-NMR

We conducted $^{77}$Se-nuclear magnetic resonance studies of the iron-based superconductor FeSe in magnetic fields of 0.6 to 19 T to investigate the superconducting and normal-state properties. The nuclear spin-lattice relaxation rate divided by the temperature $(T_1T)^{-1}$ increases below the structural transition temperature $T_\mathrm{s}$ but starts to be suppressed below $T^*$, well above the superconducting transition temperature $T_\mathrm{c}(H)$, resulting in a broad maximum of $(T_1T)^{-1}$ at $T_\mathrm{p}(H)$. This is similar to the pseudogap behavior in optimally doped cuprate superconductors. Because $T^*$ and $T_\mathrm{p}(H)$ decrease in the same manner as $T_\mathrm{c}(H)$ with increasing $H$, the pseudogap behavior in FeSe is ascribed to superconducting fluctuations, which presumably originate from the theoretically predicted preformed pair above $T_\mathrm{c}(H)$.