Commensurate Spin Density Wave Research Articles

Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice

The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.

Effects of V concentration on the physical properties of Cr1−x Al x alloy system

Electrical resistivity (ρ), magnetic susceptibility (χ) and thermoelectric power (S) studies reported previously on the (Cr1-x Al x )99V1 alloy system indicate a suppression of antiferromagnetism in the concentration range 0.015 ≤ x ≤ 0.040. The present study incorporates Sommerfeld electronic specific heat coefficient (γ), thermal conductivity (κ), Hall coefficient (R H) and analyses of the previous results in order to have a comprehensive study of the alloy system. γ(x) depicts two peaks close to the same concentrations where dS/dT|T→2K(x) have minima, i.e. at x c1 ≈ 0.015 and x c2 ≈ 0.040. Such peaks and minima, respectively, have been considered as key signatures of quantum criticality (QC) in alloys of Cr. Evidence of band structure modification in the alloy system is shown by a change of slope in the Nordheim-Gorter (N-G) relationship showing a minimum at an extrapolated concentration x = 0.035. The slope is positive for the incommensurate (I) spin-density-wave (SDW) alloys with x < 0.035 and a negative for the commensurate (C) SDW alloys with x > 0.035. A behaviour reminiscent of changes in the band structure is also observed in the Lorenz number, L(x), for the alloy with x = 0. R H(T) results in the range 0 ≤ x ≤ 0.026 have a sharp increase in the charge carrier density, n 2K = [qR H(2k)]−1, at the ISDW to paramagnetic (P) phase transition. The concentrations x = 0.015 and x = 0.040 are therefore considered ISDW to P and P to CSDW quantum critical points, respectively.

Hall coefficient of (Cr100−xAlx)95Mo5 alloy system

The temperature dependence of the Hall coefficient, RH, for the (Cr100−xAlx)95Mo5 alloy system with 0 ≤ x ≤ 8.6, in the temperature range 2 K ≤ T ≤ 380 K and in a magnetic field of 4.5 T is reported. Anomalies in the form of an upturn were observed just below the Néel transition temperature, TN, for the incommensurate (I) spin density wave (SDW) alloys with x ≤ 1.3 and commensurate (C) spin density wave (SDW) alloys with x ≥ 5.3. In addition to these anomalies, alloys with x = 0, 0.5, 0.9 and 8.6 show a peculiar behaviour below TN, in which RH increases and then decreases depicting a hump on further cooling. Remarkably RH for the alloy with x = 0 shows a sign reversal of majority charge carriers from holes to electrons on cooling below 120 K. The crossover of majority charge carriers disappears by the addition of just 0.5 at.% Al into the base alloy with x = 0. The behaviour of the Hall coefficient for the alloys with x = 0, 0.5, 0.9 and 8.6, is explained in terms of the simple two band model in which both charge carriers contribute to magneto-transport properties. The relative magnetic contribution to the Hall coefficient, ΔRH(2K)/RH(2K), indicate a suppression of antiferromagnetism in the concentration range 1.7 ≤ x ≤ 4.7.

Spin density wave in the strongly dimerized quasi-one-dimensional organic conductor (DMET-TTF) 2AuBr2

At ambient pressure, studies of resistivity, magnetic susceptibility, and carbon-13 nuclear magnetic resonance (NMR) were conducted on the quasi-one-dimensional organic conductor ${(\text{DMET-}\mathrm{TTF})}_{2}{\mathrm{AuBr}}_{2}$. Resistivity measurements showed a broad minimum at approximately 160 K, and the insulator behavior below this temperature and magnetic susceptibility results revealed a dip structure at 22 K. At the same temperature, a sharp peak in the temperature dependence of ${T}_{1}^{\ensuremath{-}1}$ associated with the antiferromagnetic (AFM). transition was found, along with drastic splitting of the NMR spectra, indicating a commensurate AFM structure. The amplitude of the magnetic moments was determined to be $0.06{\ensuremath{\mu}}_{B}$/molecule from the hyperfine coupling constant tensor and the angular dependence of the internal field in the AFM phase. The small magnetic moment signifies the AFM nesting type, i.e., commensurate spin density wave. An antiferromagnetic ordering of $(\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow})$ along the one-dimensional chain is expected from the $2{k}_{\mathrm{F}}$ instability. This behavior can be explained by the strong dimerization of the one-dimensional DMET-TTF chain.

Competition of spatially inhomogeneous phases in systems with nesting-driven spin-density wave state

In this work we study zero-temperature phases of the anisotropic Hubbard model on a three-dimensional cubic lattice in a weak coupling regime. It is known that, at half-filling, the ground state of this model is antiferromagnetic (commensurate spin-density wave). For non-zero doping, various types of spatially inhomogeneous phases, such as phase-separated states and the state with domain walls ("soliton lattice"), can emerge. Using the mean-field theory, we evaluate the free energies of these phases to determine which of them could become the true ground state in the limit of small doping. Our study demonstrates that the free energies of all discussed states are very close to each other. Smallness of these energy differences suggests that, for a real material, numerous factors, unaccounted by the model, may arbitrary shift the relative stability of the competing phases. This further implies that purely theoretical prediction of the true ground state in a particular many-fermion system is unreliable.

Charge density waves beyond the Pauli paramagnetic limit in 2D systems

Two-dimensional materials are ideal candidates to host Charge Density Waves (CDWs) that exhibit paramagnetic limiting behavior, similar to the well-known case of superconductors. Here, we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting, and temperature effects and the possibility of a competing or coexisting Spin Density Wave (SDW) order. Our numerical calculations yield rich phase diagrams with distinct high-field phases above the Pauli limiting field. For perfectly nested commensurate CDWs, a q-modulated CDW phase that is completely analogous to the superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase appears at high fields. In the more common case of imperfect nesting, the commensurate CDW ground state undergoes a series of magnetic-field-induced phase transitions first into a phase where commensurate CDW and SDW coexist and subsequently into another phase where CDW and SDW acquire a q-modulation that is, however, distinct from the pure FFLO CDW phase. The commensurate CDW + SDW phase occurs for fields comparable to but less than the Pauli limit and survives above it. Thus, this phase provides a plausible mechanism for the CDW to survive at high fields without the need for forming the more fragile FFLO phase. We suggest that the recently discovered 2D materials like the transition metal dichalcogenides offer a promising platform for observing such exotic field-induced CDW phenomena.

Blocking of iron magnetic moments and Spin density wave in FeTi2S4 and Fe2TiS4

Iron-titanium sulfides FeTi2S4 and Fe2TiS4 have been structurally and magnetically characterized using powder X Ray Diffraction with Rietveld refinement method and 57Fe Mössbauer spectroscopy at variable temperature. Both sulfides have the same crystallographic phase, based on the monoclinic Cr3S4 type structure and vary in atomic coordinates; FeTi2S4 retains the ideal atomic positions proposed for the Cr3S4 phase, while in Fe2TiS4 the metal displacements from ideal sites are noticeable. Mössbauer spectra reveal different magnetic behaviors; in FeTi2S4 there is a transition from paramagnetic to magnetic ordering at temperature Tc = 145 K, giving rise to unusually low hyperfine magnetic field of 2.5 T (at 77 K) if compared with values of iron magnetic moments reported previously, this behavior is explained on the basis of blocking Fe localized magnetic moments by the Spin density wave (SDW) originated from 3d Ti atoms. In Fe2TiS4 a transition from paramagnetic to (SDW) arises at Tc = 290 K, the SDW is spread in both Fe and Ti metals through [1 0 1] crystallographic plane and undergoes a transition of first order from Incommensurate SDW (ISWD) to Commensurate SDW (CSDW) at TIC = 255 K. The atomic positions in the unit cell are correlated to the magnetic behavior in both sulfides.

Thermal transport properties, magnetic susceptibility and neutron diffraction studies of the (Cr100-xAlx)95Mo5 alloy system

Previous electrical resistivity (ρ) and specific heat (CP) studies on the ternary (Cr100-xAlx)95Mo5 alloy system suggested that it harbours two quantum critical points (QCPs). This study reports comprehensive investigations of this alloy system through Seebeck coefficient (S), thermal conductivity (κ), magnetic susceptibility (χ) and neutron diffraction (ND) measurements in the concentration range 0 ≤ x ≤ 8.6. The results of S and χ show that spin-density-wave (SDW) antiferromagnetism is suppressed to temperatures below 2 K for concentrations in the range 1.4 ≤ x ≤ 4.4. Plots of dS/dT in the limit as T→ 2 K depict two minima, i.e. just above x = 1.4 and 4.4. This parameter has been used as a key indicator of quantum critical behaviour (QCB) in Cr alloys. Analyses against the Nordheim-Gorter relationship demonstrates a positive slope for the incommensurate (I) SDW alloys and a negative slope for the commensurate (C) SDW alloys. Extrapolations of these two slopes intercept at a concentration of 3.2 at.% Al indicating the occurrence of band structure modifications when Al is added into the Cr95Mo5 base alloy. The Lorenz number (L) for the alloys with x = 0 and 0.5 shows interesting anomalous behaviour associated with band structure effects and SDW magnetic ordering. ND measurements as a function of temperature confirm that alloys with x < 1.4 order in the incommensurate (I) SDW phase whilst alloys with x > 4.4 show commensurate (C) SDW order. Power law fits of the form TN∝1.40−x0.35±0.05 for the ISDW to P phase transition and TN∝x−4.400.63±0.03 for the P to CSDW phase transition rendered the critical exponents 0.35±0.05 and 0.63±0.03 respectively. Overall the results of S, κ, χ and ND corroborate the existence of two QCPs at x ≈ 1.4 and 4.4.

Collective mode at Lifshitz transition in iron-pnictide superconductors

We obtain the exact low-energy spectrum of two mobile holes in a t-J model for an isolated layer in an iron-pnictide superconductor. The minimum dxz and dyz orbitals per iron atom are included, with no hybridization between the two. After tuning the Hund coupling to a putative quantum critical point (QCP) that separates a commensurate spin-density wave from a hidden-order antiferromagnet at half filling, we find an s-wave hole-pair groundstate and a d-wave hole-pair excited state. Near the QCP, both alternate in sign between hole Fermi surface pockets at the Brillouin zone center and emergent electron Fermi surface pockets at momenta that correspond to commensurate spin-density waves (cSDW). The dependence of the energy splitting with increasing Hund coupling yields evidence for a true QCP in the thermodynamic limit near the putative one, at which the s-wave and d-wave Cooper pairs are degenerate. A collective s-to-d-wave oscillation of the macroscopic superconductor that couples to orthorhombic shear strain is also identified. Its resonant frequency is predicted to collapse to zero at the QCP in the limit of low hole concentration. This implies degeneracy of Cooper pairs with s, d and symmetry in the corresponding quantum critical state. We argue that the critical state describes Cooper pairs in hole-doped iron superconductors at the Lifshitz transition, where electron bands first rise above the Fermi level. We thereby predict that the s-to-d-wave collective mode observed by Raman spectroscopy in Ba1−xKxFe2As2 at optimal doping should also be observed at higher doping near the Lifshitz transition.

Commensurate and incommensurate spin-density waves in heavy electron systems

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector Q and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point (QCP) is obtained as the Néel temperature tends to zero. The transfer of pairs of electrons between the pockets can lead to a superconducting dome above the QCP (if Q is commensurate with the lattice, i.e. equal to G/2). If the vector Q is not commensurate with the lattice there are eight possible phases: commensurate and incommensurate spin and charge density waves and four superconductivity phases, two of them with modulated order parameter of the FFLO type. The renormalization group equations are studied and numerically integrated. A re-entrant SDW phase (either commensurate or incommensurate) is obtained as a function of the mismatch of the Fermi surfaces and the magnitude of |Q − G/2|.

Commensurate and incommensurate spin-density waves and the superconductivity dome in heavy electron systems

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector $\mathbf{Q}$ and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as the N\'eel temperature tends to zero. If the vector $\mathbf{Q}$ is commensurate with the lattice (umklapp with $\mathbf{Q}=\mathbf{G}/2$), pairs of electrons can be transferred between the pockets and a superconducting dome above the quantum critical point may arise. If the vector $\mathbf{Q}$ is not commensurate with the lattice, there are eight phases that need to be considered: commensurate and incommensurate spin and charge density waves and four superconductivity phases, two of them with a modulated order parameter of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The renormalization group equations are studied and numerically integrated. The phase diagram is obtained as a function of the mismatch of the Fermi surfaces and the magnitude of $|\mathbf{Q}\ensuremath{-}\mathbf{G}/2|$.

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-Tc superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d xz and 3d yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d (x + iy)z and d − = 3d (x − iy)z orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.

Time-dependent equation for the magnetic order parameter near the quantum critical point in multiband superconductors with a spin-density wave

Using a simple two-band model for Fe-based pnictides and the generalized Eilenberger equation, we present a microscopic derivation of a time-dependent equation for the amplitude of the spin density wave near the quantum critical point where it turns to zero. This equation describes the dynamics of the magnetic---$m$, as well as the superconducting order parameter---$\Delta$. It is valid at low temperatures $T$ and small $m$ (${T, m \ll \Delta}$) in a region of coexistence of both order parameters, $m$ and $\Delta$. The boundary of this region is found in the space of the nesting parameter $\{\mu_{0},\mu_{\phi}\}$ where $\mu_{0}$ describes the relative position of the electron and the hole pockets on the energy scale, and $\mu_{\phi}$ accounts for the ellipticity of the electron pocket. At low $T$ the number of quasiparticles is small due to the presence of the energy gap $\Delta$, and therefore the quasiparticles do not play a role in the relaxation of $m$. This circumstance allows one to derive the time-dependent equation for $m$ in contrast to the case of conventional superconductors for which the time-dependent Ginzburg--Landau equation can be derived near $T_{\text{c}}$ only in some special cases (high concentration of paramagnetic impurities. In the stationary case the derived equation is valid at arbitrary temperatures. We find a solution of the stationary equation which describes a domain wall in the magnetic structure. In the center of the domain wall the superconducting order parameter has a maximum, which means a local enhancement of superconductivity. Using the derived time-dependent equation for $m$, we investgate also the stability of a uniform commensurate SDW and obtain the values of $\{\mu_{0}, \mu_{\phi}\}$ at which the first order transition into the state with ${m = 0}$ takes place or the transition to the state with an inhomogeneous SDW occurs.

Electronic phase separation in iron pnictides

A mechanism for electronic phase separation in iron pnictides is proposed. It is based on the competition between commensurate and incommensurate spin-density-wave phases in a system with an imperfect doping-dependent nesting of a multi-sheeted Fermi surface. We model the Fermi surface by two elliptical electron pockets and three circular hole pockets. The interaction between a charge carrier in a hole band and a carrier in an electron band leads to the formation of spin-density-wave order. The commensurate spin density wave in the parent compound transforms to the incommensurate phase when doping is introduced. We show that, for certain parameter values, the uniform state is unstable with respect to phase separation. The resulting inhomogeneous state consists of regions of commensurate and incommensurate spin-density-wave phases. Our results are in qualitative agreement with recent observations of incommensurate spin density waves and electronic inhomogeneity in iron pnictides.

Spin dynamics and resonant inelastic x-ray scattering in chromium with commensurate spin-density wave order

We theoretically investigate spin dynamics and ${L}_{3}$-edge resonant inelastic x-ray scattering (RIXS) of chromium with commensurate spin-density wave (SDW) order, based on a multiband Hubbard model composed of 3$d$ and 4$s$ orbitals. Obtaining the ground state with the SDW mean-field approximation, we calculate the dynamical transverse and longitudinal spin susceptibility by using random-phase approximation. We find that a collective spin-wave excitation seen in inelastic neutron scattering hardly damps up to $\ensuremath{\sim}$0.6 eV. Above the energy, the excitation overlaps individual particle-hole excitations as expected, leading to broad spectral weight. On the other hand, the collective spin-wave excitation in RIXS spectra has a tendency to be masked by large spectral weight coming from particle-hole excitations with various orbital channels. This is in contrast with inelastic neutron scattering, where only selected diagonal orbital channels contribute to the spectral weight. However, it may be possible to detect the spin-wave excitation in RIXS experiments in the future if resolution is high enough.

Prediction of Polaronlike Vortices and a Dissociation Depinning Transition in Magnetic Superconductors: The Example ofErNi2B2C

In borocarbide ErNi2B2C, the phase transition to the commensurate spin density wave at 2.3 K leaves 1/20 part of Ising-like Er spins practically free. Vortices polarize these spins nonuniformly and repolarize them when moving. At a low spin relaxation rate and at low bias currents, vortices carrying magnetic polarization clouds become polaronlike and their velocities are determined by the effective drag coefficient, which is significantly bigger than the Bardeen-Stephen (BS) one. As current increases, at a critical current J(c) vortices release polarization clouds and the velocity as well as the voltage in the I-V characteristics jump to values corresponding to the BS drag coefficient. The nonuniform components of the magnetic field and magnetization drop as velocity increases, resulting in weaker polarization and discontinuous dynamic dissociation depinning transition. As current decreases, on the way back, vortices are retrapped by polarization clouds at the current J(r)<J(c).

Local magnetic inhomogeneities observed via 75As NMR in Ba(Fe1−xNix)2As2 with H0 ⊥ c-axis

We present field-swept 75As Nuclear Magnetic Resonance (NMR) measurements in the spin-density wave (SDW) state of Ba(Fe1−xNix)2As2 for x = 0.0072. The large single crystals were aligned with the external field H0 perpendicular to the c axis. The spectra are increasingly broadened as a function of doping, and are well fit by a model of a commensurate SDW with local impurities.

Fermi surfaces of iron pnictide high-Tcsuperconductors from the limit of local magnetic moments

A two-orbital $t$-$J$ model over the square lattice that describes low-energy electronic excitations in iron-pnictide high-${T}_{c}$ superconductors is analyzed with Schwinger-boson-slave-fermion mean-field theory and by exact numerical diagonalization on a finite system. When interorbital hole hopping is suppressed, a quantum critical point (QCP) is identified that separates a commensurate spin-density wave (cSDW) state at strong Hund's rule coupling from a hidden half metal state at weak Hund's rule coupling. Low-energy spin waves that disperse anisotropically from cSDW momenta are predicted at the QCP. Nested Fermi surfaces similar to those observed experimentally in iron-pnictide materials are also predicted in such case.

Effects of chemical doping and pressure on CaFe4As3

The effects of chemical doping by P, Yb, Co, and Cu, and hydrostatic pressure on CaFe${}_{4}$As${}_{3}$, were studied on single-crystalline samples. While the former two dopants substitute the nonmagnetic ions, the latter two partially occupy the Fe sites within the magnetic sublattice. The incommensurate spin density wave (IC-SDW) ordering at ${T}_{N}\ensuremath{\sim}$ 88 K in CaFe${}_{4}$As${}_{3}$ changes only by up to $\ensuremath{\sim}$40% with doping and applied pressure. Thus the IC-SDW state appears more robust than in the layered Fe pnictides. The commensurate SDW (C-SDW) state below ${T}_{2}\ensuremath{\sim}$ 26 K is suppressed in the Co-doped series, while it moves up in temperature in the P-, Yb-, and Cu-doped compounds. A new magnetic phase transition is observed at an intermediate temperature ${T}_{3}$ in Ca(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{4}$As${}_{3}$. Resistivity and magnetization measurements on CaFe${}_{4}$As${}_{3}$ were performed under hydrostatic pressure up to 5 GPa, showing a systematic decrease of ${T}_{N}$ and a domelike phase boundary at ${T}_{2}$ up to ${p}_{c}\ensuremath{\sim}$ 2.10 GPa. At higher pressures, a possible structural phase transition occurs, marked by a slowly increasing transition temperature. A phase diagram is shown to compare the effects of chemical doping and pressure.

Thermal and electrical transport in the spin density wave antiferromagnet CaFe4As3

We present here measurements of the thermopower, thermal conductivity, and electrical resistivity of the newly reported compound CaFe${}_{4}$As${}_{3}$. Evidence is presented from specific heat and electrical resistivity measurements that a substantial fraction of the Fermi surface survives the onset of spin density wave (SDW) order at the N\'eel temperature ${T}_{\mathrm{N}}=88$ K and its subsequent commensurate lock-in transition at ${T}_{2}=26.4$ K. The specific heat below ${T}_{2}$ consists of a normal metallic component from the ungapped parts of the Fermi surface and a Bardeen-Cooper-Schrieffer (BCS) component that represents the SDW gapping of the Fermi surface. A large Kadowaki-Woods ratio is found at low temperatures, showing that the ground state of CaFe${}_{4}$As${}_{3}$ is a strongly interacting Fermi liquid. The thermal conductivity $\ensuremath{\kappa}$ of CaFe${}_{4}$As${}_{3}$ is an order of magnitude smaller than those of conventional metals at all temperatures, due to a strong phonon scattering. The thermoelectric power $S$ displays a sign change from positive to negative indicating that a partial gap forms at the Fermi level with the onset of commensurate spin density wave order at ${T}_{2}=26.4$ K. The small value of the thermopower $S$ and the enhancements of the resistivity due to gap formation and strong quasiparticle interactions offset the low value of the thermal conductivity $\ensuremath{\kappa}$, yielding only a modest value for the thermoelectric figure of merit $\mathcal{Z}\ensuremath{\leqslant}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.28em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ in CaFe${}_{4}$As${}_{3}$. The results of ab initio electronic structure calculations are reported, confirming that the sign change in the thermopower at ${T}_{2}$ is reflected by a sign change in the slope of the density of states at the Fermi level. Values for the quasiparticle renormalization $Z$ are derived from measurements of the specific heat and thermopower, indicating that as $T\ensuremath{\rightarrow}0$, ${\mathrm{CaFe}}_{4}{\mathrm{As}}_{3}$ is among the most strongly correlated of the known Fe-based pnictide and chalcogenide systems.