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Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first-order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two non-zero values while the nematic director remains pinned, leading to a symmetry-preserving meta-nematic transition that terminates at a quantum critical end-point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second-order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At non-zero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first-order in 3D, but to change to second-order in 2D. As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end-points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order., Comment: 17 pages, 7 figures

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional (2D) semimetals such as WTe$_2$. Some of these systems have a polar crystal structure that gives rise to ferroelectricity, in which the interlayer polarization exhibits bistability driven by external electric fields. Here we show that bilayer $T_d$-MoTe$_2$ simultaneously exhibits ferroelectric switching and superconductivity. Remarkably, a field-driven, first-order superconductor-to-normal transition is observed at its ferroelectric transition. Bilayer $T_d$-MoTe$_2$ also has a maximum in its superconducting transition temperature ($T_\textrm{c}$) as a function of carrier density and temperature, allowing independent control of the superconducting state as a function of both doping and polarization. We find that the maximum $T_\textrm{c}$ is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping. We argue that this unusual polarization-sensitive 2D superconductor is driven by an interband pairing interaction associated with nearly nested electron and hole Fermi pockets.

Despite intense experimental efforts, the nature of the unconventional superconducting order parameter of UTe$_2$ remains elusive. This puzzle stems from different reported numbers of superconducting transitions at ambient pressure, as well as a complex pressure-temperature phase diagram. To bring new insights into the superconducting properties of UTe$_2$, we measured the heat capacity and electrical resistivity of single crystals under compressive uniaxial stress $\sigma$ applied along different crystallographic directions. We find that the critical temperature $T_{\rm c}$ of the single observed bulk superconducting transition decreases with $\sigma$ along $[100]$ and $[110]$ but increases with $\sigma$ along $[001]$. Aside from its effect on $T_{\rm c}$, we notice that $c$-axis stress leads to a significant piezoresistivity, which we associate with the shift of the zero-pressure resistivity peak at $T^\star \approx 15\, \rm K$ to lower temperatures under stress. Finally, we show that an in-plane shear stress $\sigma_{xy}$ does not induce any observable splitting of the superconducting transition over a stress range of $\sigma_{xy}\approx 0.17 \, \rm GPa$. This result suggests that the superconducting order parameter of UTe$_2$ may be single-component at ambient pressure.

In the quasi-two-dimensional (quasi-2D) copper- and iron-based superconductors, the onset of superconductivity is accompanied by a prominent peak in the magnetic spectrum at momenta close to the wave-vector of the nearby antiferromagnetic state. Such a peak is well described in terms of a spin resonance mode, i.e., a spin-1 exciton theoretically predicted for quasi-2D superconductors with a sign-changing gap. The same theories, however, indicate that such a resonance mode should be absent in a three-dimensional (3D) system with a spherical Fermi surface. This raises the question of the fate of the spin resonance mode in layered unconventional superconductors that are not strongly anisotropic, such as certain heavy-fermion compounds and potentially the newly discovered nickelate superconductor NdNiO$_2$. Here, we use the random-phase-approximation to calculate the dynamical spin susceptibility of 3D superconductors with a $d_{x^2-y^2}$-wave gap symmetry and corrugated cylindrical-like Fermi surfaces. By varying the out-of-plane hopping anisotropy $t_z/t$, we demonstrate that the appearance of a spin resonance mode is determined by the topology of the hot lines -- i.e. lines on the Fermi surface that are connected by the magnetic wave-vector. For an in-plane antiferromagnetic wave-vector, the hot lines undergo a topological transition from open lines to closed loops at a critical $t_z/t$ value. The closed hot lines cross the nodal superconducting lines, making the spin resonance mode overdamped and incoherent. In contrast, for an out-of-plane antiferromagnetic wave-vector, the hot lines remain open and the spin resonance mode remains sharp. We discuss the experimental implications of our results for the out-of-plane dispersion of the spin resonance mode and, more generally, for inelastic neutron scattering experiments on unconventional superconductors., 12 pages, 11 figures

We report results of low-temperature heat capacity, magnetocaloric effect and neutron diffraction measurements of TmVO$_{4}$, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially-filled $4f$ orbitals of the thulium (Tm$^{3+}$) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point using a magnetic field oriented along the $c$-axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well-described using a semi-classical mean field treatment of the transverse field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semi-classical behavior are observed due to quantum fluctuations. Although the phase transition is driven by the local $4f$ degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles, and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO$_{4}$ as a model material, and electronic nematicity as a paradigmatic example, for quantum criticality in insulators., 9 pages, 5 figures

The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing between two closely competing pairing instabilities, namely the conventional s-wave instability typical of bulk NbSe2 and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results demonstrate the unconventional character of the pairing interaction in few-layer transition metal dichalcogenides and highlight the exotic superconductivity in this family of two-dimensional materials. A two-fold rotational symmetry is observed in the superconducting state of NbSe2. This is strikingly different from the three-fold symmetry of the lattice, and suggests that a mixed conventional and unconventional order parameter exists in this material.

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional semimetals such as WTe

The study of subtle effects on transport in semiconductors requires high-quality epitaxial structures with low defect density. Using hybrid molecular beam epitaxy (MBE), SrTiO 3 films with a low-temperature mobility exceeding 42,000 cm 2 V −1 s −1 at a low carrier density of 3 × 10 17 cm −3 were achieved. A sudden and sharp decrease in residual resistivity accompanied by an enhancement in the superconducting transition temperature were observed across the second Lifshitz transition where the third band becomes occupied, revealing dominant intraband scattering. These films further revealed an anomalous behavior in the Hall carrier density as a consequence of the antiferrodistortive (AFD) transition and the temperature dependence of the Hall scattering factor. Using hybrid MBE growth, phenomenological modeling, temperature-dependent transport measurements, and scanning superconducting quantum interference device imaging, we provide critical insights into the important role of inter- versus intraband scattering and of AFD domain walls on normal-state and superconducting properties of SrTiO 3 .

Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such 'Ising-nematic' systems is a simple scalar. Here, using a spatially resolved optical polarimetry technique, we show that a qualitatively distinct nematic state arises in the triangular lattice antiferromagnet Fe1/3NbS2. The crucial difference is that the nematic order on the triangular lattice is a [Formula: see text] or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously reoriented by external perturbations. This discovery lays the groundwork for devices that exploit analogies with nematic liquid crystals.

Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics), resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba1-x Rb x Fe2As2 iron-based superconductors. While for [Formula: see text], the nematic director points along the in-plane diagonals of the tetragonal lattice, for [Formula: see text], it points along the horizontal and vertical axes. Remarkably, for intermediate doping, the susceptibilities of these two symmetry-irreducible nematic channels display comparable Curie-Weiss behavior, thus revealing a nearly XY-nematic state. This opens a route to assess this elusive electronic quantum liquid-crystalline state.

We demonstrate the formation of robust zero energy modes close to magnetic impurities in the iron-based superconductor FeSe$_{1-x}$Te$_x$. We find that the Zeeman field generated by the impurity favors a spin-triplet inter-orbital pairing as opposed to the spin-singlet intra-orbital pairing prevalent in the bulk. The preferred spin-triplet pairing preserves time-reversal symmetry and is topological, as robust, topologically-protected zero modes emerge at the boundary between regions with different pairing states. Moreover, the zero modes form Kramers doublets that are insensitive to the direction of the spin polarization or to the separation between impurities. We argue that our theoretical results are consistent with recent experimental measurements on FeSe$_{1-x}$Te$_x$., Comment: 6+2 pages, 3 figures

Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational (C3) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice., S.T. and A.N.P. acknowledge funding from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. STM equipment support (A.N.P.) and 2D sample synthesis (Y.S.) were provided by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601. C.R.-V. acknowledges funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 844271. A.R. acknowledges funding by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19) and the Flatiron Institute, a division of the Simons Foundation. L.K., D.M.K. and A.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769 and Advanced Imaging of Matter (AIM) EXC 2056−390715994 and funding by the Deutsche Forschungsgemeinschaft (DFG) under RTG 1995, within the Priority Program SPP 2244 ‘2DMP’ and GRK 2247. A.R. acknowledges support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. H.O. is supported by the NSF MRSEC programme grant no. DMR-1420634. Tight-binding and fRG simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0496 and rwth0589. R.S. and M.S.S. acknowledge support from the National Science Foundation under grant no. DMR-2002850. R.M.F. was supported by the DOE-BES under award no. DE-SC0020045. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354) and the CREST (grant no. JPMJCR15F3) JST.

A variety of compounds, for example doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the normal state properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. Starting from a minimal model of electrons coupled to a \emph{transverse} polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second order, first order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen–Cooper–Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund’s interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this $\textit{random Baxter-field model}$, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder., 21 pages, 18 figures, 2 tables

Due to the intertwining between electronic nematic and elastic degrees of freedom, lattice defects and structural inhomogeneities commonly found in crystals can have a significant impact on the electronic properties of nematic materials. Here, we show that defects commonly present at the surface of crystals generally shift the wave-vector of the nematic instability to a non-zero value, resulting in an incommensurate electronic smectic phase. Such a smectic state onsets above the bulk nematic transition temperature and is localized near the surface of the sample. We argue that this effect may explain not only recent observations of a modulated nematic phase in iron-based superconductors, but also several previous puzzling experiments that reported signatures consistent with nematic order before the onset of a bulk structural distortion., 16 pages, 12 figures

The authors apply uniaxial strain on the layered kagome superconductor CsV${}_{3}$Sb${}_{5}$. They show that its charge density wave (CDW) and superconductivity (SC) transitions are dominated by the change in the $c$ axis, and the effect of the explicit rotational symmetry breaking by strain is negligible on the competition between CDW and SC. Together with theoretical studies, they propose that the trilinear coupling between the ${M}_{1}^{+}$ and ${L}_{2}^{\ensuremath{-}}$ phonon modes plays an important role in the CDW.

The elastic collective modes of a moir\'e superlattice arise not from vibrations of a rigid crystal but from the relative displacement between the constituent layers. Despite their similarity to acoustic phonons, these modes, called phasons, are not protected by any conservation law. Here, we show that disorder in the relative orientation between the layers and thermal fluctuations associated with their sliding motion degrade the propagation of sound in the moir\'e superlattice. Specifically, the phason modes become overdamped at low energies and acquire a finite gap, which displays a universal dependence on the twist-angle variance. Thus, twist-angle inhomogeneity is manifested not only in the non-interacting electronic structure of moir\'e systems, but also in their phonon-like modes. More broadly, our results have important implications for the electronic properties of twisted moir\'e systems that are sensitive to the electron-phonon coupling., Comment: 5 pages, 2 figures + Supplemental Material

Employing a combination of symmetry analysis, low-energy modeling, and ab initio simulations, we predict the presence of magnetic-field-induced Weyl points close to the Fermi level in $\mathrm{Ca}\mathrm{K}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}$. Depending on the relative strengths of the magnetic field and of the spin-orbit coupling, the Weyl fermions can carry a topological charge of $\ifmmode\pm\else\textpm\fi{}1$ or $\ifmmode\pm\else\textpm\fi{}2$, making $\mathrm{Ca}\mathrm{K}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}$ a rare realization of a double-Weyl semimetal. We further predict experimental manifestations of these Weyl points, both in bulk properties, such as the anomalous Hall effect, and in surface properties, such as the emergence of prominent Fermi arcs. Because $\mathrm{Ca}\mathrm{K}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}$ displays unconventional fully gapped superconductivity below 30 K, our findings open a route to investigate the interplay between superconductivity and Weyl fermions.

We employ the phenomenological Lawrence-Doniach model to compute the contributions of the superconducting fluctuations to the third-harmonic magnetic response, denoted here by $\overline{{M}_{3}}$, which can be measured in a precise way using ac magnetic fields and lock-in techniques. We show that, in an intermediate temperature regime, this quantity behaves as the third-order nonlinear susceptibility, which shows a power-law dependence with the reduced temperature $\ensuremath{\epsilon}=\frac{T\ensuremath{-}{T}_{c}}{{T}_{c}}$ as ${\ensuremath{\epsilon}}^{\ensuremath{-}5/2}$. Very close to ${T}_{c}$, however, $\overline{{M}_{3}}$ saturates due to the nonzero amplitude of the ac field. We compare our theoretical results with experimental data for three conventional superconductors---lead, niobium, and vanadium---and for the unconventional superconductor ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ (SRO). We find good agreement between theory and experiment for the elemental superconductors, although the theoretical values for the critical field systematically deviate from the experimental ones. In the case of SRO, however, the phenomenological model completely fails to describe the data, as the third-harmonic response remains sizable over a much wider reduced temperature range compared to Pb, Nb, and V. We show that an inhomogeneous distribution of ${T}_{c}$ across the sample can partially account for this discrepancy, since regions with a locally higher ${T}_{c}$ contribute to the fluctuation $\overline{{M}_{3}}$ significantly more than regions with the ``nominal'' ${T}_{c}$ of the clean system. However, the exponential temperature dependence of $\overline{{M}_{3}}$ first reported by Pelc et al. [Nat. Commun. 10, 2729 (2019)] is not captured by the model with inhomogeneity. We conclude that, while inhomogeneity is an important ingredient to understand the superconducting fluctuations of SRO and other perovskite superconductors, additional effects may be at play, such as non-Gaussian fluctuations or rare-region effects.

We show that the observed time-reversal symmetry breaking (TRSB) of the superconducting state in Sr2RuO4 can be understood as originating from inhomogeneous strain fields near edge dislocations of the crystal. Specifically, we argue that, without strain inhomogeneities, Sr2RuO4 is a single-component, time-reversal symmetric superconductor, likely with dx2−y2 symmetry. However, due to the strong strain inhomogeneities generated by dislocations, a slowly decaying subleading pairing state contributes to the condensate in significant portions of the sample. As it phase winds around the dislocation, time-reversal symmetry is locally broken. Global phase locking and TRSB occur at a sharp Ising transition that is not accompanied by a change of the single-particle gap and yields a very small heat capacity anomaly. Our model thus explains the puzzling absence of a measurable heat capacity anomaly at the TRSB transition in strained samples and the dilute nature of the time-reversal symmetry broken state probed by muon spin rotation experiments. We propose that plastic deformations of the material may be used to manipulate the onset of broken time-reversal symmetry.

The random substitutional solid solution between the antiferromagnetic (AFM) full-Heusler alloy ${\mathrm{Ru}}_{2}\mathrm{MnSn}$ and the ferromagnetic (FM) full-Heusler alloy ${\mathrm{Ru}}_{2}\mathrm{FeSn}$ provides a rare opportunity to study FM-AFM phase competition in a near-lattice-matched, cubic system, with full solubility. At intermediate $x$ in ${\mathrm{Ru}}_{2}{\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Sn}$ this system displays suppressed magnetic ordering temperatures, spatially coexisting FM and AFM order, and strong coercivity enhancement, despite rigorous chemical homogeneity. Here, we construct the most detailed temperature- and $x$-dependent understanding of the magnetic phase competition and coexistence in this system to date, combining wide-temperature-range neutron diffraction and small-angle neutron scattering with magnetometry and specific heat measurements on thoroughly characterized polycrystals. A complete magnetic phase diagram is generated, showing FM-AFM coexistence between $x\ensuremath{\approx}0.30$ and $x\ensuremath{\approx}0.70$. Important insight is gained from the extracted length scales for magnetic phase coexistence (25--100 nm), the relative magnetic volume fractions and ordering temperatures, and remarkable $x$-dependent trends in magnetic and electronic contributions to specific heat. An unusual feature in the magnetic phase diagram (an intermediate FM phase) is also shown to arise from an extrinsic effect related to a minor Ru-rich secondary phase. The established magnetic phase diagram is then discussed with the aid of phenomenological modeling, clarifying the nature of the mesoscale phase coexistence with respect to the understanding of disordered Heisenberg models.

The superconducting transition metal dichalcogenide (TMD) $4Hb\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ consists of alternating layers of $H$ and $T$ structures, which in their bulk form are metallic and Mott insulating, respectively. Recently, this compound has been proposed as a candidate chiral superconductor, due to an observed enhancement of the muon-spin relaxation at ${T}_{c}$. $4Hb\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ also exhibits a puzzling $T$-linear specific heat at low temperatures, which is unlikely to be caused by disorder. Elucidating the origin of this behavior is an essential step in discerning the true nature of the superconducting ground state. Here, we propose a simple model that attributes the $T$-linear specific heat to the emergence of a robust multiband gapless superconducting state. We show that an extended regime of gapless superconductivity naturally appears when the pair-breaking scattering rate on distinct Fermi-surface pockets differs significantly, and the pairing interaction is predominantly intrapocket. Using a tight-binding model derived from first-principle calculations, we show that the pair-breaking scattering rate promoted by slow magnetic fluctuations on the $T$ layers, which arise from proximity to a Mott transition, can be significantly different in the various $H$-layer dominated Fermi pockets depending on their hybridization with $T$-layer states. Thus, our results suggest that the ground state of $4Hb\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ consists of Fermi pockets displaying gapless superconductivity, which are shunted by superconducting Fermi pockets that are nearly decoupled from the $T$ layers.

We formulate a fracton-elasticity duality for twisted moir\'e superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics. From a dual tensor-gauge formulation, as compared to standard crystals, we identify twice the number of conserved charges that describe topological lattice defects, namely, disclinations and a new type of defect that we dub discompressions. The key implication of these conservation laws is that both glide and climb motions of lattice dislocations are suppressed, indicating that dislocation networks may become exceptionally stable. Our results also apply to other planar incommensurate crystals and quasicrystals., Comment: 9 pages, 2 figures

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

We show that unconventional nematic superconductors with multi-component order parameter in lattices with three-fold and six-fold rotational symmetries support a charge-$4e$ vestigial superconducting phase above $T_c$. The charge-$4e$ state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is non-superconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-$4e$ state over the nematic phase, as it acts as a random-mass to the former but as a random-field to the latter. Thus, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-$4e$ superconducting phase., 5 pages plus Supplementary Material

The doped topological insulator $A_{x}\mathrm{Bi_{2}Se_{3}}$, with $A=\{\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}\}$, becomes a nematic superconductor below $T_{c}\sim3-4\,\mathrm{K}$. The associated electronic nematic director is described by an angle $\alpha$ and is experimentally manifested in the elliptical shape of the in-plane critical magnetic field $H_{c2}$. Because of the threefold rotational symmetry of the lattice, $\alpha$ is expected to align with one of three high-symmetry directions corresponding to the in-plane nearest-neighbor bonds, consistent with a $Z_{3}$-Potts nematic transition. Here, we show that the nematic coupling to the acoustic phonons, which makes the nematic correlation length tend to diverge along certain directions only, can fundamentally alter this phenomenology in trigonal lattices. Compared to hexagonal lattices, the former possesses a sixth independent elastic constant $c_{14}$ due to the fact that the in-plane shear strain doublet $(\epsilon_{xx}-\epsilon_{yy},-2\epsilon_{xy})$ and the out-of-plane shear strain doublet $(2\epsilon_{yz},-2\epsilon_{xz})$ transform as the same irreducible representation. We find that, when $c_{14}$ overcomes a threshold value, which is expected to be the case in doped $\mathrm{Bi_{2}Se_{3}}$, the nematic director $\alpha$ unlocks from the high-symmetry directions due to the competition between the quadratic phonon-mediated interaction and the cubic nematic anharmonicity. This implies the breaking of the residual in-plane twofold rotational symmetry ($C_{2x}$), resulting in a triclinic phase. We discuss the implications of these findings to the structure of nematic domains and to the shape of the in-plane $H_{c2}$ in $A_{x}\mathrm{Bi_{2}Se_{3}}$, and to presence of nodes inside the superconducting state., Comment: 24 pages, 10 figures

Rare-earth titanates are Mott insulators whose magnetic ground state -- antiferromagnetic (AFM) or ferromagnetic (FM) -- can be tuned by the radius of the rare-earth element. Here, we combine phenomenology and first-principles calculations to shed light on the generic magnetic phase diagram of a chemically substituted titanate on the rare-earth site that interpolates between an AFM and a FM state. Octahedral rotations present in these perovskites cause the AFM order to acquire a small FM component -- and vice-versa -- removing any multicritical point from the phase diagram. However, for a wide parameter range, a first-order metamagnetic transition line terminating at a critical endpoint survives inside the magnetically ordered phase. Like the liquid-gas transition, a Widom line emerges from the endpoint, characterized by enhanced fluctuations. In contrast to metallic FMs, this metamagnetic transition involves two symmetry-equivalent and insulating canted spin states. Moreover, instead of a magnetic field, we show that uniaxial strain can be used to tune this transition to zero temperature, inducing a quantum critical endpoint., Comment: 8 pages, 6 figures

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach using irreversible, plastic deformation of single crystals. We show that compressive plastic deformation induces low-dimensional superconductivity well above the superconducting transition temperature (Tc) of undeformed SrTiO3, with evidence of possible superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The enhanced superconductivity is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe deformation-induced signatures of quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order using Raman scattering. Our results suggest that strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence Tc, consistent with a theory of superconductivity enhanced by soft polar fluctuations. Our results demonstrate the potential of plastic deformation and dislocation engineering for the manipulation of electronic properties of quantum materials. Plastic deformation is shown to tune the quantum degrees of freedom in SrTiO3.

Ionic liquid gating is shown to enable voltage-induced ferromagnetism in diamagnetic FeS2, i.e., in a “nonmagnetic” material., Increasingly impressive demonstrations of voltage-controlled magnetism have been achieved recently, highlighting potential for low-power data processing and storage. Magnetoionic approaches appear particularly promising, electrolytes and ionic conductors being capable of on/off control of ferromagnetism and tuning of magnetic anisotropy. A clear limitation, however, is that these devices either electrically tune a known ferromagnet or electrically induce ferromagnetism from another magnetic state, e.g., antiferromagnetic. Here, we demonstrate that ferromagnetism can be voltage-induced even from a diamagnetic (zero-spin) state suggesting that useful magnetic phases could be electrically induced in “nonmagnetic” materials. We use ionic liquid–gated diamagnetic FeS2 as a model system, showing that as little as 1 V induces a reversible insulator-metal transition by electrostatic surface inversion. Anomalous Hall measurements then reveal electrically tunable surface ferromagnetism at up to 25 K. Density functional theory–based modeling explains this in terms of Stoner ferromagnetism induced via filling of a narrow eg band.

Recent experiments in unconventional superconductors, and in particular iron-based materials, have reported evidence of an antiferromagnetic quantum critical point (AFM-QCP) emerging inside the superconducting dome of the phase diagram. Fluctuations associated with such an AFM-QCP are expected to promote unusual temperature dependencies of thermodynamic quantities. Here, we compute the $T$ dependence of the specific heat $C(T)$ deep inside a fully gapped $s^{+-}$ superconducting state as the AFM-QCP is approached. We find that, at the AFM-QCP, the specific heat $C(T)$ vanishes quadratically with temperature, as opposed to the typical exponential suppression seen in fully-gapped BCS superconductors. This robust result is due to a non-analytic contribution to the free-energy arising from the general form of the bosonic (AFM) propagator in the SC state. Away from the AFM-QCP, as temperature is lowered, $C(T)$ shows a crossover from a $T^2$ behavior to an exponential behavior, with the crossover temperature scale set by the value of the superconducting gap and the distance to the QCP. We argue that these features in the specific heat can be used to unambiguously determine the existence of AFM-QCPs inside the superconducting domes of iron-based and other fully gapped unconventional superconductors., Comment: 10 pages, 5 figures, new Section V included