arXiv subjects

Morten H. Christensen

Publications and source records attributed to Morten H. Christensen.

At least 19 recordsLinked to original sources

arXiv2026

Kohn-Luttinger Superconductivity of Weyl Fermi Arcs in PtBi$_2$

Recent experimental observations in the noncentrosymmetric Weyl semimetal PtBi$_2$ indicate unconventional superconductivity hosted by topological surface states -- Weyl Fermi arcs -- with a node at the center of each arc. Focusing on these Fermi arcs, we calculate the electronically mediated pairing interaction using a Kohn-Luttinger approach and find that, in a large region of the phase diagram, the leading superconducting instability has an $i$-wave symmetry featuring precisely such an intra-arc node. We study the dependence of the leading superconducting instabilities on electronic interaction parameters and chemical potential and show that the $i$-wave state is robust to changes in the model parameters. Our results provide a possible mechanism for the observation of topological $i$-wave superconductivity on the surface of PtBi$_2$ and may have implications for the broader landscape of superconducting instabilities arising from repulsive interactions on the surfaces of Weyl semimetals.

cond-mat.supr-con↗

arXiv2026

Odd-Parity Magnetism in Fe-Based Superconductors

Odd-parity magnetism constitutes an intriguing phase of matter which breaks inversion symmetry while preserving time-reversal symmetry. Here we demonstrate that the Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state by combining low-energy modeling with density-functional theory. In the absence of spin-orbit coupling, the electronic spins are polarized along the $k_z$-direction and the splitting of the up and down states exhibits an $h$-wave form-factor. The magnitude of the splitting depends sensitively on specific parameters of the low-energy model, including specific out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. Interestingly, despite this state breaking inversion symmetry and exhibiting a finite out-of-plane Berry curvature and non-linear anomalous Hall effect, the Edelstein effect vanishes. Incorporating spin-orbit coupling tilts the momentum-space electronic spins into the ($k_x,k_y$)-plane and imparts finite in-plane components to the Edelstein response. Our findings highlight the Fe-based superconductors as platforms for exploring odd-parity magnetism both on its own and coexisting with unconventional superconductivity.

cond-mat.supr-con↗

arXiv2026

Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations

Electronically-driven nematic order breaks the rotational symmetry of a system, e.g., through a Pomeranchuk instability of the Fermi surface, with a concomitant distortion of the lattice. As a result, in a metal, the nematic collective mode interacts with two different sets of gapless excitations: the particle-hole excitations of the metal and the lattice fluctuations that become soft at the induced structural transition, namely, the transverse acoustic phonons. However, the \textit{dynamics} of these hybridized collective modes formed by the transverse acoustic phonons and the metallic electronic-nematic fluctuations has remained largely unexplored. Here we address this problem by developing a formalism in which the nemato-elastic coupling is obtained microscopically from the direct coupling between electrons and transverse acoustic phonons enabled by impurities present in the crystal. We then demonstrate the emergence of hybrid nemato-elastic modes that mix the characteristics of the transverse phonons and of the nematic fluctuations. Near the nematic quantum critical point in a metal, two massless modes emerge with intertwined dynamic behaviors, implying that neither mode dominates the response of the system. We systematically study the non-trivial dependence of these collective modes on the longitudinal and transverse momenta, revealing a rich landscape of underdamped and overdamped modes as the proximity to the quantum critical point and the strength of the electron-phonon coupling are changed. Since dynamics play an important role for determining superconducting instabilities, our results have implications for the study of pairing mediated by electronic nematic fluctuations.

cond-mat.str-el↗

arXiv2026

Electronic and structural properties of Rh- and Pd-based kagome layered shandites from first principles

The shandite structure hosts transition metal ions arranged in kagome layers. These layers are stacked rhombohedrally and are interspersed with post-transition metal ions and chalcogens. The electronic states near the Fermi level are dominated by the transition metal $d$-orbitals and feature saddle points near several of the high-symmetry positions of the Brillouin zone, most notably the F and L points. Combining symmetry considerations with ab initio methods, we study the electronic and structural properties of these materials with an emphasis on the connection between electronic saddle points at specific momenta and structural instabilities at these momenta. While the parent compounds studied are all found to be structurally stable under ambient conditions, we show that, in specific compounds, moving the saddle point closer to the Fermi level using either hydrostatic pressure or doping, can induce a structural instability. The importance of the electronic degrees of freedom in driving this instability is supported by the dependence of the frequency of the soft phonon mode on the electronic smearing temperature. Our first-principles calculations show that as the smearing temperature is increased, the compound becomes structurally stable again, indicating that the electron-phonon coupling is playing an important role. Our findings survey the structural properties of a large family of shandite materials and shed light on the role played by saddle points in the electronic structure in driving structural instabilities in rhombohedrally stacked kagome-layered materials.

cond-mat.mtrl-sci↗

arXiv2026

Protection of Unconventional Superconductivity from Disorder

Unconventional superconductivity is a desirable state of matter due to its potential for high transition temperatures $T_{\mathrm{c}}$ and associated favorable superconducting properties. However, the sign-changing nature of the order parameter of unconventional superconductors renders their condensates fragile to disorder, an inevitability in real materials. We uncover the generic properties of electronic band structures and associated Bloch weights able to support robust unconventional superconductivity. We demonstrate this property in several case studies of the kagome and Lieb lattices, showing how unconventional superconductors exhibit unusually weak $T_{\mathrm{c}}$ suppression by disorder, despite featuring fully compensated sign-changing order parameters. We contrast these results with those for unconventional superconductivity on the square and honeycomb lattices, which are unable to protect the condensates from disorder. Finally, we discuss material candidates for which this effect may be realized.

cond-mat.supr-con↗

arXiv2023

Unconventional superconductivity protected from disorder on the kagome lattice

Motivated by the recent discovery of superconductivity in the kagome $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) metals, we perform a theoretical study of the symmetry-allowed superconducting orders on the two-dimensional kagome lattice with focus on their response to disorder. We uncover a qualitative difference between the robustness of intraband spin-singlet (even-parity) and spin-triplet (odd-parity) unconventional superconductivity to atomic-scale nonmagnetic disorder. Due to the particular sublattice character of the electronic states on the kagome lattice, disorder in spin-singlet superconducting phases is only weakly pair-breaking despite the fact that the gap structure features sign changes. By contrast, spin-triplet condensates remain fragile to disorder on the kagome lattice. We demonstrate these effects in terms of the absence of impurity bound states and an associated weak disorder-induced $T_c$-suppression for spin-singlet order. We also discuss the consequences for quasi-particle interference and their inherent tendency for momentum-space anisotropy due to sublattice effects on the kagome lattice. For unconventional kagome superconductors, our results imply that any allowed spin-singlet order, including for example $d+id$-wave superconductivity, exhibits a disorder-response qualitatively similar to standard conventional $s$-wave superconductors.

cond-mat.supr-con↗

arXiv2023

Superconductivity from Orbital-Selective Electron-Phonon Coupling in $A\mathrm{V}_3\mathrm{Sb}_5$

Recent experiments have shown that the phase diagrams of the kagome superconductors $A\mathrm{V}_3\mathrm{Sb}_5$ are strongly impacted by changes in the $c$-axis lattice parameter. Here, we show that $c$-axis deformations impact primarily the Sb apical bonds and thus the overlap between their $p_z$ orbitals. Changes in the latter, in turn, substantially affect low-energy electronic states with significant Sb character, most notably the central electron pocket and the van Hove singularities located above the Fermi level. Based on the orbital-selective character of $c$-axis strain, we argue that these electronic states experience a non-negligible attractive electron-phonon pairing interaction mediated by fluctuations in the apical Sb bonds. We thus propose a multi-band model for superconductivity in $A\mathrm{V}_3\mathrm{Sb}_5$ that includes both the Sb pocket and the V-derived van Hove singularities. Upon comparing the theoretical phase diagram with the experimentally observed vanishing of the $T_c$ dome across a Lifshitz transition of the Sb pocket, we propose that either an $s^{+-}$ or an $s^{++}$ state is realized in $A\mathrm{V}_3\mathrm{Sb}_5$.

cond-mat.supr-con↗

arXiv2022

Competing magnetic fluctuations and orders in a multiorbital model of doped SrCo$_2$As$_2$

We revisit the intriguing magnetic behavior of the paradigmatic itinerant frustrated magnet $\rm{Sr}\rm{Co}_2\rm{As}_2$, which shows strong and competing magnetic fluctuations yet does not develop long-range magnetic order. By calculating the static spin susceptibility $χ(\mathbf{q})$ within a realistic sixteen orbital Hubbard-Hund model, we determine the leading instability to be ferromagnetic (FM). We then explore the effect of doping and calculate the critical Hubbard interaction strength $U_c$ that is required for the development of magnetic order. We find that $U_c$ decreases under electron doping and with increasing Hund's coupling $J$, but increases rapidly under hole doping. This suggests that magnetic order could possibly emerge under electron doping but not under hole doping, which agrees with experimental findings. We map out the leading magnetic instability as a function of doping and Hund's coupling and find several antiferromagnetic phases in addition to FM. We also quantify the degree of itinerant frustration in the model and resolve the contributions of different orbitals to the magnetic susceptibility. Finally, we discuss the dynamic spin susceptibility, $χ(\mathbf{q}, ω)$, at finite frequencies, where we recover the anisotropy of the peaks at $\mathbf{Q}_π= (π, 0)$ and $(0, π)$ observed by inelastic neutron scattering that is associated with the phenomenon of itinerant magnetic frustration. By comparing results between theory and experiment, we conclude that the essential experimental features of doped SrCo$_2$As$_2$ are well captured by a Hubbard-Hund multiorbital model if one considers a small shift of the chemical potential towards hole doping.

cond-mat.str-el↗

arXiv2022

Loop currents in $A$V$_3$Sb$_5$ kagome metals: multipolar and toroidal magnetic orders

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a ``real" charge density-wave (rCDW), but also time-reversal symmetry-breaking, typical of loop currents described by an ``imaginary" charge density-wave (iCDW). Here, we combine density-functional theory, group-theory, and phenomenological modeling to investigate the complex charge-ordered states that arise from interactions between the low-energy van Hove singularities present in the electronic structure of $A$V$_3$Sb$_5$. We find two broad classes of mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, triple-$\mathbf{Q}$ rCDW order, dubbed $3\mathbf{Q}$-$3\mathbf{Q}$, and double-$\mathbf{Q}$ iCDW, single-$\mathbf{Q}$ rCDW order, dubbed $2\mathbf{Q}$-$1\mathbf{Q}$. Moreover, we identify seven different types of iCDW order, stemming from the different vanadium-orbital and kagome-sublattice structures of the two pairs of van Hove singularities present above and below the Fermi level. While the $2\mathbf{Q}$-$1\mathbf{Q}$ states trigger an orthorhombic distortion that breaks the threefold rotational symmetry of the kagome lattice, the $3\mathbf{Q}$-$3\mathbf{Q}$ states induce various types of subsidiary uniform magnetic orders, from conventional ferromagnetism to magnetic octupolar, magnetic toroidal, and even magnetic monopolar order. We show that these exotic orders display unique magneto-striction, magneto-electric, and magneto-electric-striction properties that can be probed experimentally to identify which iCDW state is realized in these compounds. We briefly discuss the impact of an out-of-plane modulation of the charge order and the interplay between these complex charge-ordered states and superconductivity.

cond-mat.str-el↗

arXiv2022

Superconductivity from repulsive interactions on the kagome lattice

The discovery of superconductivity in layered vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) has added a new family of materials to the growing class of possible unconventional superconductors. However, the nature of the superconducting pairing in these materials remains elusive. We present a microscopic theoretical study of the leading superconducting instabilities on the kagome lattice based on spin- and charge-fluctuation mediated Cooper pairing. The applied methodology includes effects of both on-site and nearest-neighbor repulsive Coulomb interactions. Near the upper van Hove filling -- relevant for the $A$V$_3$Sb$_5$ materials -- we find a rich phase diagram with several pairing symmetries being nearly degenerate. In particular, while a substantial fraction of the phase diagram is occupied by a spin-singlet order parameter transforming as a two-dimensional irreducible representation of the point group, several nodal spin-triplet pairing states remain competitive. We compute the band and interaction parameter-dependence of the hierarchy of the leading superconducting instabilities, and determine the detailed momentum dependence of the resulting preferred gap structures. Crucially, for moderate values of the interaction parameters, the individual pairing states depend strongly on momentum and exhibit multiple nodes on the Fermi surface. We discuss the properties of these superconducting gap structures in light of recent experimental developments of the $A$V$_3$Sb$_5$ materials.

cond-mat.supr-con↗

arXiv2022

Hot-lines topology and the fate of the spin resonance mode in three-dimensional unconventional superconductors

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.

cond-mat.supr-con↗

arXiv2022

Topological Superconductivity Induced by Magnetic Texture Crystals

We present a detailed investigation of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between (un)conventional one/two-band spin-singlet superconductivity and a number of magnetic texture crystals. The latter define inhomogeneous magnetization profiles which consist of a periodically-repeating primitive cell. Here we focus on magnetic texture crystals with a primitive cell of the helix, whirl, and skyrmion types, which feature distinct symmetry properties. We identify a multitude of accessible topological phases which harbor flat, uni- or bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety originates from the interplay between topological phases with gapped and nodal bulk energy spectra. The types of the emerging topological superconducting phases and the features of the arising MFs are solely determined by the properties and compatibility of the so-called magnetic and pairing point/space groups. Our analysis is general and does not rely on specific parameters of the models employed here to exemplify the topological scenarios which become accessible. Therefore, our results can be extended to systems with multiple bands, are relevant for a wide range of layered materials and hybrid devices, and provide predictions for strong, weak and crystalline topological phases.

cond-mat.supr-con↗

arXiv2021

Dynamical vortices in electron-phonon superconductors

We analyze the structure of an $s-$wave superconducting gap in systems with electron-phonon attraction and electron-electron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap, $Δ(ω_m)$, necessarily changes sign along the Matsubara axis. We analyze the sign-changing gap function from a topological perspective using the knowledge that a nodal point of $Δ(ω_m)$ is the center of dynamical vortex. We consider two models with different cutoffs for the repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane upon changing the relative strength of the attractive and repulsive parts of the interaction. We discuss how the presence of dynamical vortices affects the gap structure along the real axis, detectable in ARPES experiments.

cond-mat.supr-con↗

arXiv2021

Revealing the competition between charge-density wave and superconductivity in CsV$_3$Sb$_5$ through uniaxial strain

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along the crystalline $a$ axis on the newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. In our study, when the uniaxial strain $\varepsilon$ is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\sim 33\%$ from 3.0 K to 4.0 K, giving rise to the empirical relation $T_C (\varepsilon)=3.4+0.56\varepsilon+0.12\varepsilon^2$. On the other hand, for $\varepsilon$ changing from $-0.76\%$ to $1.26\%$, $T_{\rm CDW}$ decreases monotonically by $\sim 10\%$ from 97.5 K to 87.5 K with $T_{\rm CDW}(\varepsilon)=94.5-4.72\varepsilon-0.60\varepsilon^2$. The opposite response of $T_C$ and $T_{\rm CDW}$ to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$-axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_C$ with decreasing $c$ is caused primarily by the suppression of $T_{\rm CDW}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{\rm CDW}$ with respect to the changes in the $c$-axis arises from the impact of the latter on the trilinear coupling between the $M_1^+$ and $L_2^-$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV$_3$Sb$_5$.

cond-mat.supr-con↗

arXiv2021

Theory of the charge-density wave in $A$V$_3$Sb$_5$ kagome metals

The family of metallic kagome compounds $A$V$_3$Sb$_5$ ($A$=K, Rb, Cs) was recently discovered to exhibit both superconductivity and charge order. The nature of the charge-density wave (CDW) phase is presently unsettled, which complicates the interpretation of the superconducting ground state. In this paper, we use group-theory and density-functional theory (DFT) to derive and solve a phenomenological Landau model for this CDW state. The DFT results reveal three unstable phonon modes with the same in-plane momentum but different out-of-plane momenta, whose frequencies depend strongly on the electronic temperature. This is indicative of an electronically-driven CDW, stabilized by features of the in-plane electronic dispersion. Motivated by the DFT analysis, we construct a Landau free-energy expansion for coupled CDW order parameters with wave-vectors at the $M$ and $L$ points of the hexagonal Brillouin zone. We find an unusual trilinear term coupling these different order parameters, which can promote the simultaneous condensation of both CDWs even if the two modes are not nearly-degenerate. We classify the different types of coupled multi-$\bf{Q}$ CDW orders, focusing on those that break the sixfold rotational symmetry and lead to a unit-cell doubling along all three crystallographic directions, as suggested by experiments. We determine a region in parameter space, characterized by large nonlinear Landau coefficients, where these phases - dubbed staggered tri-hexagonal and staggered Star-of-David - are the leading instabilities of the system. Finally, we discuss the implications of our results for the kagome metals.

cond-mat.supr-con↗

arXiv2020

Modeling unconventional superconductivity at the crossover between strong and weak electronic interactions

High-temperature superconductivity emerges in a host of different quantum materials, often in a region of the phase diagram where the electronic kinetic energy is comparable in magnitude with the electron-electron Coulomb repulsion. Describing such an intermediate-coupling regime has proven challenging, as standard perturbative approaches are inapplicable. Hence, it is of enormous interest to find models that are amenable to be solved using exact methods. While important advances have been made in elucidating the properties of one such minimal model -- the Hubbard model -- via numerical simulations, the infamous fermionic sign-problem significantly limits the accessible parameter space. Here, we employ Quantum Monte Carlo (QMC) methods to solve a multi-band version of the Hubbard model that does not suffer from the sign-problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free QMC studies, this model does not have pre-existing fine-tuned magnetic order, and thus treats superconducting, magnetic, and charge degrees of freedom on an equal footing. We find that, as the electron-electron repulsion increases, a dome of antiferromagnetic order emerges in the intermediate-coupling regime, accompanied by a metal-to-insulator crossover line. Superconductivity is found only near the antiferromagnetic quantum phase transition located on the metallic side of the magnetic dome. Across the antiferromagnetic quantum phase transition we find a change in the dynamical character of the magnetic fluctuations, from slow and overdamped in the metallic side to fast and propagating in the insulating side. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.

cond-mat.str-el↗

arXiv2020

Evolution of nematic fluctuations in CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ with spin-vortex crystal magnetic order

The CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ superconductors resemble the archetypal 122-type iron-based materials but have a crystal structure with distinctly lower symmetry. This family hosts one of the few examples of the so-called spin-vortex crystal magnetic order, a non-collinear magnetic configuration that preserves tetragonal symmetry, in contrast to the orthorhombic collinear stripe-type magnetic configuration common to the 122-type systems. Thus, nematic order is completely absent from its phase diagram. To investigate the evolution of nematic fluctuations in such a case, we present elastoresistance and elastic modulus measurements in CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ ($x = 0-0.05$) combined with phenomenological modeling and density functional theory. We find clear experimental signatures of considerable nematic fluctuations, including softening of the Young's modulus $Y_{[110]}$ and a Curie-Weiss type divergence of the B2g elastoresistance coefficient in CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. Overall, nematic fluctuations within this series bear strong similarities to the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ series, including a substitution-induced sign change. Our theoretical analysis addresses the effect of the specific crystal symmetry of the 1144-type structure in determining its magnetic ground state and on the nematic fluctuations.

cond-mat.supr-con↗

arXiv2020

Nematic Fluctuations in an Orbital Selective Superconductor Fe$_{1+y}$Te$_{1-x}$Se$_{x}$

We present a systematic study of the nematic fluctuations in the iron chalcogenide superconductor Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ ($0 \leq x \leq 0.53$) using the elastoresistivity technique. Near $x = 0$, in proximity to the double-stripe magnetic order of Fe$_{1+y}$Te, a diverging $B_{1g}$ nematic susceptibility is observed. Upon increasing $x$, despite the absence of magnetic order, the $B_{2g}$ nematic susceptibility increases and becomes dominant, closely following the strength of the $(π, π)$ spin fluctuations. Over a wide range of compositions ($0.17 \leq x \leq 0.53$), while the $B_{2g}$ nematic susceptibility follows a Curie temperature dependence (with zero Weiss temperature) at low temperatures, it shows deviations from Curie-Weiss behavior for temperatures higher than $50K$. This is the opposite of what is observed in typical iron pnictides, where Curie-Weiss deviations are seen at low temperatures. We attribute this unusual temperature dependence to a loss of coherence of the $d_{xy}$ orbital, which is supported by our theoretical calculations. Our results highlight the importance of orbital differentiation on the nematic properties of iron-based materials.

cond-mat.supr-con↗