arXiv subjects
Publications and source records attributed to Lennart Klebl.
We develop a class of microscopic lattice models in which pair density wave order emerges in the asymptotically exact weak coupling limit. The underlying mechanism is due to non-symmorphic momentum symmetry implied by the models' projective space group representation of electrons. Our mechanism suggests moiré systems and extended s-wave altermagnets as potential hosts for pair density wave order.
We investigate the emergence of electronic order and unconventional superconductivity in M-valley moiré materials. Starting from a first-principles Wannier model of AB-stacked twisted SnSe2, we tackle the (gate-screened) long-ranged Coulomb interaction with functional renormalization group simulations resolving the momentum structure and energy scales of the leading Fermi surface instabilities. Upon doping an antiferromagnetic stripe state at half-filling ($ν=3$ electrons per moiré unit cell) of the moiré flat bands, magnetic order gives way to unconventional superconductivity mediated by valley-selective spin fluctuations: Large hole doping ($ν\approx1$) leads to weak-coupling superconductors with various pairing symmetries, while slight electron- and hole-doping ($ν\approx2,4$) stabilizes a spin-singlet, extended s-wave state that benefits from scattering between virtual particle and hole states that are detuned from the Fermi level. These findings establish M-point moiré materials as a quantum simulation platform with phenomenological parallels to the class of iron pnictide superconductors.
We study an interacting kagome-lattice realization of a quadratic band-touching semimetal at 2/3 filling with onsite and nearest-neighbor repulsive interactions. Combining functional renormalization group and slave-boson approaches, we map its phase diagram from intermediate to strong coupling and uncover a hierarchy of unconventional electronic orders. The leading instabilities comprise loop-current order, spontaneous altermagnetism arising from a spin-Pomeranchuk instability, and spin-loop-current order with distinctive and largely unexplored properties. We demonstrate how the interplay of band kinematics, electronic interactions, and quantum geometry governs the selection of these phases. Our findings establish quadratic band-touching semimetals as a promising platform for unconventional symmetry breaking and suggest analogous phenomena in other parabolic semimetals.
We formulate a functional renormalization group (FRG) ansatz for correlated electron models that incorporates electronic interactions as well as electron-phonon coupling (EPC) stemming from dispersive phonon bands. Particularizing to the RG flow of the electron-electron interaction vertex, we treat phonon- and electron-mediated Fermi liquid instabilities on equal footing as we analyze tentative electronic order parameters related to charge, spin, nematicity, and superconducting pairing. We illustrate the approach at the example of Peierls-type transitions we find for the Hubbard model on the square lattice coupled to acoustic phonon bands. Our method allows to incorporate full electronic and phononic ab initio input, and thus lends itself to the analysis of electronic order from intertwined electronic interactions and EPC at a microscopically most substantiated level.
Achieving sub-millikelvin electron temperatures in nanoelectronic devices could unveil new transport phenomena, extend quantum coherence times, and enhance the precision of quantum metrology. However, maintaining such low temperatures continuously remains a long-standing challenge. Here, we propose and simulate an on-chip cooling cycle that harnesses the entropy difference between an electron liquid (EL) and a Wigner crystal (WC) in flavor-degenerate flat-band materials. Cooling is driven by a current through a device with a locally gated region. Within this region, the charge carrier density is tuned such that a WC forms beneath the gate. As carriers transition from an EL to WC phase, their entropy increases, extracting heat and the sliding WC advects this heat along the device. The heat is then released when carriers transition back to the EL phase, which establishes distinct hot and cold regions and a steady temperature gradient over the device. Simulations show net cooling for sufficiently low current densities, typically below $1~\mathrm{nA}/μ\mathrm{m}$, whereas Joule heating dominates at higher currents. Within the gated region, we estimate cooling powers of up to $8.4~\mathrm{aW}/μ\mathrm{m}$ at a bath temperature of $4~\mathrm{mK}$. Our approach can achieve electron temperatures well below $1~\mathrm{mK}$ under suitable conditions, promising a route towards continuous on-chip cooling in this temperature regime. Our approach applies to any flat-band material with low-energy flavor degeneracy (valley and/or orbital) and low disorder, including gapped Bernal-stacked bilayer graphene, rhombohedral-stacked multilayer graphene, and magic-angle twisted bilayer graphene.
The kagome superconductor family AV3Sb5 (A=Cs, Rb, K) provides a rich platform for exploring diverse electronic symmetry breaking phenomena, including superconductivity and various forms of density wave orders. Although these compounds share the identical lattice structure in the normal state, they exhibit distinct forms of symmetry breaking upon entering the charge density wave (CDW) phase, and the microscopic origin of which remain elusive. Here, we investigate the lattice and charge degrees of freedom in AV3Sb5 using angle-resolved polarized Raman spectroscopy. Our comprehensive polarization-resolved measurements reveal that the lifting of the twofold-degeneracy of the E2g phonon mode in the CDW phase-previously reported only in CsV3Sb5 with a 3 GHz splitting-also appears ubiquitously in the other two compounds. In contrast, the collective CDW excitations exhibit markedly different polarization dependences depending on the alkali-metal species. These distinct behaviors in the lattice and charge channels provide crucial insight into the enigmatic material-dependent symmetry breaking phenomena that appear in the CDW phase. Furthermore, our experiments, together with first-principles calculations and an effective Hamiltonian model, shed light on the nature of the charge order structure in AV3Sb5 kagome superconductors.
We propose extended s-wave altermagnets (sAMs) as a class of magnetic states which are fully gapped, spin-compensated, and feature spin-polarized bands. sAMs are formed through valley-exchange symmetries, which act as momentum-space translations beyond standard crystallographic spin-group classifications. Using an effective two-valley model, we demonstrate that sAMs exhibit isotropic spin splitting, enable spin-selective transport in tailored heterostructures, and give rise to descendant pair density wave order. From a microscopic sAM minimal model, we develop the guiding principles to identify sAMs in quantum magnets.
By means of slave-boson theory for the Hubbard model on the checkerboard lattice, we calculate dynamical altermagnetic spin susceptibilities from the metallic to the Mott-insulating regime. We track magnon dispersion and lifetime renormalization, allowing us to uncover a crossover from a chirality-selective dissipation of magnon modes to coherent yet strongly deformed chiral magnon branches across the metal insulator transition. Our formalism lends itself to a quantitative description of collective spin dynamics in correlated altermagnets.
We present an extension to the two-dimensional functional renormalization group to efficiently treat interactions on the surface or at interfaces of three-dimensional systems. As an application, we consider a semi-infinite stack of two-dimensional square lattices, including a Hubbard interaction on the surface layer and an alternating interlayer coupling. We investigate how strongly correlated states of the decoupled two-dimensional Hubbard model on the surface evolve under inclusion of such an SSH-like interlayer coupling. For large parts of the phase diagram as a function of the interlayer hopping parameters, the physics of the two-dimensional system prevails, with antiferromagnetic, superconducting $d$-wave, and ferromagnetic correlations taking center stage. However, for intermediate interlayer couplings the superconducting state at intermediate interaction strengths separates into two regimes by a small region of incommensurate spin-density-wave and spin-bond order, enabling the potential realization of chiral spin-bond order.
Superlattice engineering in van der Waals heterostructures (e.\,g.\ by moiré engineering) provides a powerful platform for designing electronic bands and realising correlated and topological quantum phenomena. Here, we pioneer a scheme to tailor superpotentials based on intrinsic substrate electronic orders. We show that this establishes a robust, self-aligned, and highly versatile route to band-structure control as we demonstrate in graphene by engineering two distinct, nearly commensurate superlattices using the charge density waves of 1T-NbSe$_2$. In these superlattices the graphene's Dirac cones are folded either to the $Γ$-point or to the K-points of the mini-Brillouin zone. Using scanning tunnelling microscopy, we observe that the $Γ$-folded system preserves C$_3$ symmetry, while the K-folded system exhibits spontaneous symmetry breaking. Combining density functional theory with an interlayer interaction model, we reveal that this difference is not electronically driven but originates from a structural instability. Our work establishes superlattice engineering for designer quantum states and unveils a structural mechanism for controlled emergent symmetry breaking.
We analyze the phase transition between a symmetric metallic parent state and itinerant altermagnetic order. The underlying mechanism we reveal in our microscopic model of electrons on a Lieb lattice does not involve orbital ordering, but derives from sublattice interference.
Translation symmetry-breaking order is assumed to be suppressed by the lack of Fermi surface nesting near certain higher-order Van Hove singularities (HOVHS). We show the anisotropic band-flattening inherent to such HOVHS, combined with broadening of the Fermi surface due to elevated critical temperatures, results in the Fermi surface becoming approximately nested at a wavevector unrelated to the precise shape of the Fermi surface - leading to a $\sqrt{3}\times\sqrt{3}$ Kekulé density wave formation. The effect is demonstrated using unbiased renormalization group calculations for a model of the breathing kagome lattice. Our mechanism - termed diffuse nesting - represents an entirely new notion in the study of Fermi surface instabilities.
Solving the many-electron problem, even approximately, is one of the most challenging and simultaneously most important problems in contemporary condensed matter physics with various connections to other fields. The standard approach is to follow a divide and conquer strategy that combines various numerical and analytical techniques. A crucial step in this strategy is the derivation of an effective model for a subset of degrees of freedom by a procedure called downfolding, which often corresponds to integrating out energy scales far away from the Fermi level. In this work we present a rigorous formulation of this downfolding procedure, which complements the renormalization group picture put forward by Honerkamp [PRB 85, 195129 (2012)}]. We derive an exact effective model in an arbitrarily chosen target space (e.g. low-energy degrees of freedom) by explicitly integrating out the the rest space (e.g. high-energy degrees of freedom). Within this formalism we state conditions that justify a perturbative truncation of the downfolded effective interactions to just a few low-order terms. Furthermore, we utilize the exact formalism to formally derive the widely used constrained random phase approximation (cRPA), uncovering underlying approximations and highlighting relevant corrections in the process. Lastly, we detail different contributions in the material examples of fcc Nickel and the infinite-layer cuprate SrCuO$_2$. Our results open up a new pathway to obtain effective models in a controlled fashion and to judge whether a chosen target space is suitable.
Graphene-based multilayer systems serve as versatile platforms for exploring the interplay between electron correlation and topology, thanks to distinctive low-energy bands marked by significant quantum metric and Berry curvature from graphene's Dirac bands. Here, we investigate Mott physics and local spin moments in Dirac bands hybridized with a flat band of localized orbitals in functionalized graphene. Via hybridization control, a topological transition is realized between two symmetry-distinct site-selective Mott states featuring local moments in different Wyckoff positions, with a geometrically enforced metallic state emerging in between. We find that this geometrically controlled real-space switching of local moments and associated metal-insulator physics may be realized through proximity coupling of epitaxial graphene on SiC(0001) with group IV intercalants, where the Mott state faces geometrical obstruction in the large-hybridization limit. Our work shows that chemically functionalized graphene provides a correlated electron platform, very similar to the topological heavy fermions in graphene moiré systems but at significantly enhanced characteristic energy scales.
Recent observations of superconductivity in twisted bilayer WSe$_2$ have extended the family of moiré superconductors beyond twisted graphene. In WSe$_2$ two different twist angles were studied, 3.65° and 5.0°, and two seemingly distinct superconducting phase diagrams were reported, raising the question of whether the superconducting phases in the two devices share a similar origin. Here we address the question by experimentally mapping the evolution of the phase diagram across devices with twist angles spanning the range defined by the initial reports, and comparing the results to twist angle-dependent theory. We find that the superconducting state evolves smoothly with twist angle and at all twist angles is proximal to a Fermi surface reconstruction with, presumably, antiferromagnetic ordering, but is neither necessarily tied to the Van Hove singularity, nor to the half band insulator. Our results connect the previously distinct phase diagrams at 3.65° and 5°, and offer new insight into the origin of the superconductivity in this system and its evolution as the correlation strength increases. More broadly, the smooth phase diagram evolution, repeatability between different devices, and dynamic gate tunability within each device, establish twisted transition metal dichalcogenides as a unique platform for the study of correlated phases as the ratio of interaction strength to bandwidth is varied.
Recently, symmetry-broken ground states, such as correlated insulating states, magnetic order and superconductivity, have been discovered in twisted bilayer graphene (tBLG) and twisted trilayer graphene (tTLG) near the so-called magic-angle. Understanding the magnetic order in these systems is challenging, however, as atomistic methods become extremely expensive near the magic angle and continuum approaches fail to capture important atomistic details. In this work, we develop an approach to incorporate short-ranged Hubbard interactions self-consistently in a continuum model. In addition, we include long-ranged Coulomb interactions, which are known to be important when doping the flat bands of tBLG and tTLG. Therefore, for the first time, magnetic order in moiré graphene multilayers is self-consistently explored in a continuum model with atomistic detail. With this approach, we perform a systematic analysis of the magnetic phase diagram of tBLG as a function of doping level and twist angle, near the magic angle. Our results are consistent with previous perturbative atomistic Hartree+U calculations. Furthermore, we investigated magnetic order of tTLG, which were found to be similar to those in tBLG. In the future, the developed continuum model can be utilized to investigate magnetic ordering tendencies from short-range exchange interactions in other moiré graphene multilayers as a function of doping, twist angle, screening environment, among other variables.
The recent observation of superconductivity in the vicinity of Fermi surface reconstructed insulating or metallic states has established twisted bilayers of WSe\textsubscript{2} as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries and topology. In this work, we use a first-principles, material-specific theoretical treatment that is unbiased with respect to electronic instabilities to study the emergence of electronic ordering in twisted WSe\textsubscript{2} driven by gate-screened Coulomb interactions. We construct exponentially localized moiré Wannier orbitals that faithfully capture the bandstructure and topology of the system, project the gate-screened Coulomb interaction onto them and use unbiased functional renormalization group techniques to resolve the momentum and orbital structure of the leading instabilities and the relevant energy scales. We find an interplay between intervalley-coherent antiferromagnetic (IVC-AFM) order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near a displacement field and twist-angle-tunable van-Hove singularity. Our microscopic approach establishes incommensurate IVC-AFM spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $θ= 5.08^{\circ}$ twisted WSe\textsubscript{2} and explains key aspects of recent experiments including the asymmetric density dependence of the spin ordering with respect to the van-Hove line, the single and double-peak structure of the DOS in the ordered (hole-doped) IVC-AFM phase, the emergence of superconductivity as the density is varied across the van-Hove line and the evolution of the displacement field-density phase diagram with twist angles between $3.7^{\circ} \dots 5^{\circ}$.
We construct an interacting Wannier model for both AA-stacked and AB-stacked twisted SnSe2, revealing a rich landscape of correlated quantum phases. For the AA-stacked case, the system is effectively described by a three-orbital triangular lattice model, where each orbital corresponds to a valley and exhibits an approximate one-dimensional hopping structure due to a new momentum-space non-symmorphic symmetry. By exploring the interacting phase diagram using a combination of theoretical methods, including Hartree-Fock mean-field theory and exact solutions of the spin model in certain limits, we identify several exotic quantum phases. These include a dimerized phase with finite residual entropy, valence bond solids, and quantum paramagnetism. In the AB-stacked case, the system realizes an interacting kagome lattice model, where the Wannier orbitals associated with the three valleys form three sublattices. In the strong coupling regime, we use cluster mean-field methods to demonstrate the emergence of a classical spin liquid phase due to the frustrated lattice structure. The high tunability of the moiré system, which allows control over both the filling and interaction strength (via twist angle), renders twisted SnSe2 a versatile platform for realizing a wide range of exotic correlated quantum phases.