Louk Rademaker, Gustavo Alvarez-Suchini, Ken Nakatsukasa, Yan Wang, Steven Johnston
We study the effect of combining spin fluctuations and forward scattering electron-phonon ({\eph}) coupling on the superconductivity in the FeSe/SrTiO$_3$ system modeled by a phenomenological two-band Hubbard model with long-range {\eph} interactions. We treat the electron and phonon degrees of freedom on an equal footing using a \emph{fully} self-consistent FLEX plus Migdal-Eliashberg calculation, which includes a self-consistent determination of the spin fluctuation spectrum. Based on FeSe monolayers, we focus on the case where one of the bands lies below the Fermi level (i.e. incipient), and demonstrate that the combined interactions can enhance or suppress $T_c$, depending on their relative strength. For a suitable choice of parameters, the spin-fluctuation mechanism yields a $T_c \approx 46.8$ K incipient $s_\pm$ superconductor, consistent with surface-doped FeSe thin films. A forward-focused {\eph} interaction further enhances the $T_c$, as observed in monolayer FeSe on SrTiO$_3$.
Louk Rademaker
The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.
Louk Rademaker, Tom van der Reep, Nick Van den Broeck, Bob van Waarde, Marc de Voogd, Tjerk Oosterkamp
Using the relativistic concept of time dilation we show that a superposition of gravitational potentials can lead to nonunitary time evolution. For sufficiently weak gravitational potentials one can still define, for all intents and purposes, a global coordinate system. A probe particle in a superposition of weak gravitational fields will, however, experience dephasing due to the different time dilations. The corresponding instability timescale is accessible to experiments, and can be used as a degree of macroscopicity. Finally, we suggest an experiment with smoothly tunable amplification in a microwave interferometer that allows a quantitative study of the quantum to classical boundary.
Louk Rademaker, Kai Wu, Jan Zaanen
We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α=J_{\perp}/Jz. In the disordered phase at large α, a coherent quasiparticle peak appears representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c-axis optical conductivity measurements.
Waseem Akbar, Andrzej Biborski, Louk Rademaker, Michał Zegrodnik
We investigate strong coupling topological superconductivity in twisted moiré bilayer WSe$_2$. Our approach is based on an effective $t$-$J$ model with displacement-field-dependent complex hoppings, which is treated with the variational Gutzwiller projection method. The calculated phase diagram contains domes of topologically nontrivial superconducting phases, with Chern numbers $C=\pm 2,\;\pm 4$. The order parameter is characterized by a mixed $d$+$id$-wave (singlet) and $p$-$ip$-wave (triplet) gap symmetry. We also report on the appearance of an additional topologically trivial extended $s$-wave and $f$-wave paired phase. As we show, by changing the electron density and displacement field, one can tune the singlet and triplet contributions to the pairing, as well as induce topological phase transitions between superconducting states characterized by different values of the Chern number. We analyze the physical origin of the reported effects and discuss it briefly in the view of new possibilities for designing unconventional superconductivity in moiré systems.
Louk Rademaker, Marco Gibertini
We study free, capped and encapsulated bilayer jacutingaite Pt$_2$HgSe$_3$ from first principles. While the free standing bilayer is a large gap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublattice-dependent next-nearest-neighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and described by an imbalanced Kane-Mele model that takes into account the sublattice imbalance and the corresponding inversion-symmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a 0+0 state, where each layer is trivial, to a 0+1 state, where an unusual topological state relying on Rashba-like spin orbit coupling emerges in only one of the layers.
Louk Rademaker, Dmitry A. Abanin
Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here we study quantum dynamics of an isolated 1d spin-glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via resonance avalanche mechanism, that is also responsible for the destruction of MBL in non-glassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.
Louk Rademaker
We extend the analytical arguments of Metlitski and Grover (arXiv:1112.5166) to compute the entanglement spectrum and entanglement entropy of coplanar antiferromagnets with $SO(3)$ order parameter symmetry. The low-energy states in the entanglement spectrum exhibit the tower of states structure, as is expected for systems that undergo spontaneous symmetry breaking. Our results are consistent with numerical results on the triangular and Kagomé lattice.
Louk Rademaker, Valerii V. Vinokur, Alexey Galda
We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of dynamic Mott transition in a system of interacting superconducting vortices.
Louk Rademaker, Jeroen van den Brink, Jan Zaanen, Hans Hilgenkamp
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems an exciton is the bound state of a double occupied and empty site. In the strong coupling limit the exciton acts as a hard-core boson. Its physics are captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean field theory we constructed the ground state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally we studied the collective modes and susceptibilities of the three phases. In the superfluid phase we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).
Lihuan Sun, Louk Rademaker, Diego Mauro, Alessandro Scarfato, Árpád Pásztor, Ignacio Gutiérrez-Lezama, Zhe Wang, Jose Martinez-Castro, Alberto F. Morpurgo, Christoph Renner
Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe$_2$ heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman ($λ_{\text{vZ}}\approx 2$ meV) and a Rashba ($λ_\text{R}\approx 15$ meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.
Robert-Jan Slager, Louk Rademaker, Jan Zaanen, Leon Balents
We show that the local in-gap Greens function of a band insulator $\mathbf{G}_0 (ε,\mathbf{k}_{\parallel},\mathbf{r}_{\perp}=0)$, with $\mathbf{r}_\perp$ the position perpendicular to a codimension-1 or -2 impurity, reveals the topological nature of the phase. For a topological insulator, the eigenvalues of this Greens function attain zeros in the gap, whereas for a trivial insulator the eigenvalues remain nonzero. This topological classification is related to the existence of in-gap bound states along codimension-1 and -2 impurities. Whereas codimension-1 impurities can be viewed as 'soft edges', the result for codimension-2 impurities is nontrivial and allows for a direct experimental measurement of the topological nature of 2d insulators.
Giulia Venditti, Carlo Beenakker, Louk Rademaker
In 1925, Dr. Geertruida Luberta "Berta" de Haas-Lorentz published the paper "Iets over het mechanisme van inductieverschijnselen" in the journal Physica. Her paper was the first to discuss perfect diamagnetism of superconductors, eight years before the discovery of the Meissner effect, when the essential difference between the two phenomena was not understood. Unfortunately, her work was almost forgotten by the scientific community. To counter this, we translate her seminal 1925 paper from Dutch into English. We provide an overview of the life of Dr. De Haas-Lorentz, and comment on her pioneering contribution to the theory of superconductivity.
Marta Brzezińska, Sergii Grytsiuk, Malte Rösner, Marco Gibertini, Louk Rademaker
Recent experiments in twisted bilayer transition-metal dichalcogenides have revealed a variety of strongly correlated phenomena. To theoretically explore their origin, we combine here ab initio calculations with correlated model approaches to describe and study many-body effects in twisted bilayer WSe$_2$ under pressure. We find that the interlayer distance is a key factor for the electronic structure, as it tunes the relative energetic positions between the K and the $Γ$ valleys of the valence band maximum of the untwisted bilayer. As a result, applying uniaxial pressure to a twisted bilayer induces a charge-transfer from the K valley to the flat bands in the $Γ$ valley. Upon Wannierizing moiré bands from both valleys, we establish the relevant tight-binding model parameters and calculate the effective interaction strengths using the constrained random phase approximation. With this, we approximate the interacting pressure-doping phase diagram of WSe$_2$ moiré bilayers using self-consistent mean field theory. Our results establish twisted bilayer WSe$_2$ as a platform that allows the direct pressure-tuning of different correlated phases, ranging from Mott insulators, charge-valley-transfer insulators to Kondo lattice-like systems.
Louk Rademaker
We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion will delocalize with $W_c \approx 1.4t$ and with localization length critical exponent $ν= 1.5 \pm 0.3$. The delocalization transition can be understood by means of a mapping onto a non-interacting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.
Louk Rademaker, Aron Beekman, Jasper van Wezel
Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A and type-B) ways of spontaneously breaking a continuous symmetry. Although type-B Nambu--Goldstone modes arise in various systems, the ferromagnet was considered pathological due to the stability and symmetry-breaking nature of its exact ground state. However, here we show that symmetry-breaking in ferrimagnets closely resembles the ferromagnet. In particular, there is an extensive ground state degeneracy, there is no Anderson tower of states, and the maximally polarized ground state is thermodynamically stable. Our results are derived analytically for the Lieb--Mattis ferrimagnet and numerically for the Heisenberg ferrimagnet. We argue that these properties are generic for type-B symmetry-broken systems, where the order parameter operator is a symmetry generator.
Louk Rademaker, Kai Wu, Hans Hilgenkamp, Jan Zaanen
Using the self-consistent Born approximation we study the delocalization of interlayer excitons in the bilayer Heisenberg quantum antiferromagnet. Under realistic conditions we find that the coupling between the exciton motion and the spin system is strongly enhanced as compared to the case of a single carrier, to a degree that it mimics the confinement physics of carriers in Ising spin systems. We predict that the "ladder spectrum" associated with this confinement physics should be visible in the c-axis exciton spectra of insulating bilayer cuprates such as YBa2Cu3O6. Our discovery indicates that finite density systems of such excitons should show very rich physical behavior.
Louk Rademaker, Jeroen van den Brink, Hans Hilgenkamp, Jan Zaanen
We show that an interlayer exciton condensate doped into a strongly correlated Mott insulator exhibits a remarkable enhancement of the bandwidth of the magnetic excitations (triplons). This triplon is visible in the dynamical magnetic susceptibility and can be measured using resonant inelastic X-ray scattering. The bandwidth of the triplon scales with the exciton superfluid density, but only in the limit of strong correlations. As such the triplon bandwidth acts as a probe of exciton-spin interactions in the condensate.
Louk Rademaker, Zohar Nussinov, Leon Balents, Vladimir Dobrosavljevic
We investigate the structure of metastable states in self-generated Coulomb glasses. In dramatic contrast to disordered electron glasses, we find that these states lack marginal stability. Such absence of marginal stability is reflected by the suppression of the single-particle density of states into an exponentially soft gap of the form $g(ε) \sim e^{-V / ξ|ε|}$. To analytically explain this behavior, we extend the stability criterion of Efros and Shklovskii to incorporate local charge correlations, in qualitative agreement with our numerical findings. Our work suggests the existence of a new class of self-generated glasses dominated by strong geometric frustration.
Louk Rademaker, Jan Zaanen
The ultimate consequence of quantum many-body physics is that even the air we breathe is governed by strictly unitary time evolution. The reason that we perceive it nonetheless as a completely classical high temperature gas is due to the incapacity of our measurement machines to keep track of the dense many-body entanglement of the gas molecules. The question thus arises whether there are instances where the quantum time evolution of a macroscopic system is qualitatively different from the equivalent classical system? Here we study this question through the expansion of noninteracting atomic clouds. While in many cases the full quantum dynamics is indeed indistinguishable from classical ballistic motion, we do find a notable exception. The subtle quantum correlations in a Bose gas approaching the condensation temperature appear to affect the expansion of the cloud, as if the system has turned into a diffusive collision-full classical system.