Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to realize a tunable SOTSC as a two-dimensional nanowire array. We show that the coupling between the Majorana modes of adjacent wires can be controlled by phase-biasing the device, allowing one to access a variety of topological phases. We characterize the system using scattering theory, which provides access to its transport properties and its topological invariants. The setup is robust against disorder, both in the nanowires themselves and in the Josephson junctions formed between adjacent wires. Further, we identify a parameter regime in which an initially trivial system is rendered topological upon adding disorder, providing an example of a second-order topological Anderson phase.

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protocols proposed in this work for the detection of NAGD. In particular, we formulate interference measurements providing full access to NAGD. Apart from a factor due to the dynamic phase and its fluctuations, the averaged evolution operator contains the averaged Berry matrix. A polar decomposition of this nonunitary matrix into the product of a unitary, $V$, and a positive-semidefinite Hermitian matrix, $R$, reveals the physics of the NAGD contributions. Unlike the conventional dynamic dephasing rate, the NAGD eigenrates encoded by $R$ depend on the loop orientation sense and, in particular, change sign under a reversal of the direction. A negative rate then implies amplification of coherences as compared to the ones when only dynamic dephasing is present. The non-Abelian character of geometric dephasing is rooted in the noncommutativity of $V$ and $R$ and causes smoking-gun signatures in interference experiments. We also clarify why systems subject to topological protection do not show geometric dephasing. Without full protection, however, geometric dephasing can arise and has to be taken into account. As concrete application, we propose spin-echo NAGD detection protocols for modified Majorana braiding setups.

We report on the evolution of the thermal metal-insulator transition in polycrystalline samples of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ upon hole doping via substitution of ${\mathrm{Ca}}^{2+}$ for ${\mathrm{Nd}}^{3+}$. Ca substitution mediates a filling-controlled Mott-like transition with minimal resolvable structural changes and without altering site symmetry. Local structure confirms that Ca substitution does not result in local chemical phase separation, and absorption spectroscopy establishes that Ir cations maintain a spin-orbit entangled electronic configuration. The metal-insulator transition coincides with antiferromagnetic ordering on the Ir sublattice for all measured samples, and both decrease in onset temperature with Ca content. Weak low-temperature upturns in susceptibility and resistivity for samples with high Ca content suggest that Nd sublattice antiferromagnetism continues to couple to carriers in the metallic regime.

Photonic topological systems, the electromagnetic analog of the topological materials in condensed matter physics, create many opportunities to design optical devices with novel properties. We present an experimental realization of the bi-anisotropic meta waveguide photonic system replicating both quantum Hall (QH) and quantum spin Hall (QSH) topological insulating phases. With careful design, a composite QH-QSH photonic topological material is created and experimentally shown to support reflection-free edgemodes, a heterogeneous topological structure that is unprecedented in condensed matter physics. The effective spin degree of freedom of such topologically protected modes determines their unique pathways through these systems, free from backscattering and able to travel around sharp corners. As an example of their novel properties, we experimentally demonstrate reflection-less photonic devices including a two-port isolator, a unique three-port topological device, and a full four-port circulator based on composite QH and QSH structures.

We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.

Some of the exciting phenomena uncovered in strongly correlated systems in recent years—for instance, quantum topological order, deconfined quantum criticality, and emergent gauge symmetries—appear in systems in which the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer models, and vertex models. In this work, we use a slave boson description coupled to a large-$S$ path integral formulation to devise a generalized route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature. Field-theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric understanding of the constraint, and they lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photon excitations on the diamond lattice. Finally, instanton considerations allow us to infer properties of the finite-temperature behavior in two dimensions.

We develop the symmetry classification of superconducting gap functions in electron bands that do not transform under the crystal point-group operations like the pure spin-$1/2$ states. The Bloch state bases in twofold degenerate bands with spin-orbit coupling are defined across the Brillouin zone in a way which satisfies the symmetry and continuity requirements. These bases are used to construct general multiband pairing Hamiltonians in centrosymmetric crystals. Focusing on single band pairing, four exceptional cases are identified in which the triplet gap function does not transform under the point-group operations as a pseudovector, with a significant impact on the nodal structure.

When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of “magic angles” where correlation effects can induce a host of exotic phases. Here we study a class of related models of $n$-layered graphene with an alternating relative twist angle $\pm \theta$ which exhibits magic angle flat bands coexisting with several Dirac dispersing bands at the moiré $K$ point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at different angles, revealing a remarkable hierarchy mathematically relating all these magic angles to the TBG case. For the trilayer case ($n=3$), we show that the sequence of magic angle is obtained by multiplying the bilayer magic angles by $\sqrt{2}$, whereas the quadrilayer case ($n=4$) has two sequences of magic angles obtained by multiplying the bilayer magic angles by the golden ratio $\phi =(\sqrt{5}+1)/2\approx 1.62$ and its inverse. We also show that for larger $n$, we can tune the angle to obtain several narrow (almost flat) bands simultaneously and that for $n\to \infty$, there is a continuum of magic angles for $\theta \lesssim 2^{\circ }$. Furthermore, we show that tuning several perfectly flat bands for a small number of layers is possible if the coupling between different layers is different. The setup proposed here can be readily achieved by repeatedly applying the “tear and stack” method without the need of any extra tuning of the twist angle and has the advantage that the first magic angle is always larger than the bilayer case.

Precise modeling of the magnetization dynamics of nanoparticles with finite-size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse-grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature-dependent susceptibilities, which is essential to model finite-size effects. Together with the zero-field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a ferrimagnetic ${\mathrm{Gd}}_{30}{\left(\mathrm{FeCo}\right)}_{70}$ particle with a diameter of 5 nm and a height of 10 nm under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Finally, we apply a 50-fs heat pulse with a maximum temperature of 1193 K to a ${\mathrm{Gd}}_{24}{\left(\mathrm{FeCo}\right)}_{76}$ particle of the same size to test the proposed model for all-optical switching (AOS). We observe switching with a ferromagneticlike state, which was identified to be the key for AOS in GdFeCo. Although the coarse-grained model in general shows remarkably good agreement with atomistic simulations, the computed switching probability is lower than expected. The magnetization trajectories seem to be too far away from equilibrium for ultrashort and very high heat pulses, which are typical for AOS. This leads to the conclusion that either the model needs higher-order corrections to accurately describe AOS, or that the two-spin model is not capable of describing deterministic AOS at all.

Semiclassical quantization rules compactly describe the energy dispersion of Landau levels, and are predictive of quantum oscillations in transport and thermodynamic quantities. Such rules—as formulated by Onsager, Lifshitz, and Roth—apply when the spin-orbit interaction dominates over the Zeeman interaction (or vice versa), but do not generally apply when the two interactions are comparable in strength. In this work, we present a generalized quantization rule which treats the spin-orbit and Zeeman interactions on equal footing, and therefore has wider applicability to spin-orbit-coupled materials lacking a spatial-inversion center, or having magnetic order. More generally, our rule describes the Landau quantization of any number of nearly degenerate energy bands, in any symmetry class. The resultant Landau level spectrum is generically nonequidistant but may contain spin (or pseudospin) degeneracies. To tune to such degeneracies in the absence of crystalline point-group symmetries, three real parameters are needed. We have exhaustively identified all symmetry classes of cyclotron orbits for which this number is reduced from three, thus establishing symmetry-enforced “noncrossing rules” for Landau levels. In particular, only one parameter is needed in the presence of spatial rotation or inversion; this single parameter may be the magnitude or orientation of the field. Signatures of single-parameter tunability include (i) a smooth crossover between period-doubled and period-undoubled quantum oscillations in the low-temperature Shubnikov–de Haas effect, as well as (ii) “magic-angle” magnetoresistance oscillations. We demonstrate the utility of our quantization rule, as well as the tunability of Landau level degeneracies, for the Rashba-Dresselhaus two-dimensional electron gas, subject to an arbitrarily oriented magnetic field.

We identify three-dimensional higher-order superconductors characterized by the coexistence of one-dimensional Majorana hinge states and gapless surface states. We show how such superconductors can be obtained starting from the model of a spinful quadrupolar semimetal with two orbitals and adding an $s$-wave superconducting pairing term. By considering all the possible $s$-wave pairings satisfying Fermi-Dirac statistics we obtain six different superconducting models. We find that for two of these models a flat band of hinge Majorana states coexist with surface states, and that these models have a nonvanishing quadrupolelike topological invariant. Two of the other models, in the presence of a Zeeman term, exhibit helical and dispersive hinge states localized only at two of the four hinges. We find that these states are protected by combinations of rotation and mirror symmetries, and that the pair of corners exhibiting hinge states switches upon changing the sign of the Zeeman term. Furthermore, we show that these states can be localized to a single hinge with suitable perturbations. The remaining two models retain gapless bulk and surface states that spectroscopically obscure any possible hinge states.

We study the effects of heterostrain on moiré bands in twisted bilayer graphene and bilayer transition metal dichalcogenide (TMD) systems. For bilayer graphene with a twist angle near $1^{\circ }$, we show that heterostrain significantly increases the energy separation between conduction and valence bands as well as the Dirac velocity at charge neutrality, which resolves several puzzles in scanning tunneling spectroscopy and quantum oscillation experiments at once. For bilayer TMD, we show that applying small heterostrain generally leads to flat moiré bands that are highly tunable.

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.

Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5 K into nonguided and guided modes is determined by direct spectral imaging. This enables measurement of the absolute coupling efficiency into the guided modes, the beta factor, directly, without assumptions on decay rates used previously. Notably, we found beta factors above 90% over a wide spectral range of 40 meV in the fast light regime, reaching a maximum of ($99\pm 1$)%. We measure the directional emission of the circularly polarized transitions in a magnetic field into counterpropagating guided modes, to deduce the mode circularity at the quantum dot sites. We find that points of high directionality, up to 97%, correlate with a reduced beta factor, consistent with their positions away from the mode field antinode. By comparison with calibrated finite-difference time-domain simulations, we use the emission energy, mode circularity, and beta factor to estimate the quantum dot position inside the photonic crystal waveguide unit cell.

Point-contact spectroscopy of several nonsuperconducting topological materials reveals a low-temperature phase transition that is characterized by a Bardeen-Cooper-Schrieffer type of criticality. We find such a behavior of differential conductance for topological surfaces of nonmagnetic and magnetic ${\mathrm{Pb}}_{1-y-x}{\mathrm{Sn}}_y{\mathrm{Mn}}_x\mathrm{Te}$. We examine a possible contribution from superconducting nanoparticles, and show to what extent our data are consistent with Brzezicki's et al. theory (arXiv:1812.02168), assigning the observations to a collective state adjacent to atomic steps at topological surfaces.

The entanglement entropy of a quantum critical system can provide universal numbers that depend on the geometry of the entangling bipartition. We calculate a universal number called $\kappa$, which arises when a quantum critical system is embedded on a two-dimensional torus and bipartitioned into two cylinders. In the limit when one of the cylinders is a thin slice through the torus, $\kappa$ parameterizes a divergence that occurs in the entanglement entropy subleading to the area law. Using large-scale Monte Carlo simulations of an Ising model in $2+1$ dimensions, we access the second Rényi entropy, and determine that, at the Wilson-Fisher (WF) fixed point, ${\kappa }_{2,\text{WF}}=0.0174\left(5\right)$. This result is significantly different from its value for the Gaussian fixed point, known to be ${\kappa }_{2,\text{Gaussian}}\approx 0.0227998$.

Dynamical phase transitions (DPTs), characterized by nonanalytic behaviors in time domain, extend the equilibrium phase transitions to far-from-equilibrium situations. It has been predicted that DPTs can be precisely identified by the discontinuities of the Pancharatnam geometric phase (PGP) during the time evolution. However, PGP always mixes with dynamical phase and the experimental observation of DPTs by PGP is still absent. Here, we theoretically present a novel scheme for eliminating the dynamical phase by taking advantage of chiral symmetry in the Su-Schrieffer-Heeger (SSH) model and experimentally observe DPTs by directly measuring PGP in a quenched topological nanomechanical lattice. Time-dependent topological structures of the SSH model are configured by eight strong-coupled high-quality-factor nanomechanical oscillators. By measuring the vibration phase and the normalized amplitude of the edge oscillator, we show a direct classical analog of DPTs. Furthermore, we experimentally demonstrate the robustness of DPTs against weak structure disorders, and numerically explore the relation between DPTs and the equilibrium phase boundary. This work not only establishes the quantitative method to identify DPTs, but also opens the door for studying nonequilibrium topological dynamics with a well-controlled nanomechanical system.

The impulsive generation of two-magnon modes in antiferromagnets by femtosecond optical pulses, so-called femto-nanomagnons, leads to coherent longitudinal oscillations of the antiferromagnetic order parameter that cannot be described by a thermodynamic Landau-Lifshitz approach. We argue that this dynamics is triggered as a result of a laser-induced modification of the exchange interaction. In order to describe the oscillations, we have formulated a quantum mechanical description in terms of magnon pair operators and coherent states. Such an approach allowed us to derive an effective macroscopic equation of motion for the temporal evolution of the antiferromagnetic order parameter. An implication of the latter is that the photoinduced spin dynamics represents a macroscopic entanglement of pairs of magnons with femtosecond period and nanometer wavelength. By performing magneto-optical pump-probe experiments with 10 femtosecond resolution in the cubic ${\mathrm{KNiF}}_3$ and the uniaxial ${\mathrm{K}}_2{\mathrm{NiF}}_4$ collinear Heisenberg antiferromagnets, we observed coherent oscillations at the frequency of 22 and 16 THz, respectively. The detected frequencies as a function of the temperature fit the two-magnon excitation up to the Néel point. The experimental signals are described as dynamics of magnetic linear dichroism due to longitudinal oscillations of the antiferromagnetic vector.

We modify the “floating crystal” trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential.

In order to explain the emergence of the anomalous pseudogap state and high-temperature superconductivity in the cuprates, intense research activity over three decades has focused on unraveling the connection between the various instabilities of the underdoped regime. In the high-temperature superconductor $\left({\mathrm{Ca}}_x{\mathrm{La}}_{1-x}\right)\left({\mathrm{Ba}}_{1.75-x}{\mathrm{La}}_{0.25+x}\right){\mathrm{Cu}}_3{\mathrm{O}}_y$ (CLBLCO) isovalent chemical substitution produces smooth changes to the ${\mathrm{CuO}}_2$ plane buckling and the Cu ii-to-apical-oxygen distance, allowing us to study the interdependence of charge density wave (CDW) order, superconductivity, and the pseudogap at constant hole doping in two adiabatically connected representations of the 123 cuprate structure. In this study, resonant soft x-ray scattering measurements reveal CDW correlations in CLBLCO and demonstrate a lack of correlation between $T_{\text{CDW}}$ and the pseudogap crossover temperature $T^{*}$. This result disfavors a scenario in which the opening of the pseudogap at $T^{*}$ results from fluctuating CDW correlations.