We study the stability and phenomenology of line-node semimetals in the presence of Coulomb interactions. Our results indicate a phase transition to a chiral insulating state that occurs at a finite interaction threshold, which we determine. We also compute the Landau levels for out-of-plane and in-plane magnetic fields in the symmetric and symmetry-broken phases. We find that the magnetic field couples to the chiral order parameter, implying that this degree of freedom can be manipulated in situ in experiments. Finally, we check the existence of edge states in the symmetry-broken phase. On the system's boundary, we note that the metallic “drum-head” states that exist in the symmetric phase are gapped out. However, the symmetry-broken phase permits topological defects in the macroscopic order parameter in the form of domain walls, which host metallic “interface states.” These consist of linelike gap-closings that occur on the two-dimensional interfaces.

In the ferromagnetic (FM) Weyl semimetal CeAlSi both space-inversion and time-reversal symmetries are broken. Our quantum oscillation (QO) data indicate that the FM ordering modifies the Fermi-surface topology and also leads to an unusual drop in the QO amplitude. In the FM phase, we find a pressure-induced suppression of the anomalous and the loop Hall effects. This cannot be explained based on the electronic band structure or magnetic structure, both of which are nearly pressure independent. Instead, we show that a simplified model describing the scattering of Weyl fermions off FM domain walls can potentially explain the observed topological features. Our study highlights the importance of domain walls for understanding transport in FM Weyl semimetals.

A chiral quantum Hall (QH) edge state placed in proximity to an $s$-wave superconductor experiences induced superconducting correlations. Recent experiments have observed the effect of proximity coupling in QH edge states through signatures of the mediating process of Andreev reflection. We present the microscopic theory behind this effect by modeling the system with a many-body Hamiltonian, consisting of an $s$-wave superconductor, subject to spin-orbit coupling and a magnetic field, which is coupled by electron tunneling to an integer QH edge state. By integrating out the superconductor we obtain an effective pairing Hamiltonian in the QH edge state. We clarify the qualitative appearance of nonlocal superconducting correlations in a chiral edge state and analytically predict the suppression of electron-hole conversion at low energies (Pauli blocking) and negative resistance as experimental signatures of Andreev reflection in this setup. In particular, we show how two surface phenomena of the superconductor, namely, Rashba spin-orbit coupling and a supercurrent due to the Meissner effect, are essential for the Andreev reflection. Our work provides a promising pathway to the realization of Majorana zero modes and their parafermionic generalizations.

We report on a neutron diffraction study of single-crystal ${\mathrm{CePtAl}}_3$ complemented by measurements of the specific heat under applied magnetic field. Below $T_{\mathrm{N}}\approx 3$ K, ${\mathrm{CePtAl}}_3$ develops incommensurate antiferromagnetic order with a single modulation vector $\mathbf{k}$ = $\left(0.67600\right)$. Residual magnetic scattering intensity above $T_{\mathrm{N}}$ and a broadening of the specific heat anomaly at $T_{\mathrm{N}}$ may be consistently described in terms of a Gaussian distribution of transition temperatures with a standard deviation $\sigma \approx 0.5$ K. The distribution of $T_{\mathrm{N}}$ may be attributed to the observation of occupational and positional disorder between the Pt and Al sites consistent with structural information inferred from neutron diffraction. Measurements under magnetic field reveal changes of the magnetic domain populations when the field is applied along the $\left[010\right]$ direction consistent with a transition from cycloidal to amplitude-modulated magnetic order $\sim$2.5 T.

Using a nonperturbative classical approach, we study the dynamics of a mobile particle interacting with an infinite one-dimensional (1D) chain of harmonic oscillators. This minimal system is an effective model for many 1D transport phenomena, such as molecular motion in nanotubes and ionic conduction through solid-state materials. As expected, coupling between the mobile particle and the chain induces dissipation of the mobile particle's energy. However, both numerical and analytic results demonstrate an unconventional nonmonotonic dependence of the drag on particle speed. In addition, when this system is subjected to a constant bias, it supports multiple steady-state drift velocities.

We demonstrate experimentally and theoretically the presence of the post-collision interaction (PCI) effect in sulfur ${\mathrm{KL}}_{2,3}{\mathrm{L}}_{2,3}$ Auger electron spectra measured in the gas-phase thiophene and in solid-state organic polymers: polythiophene (PT) and poly(3-hexylthiophene-2,5-diyl), commonly known as P3HT. PCI manifests itself through a distortion and a blueshift of the normal Auger S ${\mathrm{KL}}_{2,3}{\mathrm{L}}_{2,3}$ spectrum when S $1s$ ionization occurs close to the ionization threshold. Our investigation shows that the PCI-induced shift of the Auger spectra is stronger in the solid-state polymers than in the gas-phase organic molecule. Theoretical modeling within the framework of the eikonal approximation provides good agreement with the experimental observations. In a solid medium, two effects influence the interaction between the photoelectron and the Auger electron. In detail, stronger PCI in the polymers is attributed to the photoelectron scattering in the solid, which overcompensates the polarization screening of electron charges which causes a reduction of the interaction. Our paper demonstrates the general nature of the PCI effect occurring in different media.

In recent decades, the laws of thermodynamics have been pushed down to smaller and smaller scales, within the theoretical field of stochastic thermodynamics and state-of-the-art experiments performed on microfabricated mesoscopic systems. These measurements concern thermal properties of electrons, photons, and mesoscopic mechanical objects. Here we report on the measurements of thermal fluctuations of a single mechanical mode in equilibrium with a heat reservoir. The device under study is a nanomechanical beam with a first flexural mode resonating at $3.8\mathrm{MHz}$, cooled down to temperatures in the range from 100 to $400\mathrm{mK}$. The technique is constructed around a microwave optomechanical setup using a cryogenic high electron mobility transistor, and is based on two parametric amplifications implemented in series: an in-built optomechanical “blue detuned” pumping plus a traveling wave parametric amplifier stage. We demonstrate our ability to resolve energy fluctuations of the mechanical mode in real time up to the fastest relevant speed given by the mechanical relaxation rate. The energy probability distribution is then exponential, matching the expected Boltzmann distribution. The variance of fluctuations is found to be ${\left(k_{B}T\right)}^2$ with no free parameters. Our microwave detection floor is about three times the standard quantum limit at $6\mathrm{GHz}$; the resolution of our fastest acquisition tracks reached about $100\mathrm{phonons}$, and is directly related to the rather poor optomechanical coupling of the device ($g_0/2\pi \approx 0.5\mathrm{Hz}$). This result is deeply in the classical regime, but shall be extended to the quantum case in the future with systems presenting a much larger $g_0$ (up to $2\pi \times 250\mathrm{Hz}$), potentially reaching the resolution of a single mechanical quantum. We believe that it will open an experimental field, phonon-based quantum stochastic thermodynamics, with fundamental implications for quantum heat transport and macroscopic mechanical quantum coherence.

We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ [where spin symmetry is enlarged to $\mathrm{SU}\left(M\right)]$ study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of $T_c$ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in $T_c$ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.

We measure telegraph noise of current fluctuations in an electrostatically defined quantum dot in bilayer graphene by real-time detection of single electron tunneling with a capacitively coupled neighboring quantum dot. Suppression of the second and third cumulant (related to shot noise) in a tunable graphene quantum dot is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels. Furthermore, we use this method to investigate the first spin excited state, an essential prerequisite to measure spin relaxation.

We propose a class of geometric measures of entanglement for pure states by exploiting the matrix product state formalism. These measures are completely divested from the notion of separability and can be freely tuned as a function of the bond dimension to target states which vary in entanglement complexity. We first demonstrate its value in a toy spin-1 model where, unlike the conventional geometric entanglement, it successfully identifies the AKLT ground state. We then investigate the phase diagram of a Haldane chain with uniaxial and rhombic anisotropies, revealing that our measure can successfully detect all its phases; all of which are invisible to the conventional geometric entanglement. Finally we investigate the disordered spin-$1/2$ Heisenberg model, where we find that differences in our measure can be used as lucrative signatures of the ergodic-localized entanglement transition.

We report a comprehensive experimental investigation of the magnetic structure of the cycloidal phase in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which mediates the spin reorientation transition and establishes its magnetic phase diagram. In zero applied field, single-crystal neutron diffraction data confirm the scenario deduced from an earlier resonant x-ray scattering study: For $46.7\mathrm{K}$ $<T<$ 49.0 K the magnetic moments form a cycloid in the $a\text{−}b$ plane with a propagation wave vector of $(\delta ,0,1)$ with $\delta \simeq 0.025$ and an ordered moment of about $1{\mu }_{\mathrm{B}}$, with the eccentricity of the cycloid evolving with temperature. In an applied magnetic field applied parallel to the $b$ axis, the intensity of the $(\delta ,0,1)$ satellite peaks decreases continuously up to about ${\mu }_{0}H\simeq 5\mathrm{T}$, above which field the system becomes field polarized. Both the eccentricity of the cycloid and the wave vector increase with field, the latter suggesting an enhancement of the antisymmetric Dzyaloshinskii-Moriya interaction over the symmetric exchange interactions via magnetostriction effects. Transitions between the various low-temperature magnetic phases have been carefully mapped out using magnetometry and resistivity. The resulting phase diagram reveals that the cycloid phase exists in a temperature window that expands rapidly with increasing field, before transitioning to a polarized paramagnetic state at 5 T. High-field magnetoresistance measurements show that below $T\simeq 70\mathrm{K}$ the resistivity increases continuously with decreasing temperature, indicating the inherent insulating nature at low temperatures of our high-quality, untwinned, single crystals. We discuss our results with reference to previous reports of the magnetic phase diagram of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ that utilized samples which were more metallic and/or polydomain.

We devise a semiclassical model to describe the transport properties of low-dimensional fermionic lattices under the influence of external quantum stochastic noise. These systems behave as quantum stochastic resistors, where the bulk particle transport is diffusive and obeys the Ohm/Fick's law. Here, we extend previous exact studies beyond the one-dimensional limit to ladder geometries and explore different dephasing mechanisms that are relevant to different physical systems, from solid-state to cold atoms. We show how the semiclassical description is useful to explain the nontrivial dependence of the conductance of these systems on the chemical potential of the reservoirs. This description provides an intuitive and simpler interpretation of transport in quantum stochastic resistors in good quantitative agreement with the exact numerical solution. Moreover, we find that the conductance of quantum ladders is insensitive to the coherence of the dephasing process along the direction transverse to transport, despite the fact that the system reaches different stationary states.

The tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as the density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain, having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lead to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply hybrid-CCNN to discover and identify new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and seek insights into the phases by training multiple CCNN classifiers. A learned spatial weighting, introduced to the CCNNs in this work, enables discovery of spatial structure at scales beyond the filter size. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify a previously undetected boundary-ordered phase as well as motifs of more exotic ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.

In this work, we investigated polarization-resolved photoinduced carrier relaxation dynamics associated with charge ordering (CO) in geometrically frustrated organic conductors $\theta \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}M\mathrm{Zn}{\left(\mathrm{SCN}\right)}_4$ (M = Rb, Cs) as a function of temperature. In $\theta \text{−}\mathrm{Rb}$ (M = Rb), a polarization-dependent (anisotropic) and independent (isotropic) dynamics show similar temperature dependence. Moreover, discontinuous changes in transient reflectivity amplitude and an enhancement of a relaxation time are observed only upon heating near $T_{\mathrm{co}}=195\mathrm{K}$. This is associated with the first order phase transition due to long-range CO. However, in $\theta \text{−}\mathrm{Cs}$ (M = Cs) where the frustration is stronger than that in $\theta \text{−}\mathrm{Rb}$, as temperature decreases below $T_{\mathrm{nco}}\approx$ 150 K, the anisotropic component only slightly decreases while the isotropic one increases gradually without hysteresis. The behaviors indicate that CO is formed nonuniformly, that is, multiple short-range CO domains appear and are distributed with different orientations. Moreover, we found that the anisotropic dynamics with long-relaxation times suppress below $T_{\mathrm{s}}\approx$ 50 K, which is lower than the charge glass transition temperature of $T_{\mathrm{g}}\sim$ 100 K, whereas the isotropic dynamics grows monotonically. The distinct difference between them suggests the occurrence of a structural transition in which the lattice deforms randomly to match a glassy charge distribution due to the charge-lattice coupling.

Despite the exciting implications of the Kitaev spin Hamiltonian, finding and confirming the quantum spin-liquid state have proven incredibly difficult. Recently, the applicability of the model has been expanded through the development of a microscopic description of a spin-1 Kitaev interaction. Here we explore a candidate spin-1 honeycomb system, ${\mathrm{KNiAsO}}_4$, which meets many of the proposed criteria to generate such an interaction. Bulk measurements reveal an antiferromagnetic transition at $\sim 19$ K which is generally robust to applied magnetic fields. Neutron diffraction measurements show magnetic order with a $\mathbf{k}=(\frac{3}{2},0,0)$ ordering vector which results in the well-known “zigzag” magnetic structure thought to be adjacent to the spin-liquid ground state. Field-dependent diffraction shows that while the structure is robust, the field can tune the direction of the ordered moment. Inelastic neutron scattering experiments show a well-defined gapped spin-wave spectrum with no evidence of the continuum expected for fractionalized excitations. Modeling of the spin waves shows that the extended Kitaev spin Hamiltonian is are generally necessary to model the spectra and reproduce the observed magnetic order. First-principles calculations suggest that the substitution of Pd on the Ni sublattice may strengthen the Kitaev interactions while simultaneously weakening the exchange interactions thus pushing ${\mathrm{KNiAsO}}_4$ closer to the spin-liquid ground state.