We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that the leading singularities of correlation functions can be analyzed within an effective renormalizable model in which the kinetic energy of in-plane phonons and subleading geometrical nonlinearities in the expansion of the strain tensor are neglected. For membranes at zero temperature, governed by zero-point motion, the RG equations of the effective model provide a systematic derivation of logarithmic corrections to the bending rigidity and to the elastic Young modulus derived in earlier investigations. In the limit of a weakly applied external tension, the stress-strain relation at $T=0$ is anomalous: the linear Hooke's law is replaced with a singular law exhibiting logarithmic corrections. For small, but finite temperatures, we use techniques of finite-size scaling to derive general relations between the zero-temperature RG flow and scaling laws of thermodynamic quantities such as the thermal expansion coefficient $\alpha$, the entropy $S$, and the specific heat $C$. A combination of the scaling relations with an analysis of thermal fluctuations shows that, for small temperatures, the thermal expansion coefficient $\alpha$ is negative and logarithmically dependent on $T$, as predicted in earlier work. Although the requirement ${lim}_{T\to 0}\alpha =0$, expected from the third law of thermodynamics is formally satisfied, $\alpha$ is predicted to exhibit such a slow variation to remain practically constant down to unaccessible small temperatures.

Destroying superfluidity is a fundamental process and in fermionic superfluid such as ${}^3\mathrm{He}\text{−}B$ it splits Cooper pairs into thermal excitations, quasiparticles. At the lowest temperatures, a gas of these quasiparticle excitations is tenuous enough for the propagation to be ballistic. We describe here an exploitation of the ballistic quasiparticles as the “photons” to observe the local destruction of superfluid ${}^3\mathrm{He}\text{−}B$ by a mechanical resonator. We use a 5 by 5 pixel quasiparticle camera to image an emergence of quasiparticle excitations and a tangle of quantized vortices accompanying the pair-breaking. The detected quantum tangle is asymmetric around the mechanical resonator and is governed by the stability of vortices on the resonator surface. The vortex distribution shows that a conventional production of a quantum tangle via repetitive emission of vortex rings starts on the top surface of the generator and spreads around whole surface at high velocity when escaping vortex rings get retrapped by the moving resonator.

Functionals of the meta-generalized gradient approximation (MGGA) are widely used nowadays in chemistry and solid-state physics for the simulation of electronic systems such as molecules, solids, or surfaces. Due to their dependency on the kinetic energy density, they are in principle more accurate than GGA functionals for various properties (geometry, binding energy, electronic structure, etc.), while being nearly as fast since they are still of the semilocal form. Thus, when an accuracy better than GGA is required, one may consider using a MGGA instead of the much more costly hybrid functionals or methods such as the random-phase approximation or $GW$. In this work, the self-consistent implementation of MGGA functionals in augmented plane wave based methods is presented. Technical aspects of the implementation are discussed, and calculations of band gaps, lattice constants, and magnetic moments are presented in order to validate our implementation. To test the changes of the electron density due to a MGGA, the electric field gradient on transition-metal atoms is calculated.

The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised—the corner transfer matrix renormalization group (CTMRG) and variational uniform matrix product state (VUMPS) algorithm are the most common—but it remains unclear whether they always lead to the same results. In this paper, we identify a subclass of PEPS for which we can reformulate the contraction as a variational problem that is algorithm independent. We use this variational feature to assess and compare the accuracy of CTMRG and VUMPS contractions. Moreover, we devise a new variational contraction scheme, which we can extend to compute general $N$-point correlation functions.

The phonon dispersion of the organic semiconductor, rubrene, is experimentally measured by the inelastic x-ray scattering experiments performed at room temperature. In organic crystals, weak van der Waals interaction among the molecules increases the amplitude of the lattice vibration. Therefore, phonons are essential in organic crystals. However, there are few experimental reports on phonon dispersion in organic semiconductors and no reports on modern high-mobility organic semiconductors, which hampers the complete understanding of many phenomena in organic semiconductors. The dispersion of low-energy optical and acoustic phonon modes, including both intermolecular and intramolecular modes, is measured along the orthorhombic principal axes. Short-wavelength modes are expected to be affected by the anisotropic molecular shape, and the experimental result suggests that even the phonons having a wavelength of 140 Å are well modified, showing strong mixing of local and nonlocal phonon modes. This study provides a robust foundation for investigating organic semiconductors and understanding the lattice dynamics of highly anisotropic motifs.

The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs with on-site disorder. We determine the Thouless time from two main quantities: the spectral form factor and the power spectrum. Both quantities probe the long-range spectral correlations in the system and allow us to determine the Thouless time as the timescale after which the system is well described by random matrix theory. We find that the scaling of the Thouless time is consistent with the existence of a subdiffusive regime anticipating the localized phase. Furthermore, to reduce finite-size effects, we break energy conservation by introducing a Floquet version of the model and show that it hosts a similar subdiffusive regime.

Single-electron pumps based on tunable-barrier quantum dots are the most promising candidates for a direct realization of the unit ampere in the recently revised International System of Units (SI): they are simple to operate and show high precision at high operation frequencies. The current understanding of the residual transfer errors at low temperature is based on the evaluation of back-tunneling effects in the decay cascade model. This model predicts a strong dependence on the ratio of the time-dependent changes in the quantum dot energy and the tunneling barrier transparency. Here we employ a two-gate operation scheme to verify this prediction and demonstrate control of the back-tunneling error. We derive and experimentally verify a quantitative prediction for the error suppression, thereby confirming the basic assumptions of the back-tunneling (decay cascade) model. Furthermore, we demonstrate a controlled transition from the back-tunneling dominated regime into the thermal (sudden decoupling) error regime. The suppression of transfer errors by several orders of magnitude at zero magnetic field was additionally verified by a sub-ppm precision measurement.

The cubic spinel ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ has been receiving immense research interest because of its emergent phases and the interplay of spin, orbital, and lattice degrees of freedom. Despite the intense research, several fundamental questions are yet to be answered, such as the refinement of the crystal structure in the different magnetic and orbital ordered phases. Here, using high-resolution synchrotron powder diffraction on stoichiometric crystals of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ we resolved the long sought-after cubic to tetragonal transition at $\sim 65\mathrm{K}$, reducing the lattice symmetry to $I{4}_1/amd$. With further lowering the temperature, at $\sim 9\mathrm{K}$, the crystal structure becomes polar, hence the compound becomes multiferroic—likely reducing the space group to $I{4}_{1}md$. The elucidation of the lattice symmetry throughout different phases of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ provides a basis for the understanding this enigmatic system and also highlights the importance of structural deformation in correlated materials.

Simple cubic phosphorus exhibits superconductivity with a maximum $T_c$ of up to 12 K under pressure. The pressure dependence of $T_c$ cannot be consistently explained with a simple electron-phonon mechanism, which has stimulated investigations into the role of electronic correlations and plasmonic contributions. Here we solve the gap equation of density functional theory for superconductors using different electron-electron and electron-phonon contributions to the kernel. We find that the phonon contribution alone yields an overestimation of $T_c$, while the addition of the static electronic contribution results in an underestimation. Taking into account the full frequency dependence of the screened interaction, the one-shot $GW$ approximation predicts $T_c$ values in good agreement with the experiments in the pressure range appropriate for the cubic phase. We also explore the use of quasiparticle bands in the calculation of the electronic and phononic kernels, and show that this modification significantly improves $T_c$ in the high-pressure region.

We study delta-$T$ noise—excess charge noise at zero voltage but finite temperature bias—for weak tunneling in one-dimensional interacting systems. We show that the sign of the delta-$T$ noise is generically determined by the nature of the dominating tunneling process. More specifically, the sign is governed by the leading charge-tunneling operator's scaling dimension. We clarify the relation between the sign of delta-$T$ noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-$T$ noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Boson-like particles do not necessarily produce negative delta-$T$ noise. Importantly, the bosonic nature of particles generating the negative delta-$T$ is not necessarily intrinsic, but can be induced by the interactions. This, in particular, implies that negative delta-$T$ noise for tunneling between the edge states cannot serve as a smoking gun for detecting “intrinsic anyons”. We also establish a connection between the delta-$T$ noise and the temperature derivative of the Nyquist-Johnson (thermal) noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-$T$ noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both these setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons rather than single-electron tunneling. Our findings show that delta-$T$ noise can be used to probe the nature of collective excitations in interacting one-dimensional systems.

Fracton order features point excitations that either cannot move at all or are only allowed to move in a lower-dimensional submanifold of the whole system. In this paper, we generalize the $(2+1)$-dimensional $\left[\right(2+1\left)\mathrm{D}\right]$ U(1) Chern-Simons (CS) theory, a powerful tool in the study of $(2+1)\mathrm{D}$ topological orders, to include infinite gauge field components and find that they can describe interesting types of $(3+1)$-dimensional fracton order beyond what is known from exactly solvable models and tensor gauge theories. On the one hand, they can describe foliated fractonic systems for which increasing the system size requires insertion of nontrivial $(2+1)\mathrm{D}$ topological states. The CS formulation provides an easier approach to study the phase relation among foliated models. More interestingly, we find simple examples that lie beyond the foliation framework, characterized by 2D excitations of infinite order and irrational braiding statistics. This finding extends our realm of understanding of possible fracton phenomena.

We report the observation of cyclotron resonance (CR) transitions of holes in the magnetotransmission spectra of gallium-doped germanium at low temperatures, using intense, pulsed THz free-electron laser radiation with a photon energy lower than the ionization energy of the Ga dopants (11 meV). The THz radiation, in the range of 12–89 ${\mathrm{cm}}^{-1}$, both creates free holes through photoionization of Ga and induces the CR of these holes. For photon energies above the lowest energy internal Ga transition (55 ${\mathrm{cm}}^{-1}$), intradopant transitions are simultaneously observed with narrow CR peaks. For energies below 55 ${\mathrm{cm}}^{-1}$, with increasing THz radiation intensity first the lowest Landau level transitions of all heavy-hole and light-hole subbands appear. This marks the onset of photoionization, which is found to be more efficient for lower laser frequencies, consistent with field-ionization (Keldysh parameter $<<$ 1). For the highest laser intensities, the CR peaks of the heavy (light) holes shift to higher (lower) magnetic field, as a result of the increasing population of the higher-energy nonequidistant Landau levels, consistent with the effective-mass theory of the hole subbands in Ge.

With the aim of including small amplitude quantum nuclear dynamics in solid-state calculations, we derive a set of equations by applying Wick's theorem to the square of the Fröhlich Hamiltonian. These are noninteracting fermionic and bosonic Hamiltonians with terms up to quadratic order in the field operators. They depend on one another's density matrices and are therefore to be solved self-consistently. A Bogoliubov transformation is required to diagonalize both the fermionic and bosonic Hamiltonians since they represent noninteracting quantum field theories with an indefinite number of particles. The Bogoliubov transform for phonons is non-Hermitian in the general case, and the corresponding time evolution is nonunitary. Several sufficient conditions for ensuring that the bosonic eigenvalues are real are provided. The method was implemented in an all-electron code and shown to correctly predict the renormalization of the Kohn-Sham band gap of diamond and silicon due to the electron-phonon interaction. The theory also verifies that niobium and ${\mathrm{MgB}}_2$ are phonon-mediated superconductors and predicts the existence and magnitude of their superconducting gaps. Lastly, we confirm that copper is not a superconductor even at zero temperature.

Ferromagnetic ${\mathrm{SrRuO}}_3$ was proposed as a candidate material to exhibit an inverted magnon chirality due to a strong impact of spin-orbit coupling and Weyl fermions. By polarized inelastic neutron scattering under magnetic fields we determine the chirality of the ferromagnetic zone-center excitation as a function of temperature. Well in the ferromagnetic phase the excitation is perfectly chiral with the usual (right-handed) sign and only when the spontaneous magnetization is almost completely suppressed the chirality of the zone center magnetic excitations is reduced but does not change sign.

We numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regimes of finite-size systems into three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in systemwide many-body resonances; (ii) there is a substantial intermediate subregime where typical samples do have such resonances but the pair of eigenstates with the minimum spectral gap does not, so the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness subregime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain nonresonant and the system thus still appears MBL in most respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i) and the other subregimes are entirely in the thermal phase, even though they look localized in most respects, so are in the finite-size MBL regime.

We explore the interplay between randomness and magnetic frustration in the series of $S=\frac{1}{2}$ Heisenberg square-lattice compounds ${\mathrm{Sr}}_2{\mathrm{CuTe}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_6$. Substituting W for Te alters the magnetic interactions dramatically, from strongly nearest-neighbor to next-nearest-neighbor antiferromagnetic coupling. We perform neutron scattering measurements to probe the magnetic ground state and excitations over a range of $x$. We propose a bond-disorder model that reproduces ground states with only short-ranged spin correlations in the mixed compounds. The calculated neutron diffraction patterns and powder spectra agree well with the measured data and allow detailed predictions for future measurements. We conclude that quenched randomness plays the major role in defining the physics of ${\mathrm{Sr}}_2{\mathrm{CuTe}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_6$ with frustration being less significant.

Small-angle neutron scattering (SANS) measurements are performed on the ferromagnetic superconductor ${\mathrm{EuFe}}_2{\left({\mathrm{As}}_{0.8}{\mathrm{P}}_{0.2}\right)}_2$ ($T_{\mathrm{sc}}=22.5\mathrm{K}$) to probe the delicate interplay between ferromagnetism and superconductivity. A clear signature of large ferromagnetic domains is found below the ferromagnetic ordering temperature $T_{\mathrm{C}}=18.5\mathrm{K}$. In a small temperature interval of $\sim 1.5\mathrm{K}$ below $T_{\mathrm{C}}$, additional SANS signal is observed, of which the indirect Fourier transform reveals characteristic length scales in between $\sim 80\mathrm{nm}$ and $\sim 160\mathrm{nm}$. These nanometer-scaled domain structures are identified to result from an intermediate inhomogeneous Meissner effect denoted the domain Meissner state, which was recently observed on the surface of ${\mathrm{EuFe}}_2{\left({\mathrm{As}}_{0.79}{\mathrm{P}}_{0.21}\right)}_2$ crystals by means of magnetic force microscopy [V. S. Stolyarov et al., Sci. Adv. 4, 1061 (2018)], ascribed to the competition between ferromagnetism and superconductivity. Our measurements clearly render the domain Meissner state as a bulk phenomenon and provide a key solution to the mystery regarding the intriguing coexistence of strong ferromagnetism and bulk superconductivity in these compounds.

Discovering ferroic phase transitions and their consequential physical properties is at the core of condensed matter science due to rich physics and tremendous technological promises. ${\mathrm{BaCoSiO}}_4$, a chiral antiferromagnet, belongs to the tetrahedron-based chiral system, and exhibits diverse ferroic orders with coexisting chirality, polarity, trimerization, ferrorotational distortions, and magnetism. However, their mutual couplings remain to be explored. In this work, we used a comprehensive combination of several experimental tools—in situ x-ray, transmission electron microscopy, magnetization, and magnetoelectric measurements of single-crystalline ${\mathrm{BaCoSiO}}_4$—to investigate hierarchical phase transitions, their microscopic domain structures, and the resulting magnetoelectricity. We found that two different structural chiralities develop through distinct processes: global homochirality and local heterochirality induced by the ferrorotational distortions on top of existing polarization. In addition, magnetic chirality, with the simultaneous presence of net magnetic moment and magnetic toroidal moment, develops below 3.2 K due to the global chirality, which leads to magnetic field tunable toroidal magnetoelectricity. Thus, ${\mathrm{BaCoSiO}}_4$ exhibits uniquely all four types of ferroic orders and provides an avenue to explore, for example, tunable or dynamic coupling of multiple ferroic degrees of freedom.

A layered phosphide superconductor, $A{\mathrm{P}}_{2-x}{X}_x$ ($A$ = Zr and Hf; $X$ = Se and S), is expected to be a foothold for the quest of new superconductors. Here, we report direct experimental observation of the electronic structure of ${\mathrm{ZrP}}_{2-x}{\mathrm{Se}}_x$ ($x=0.55$, 0.60, 0.75, and 0.85), using high-resolution bulk-sensitive hard x-ray photoemission spectroscopy. Core-level spectra of P show two distinct components separated by an energy of 1.2 eV. These reveal that the P atoms at two crystallographic sites have different valence charges, $-1$ and $-3$, playing different chemical roles, and furthermore that the occupation ratio between them varies monotonically with $x$. We observed valence-band features at $-6.5, -4.0$, and $-1.4$ eV together with a clear Fermi edge. The consistency with first-principles calculation indicates that the electronic states at Fermi level are mainly ascribed to the Zr $4d$ band. Notably, a hump feature near the Fermi level shows an upward energy shift by 0.49 eV with decreasing $x$ from 0.85 to 0.55. The energy shifts of spectral features substantiate that replacing ${\mathrm{Se}}^{2-}$ with ${\mathrm{P}}^{3-}$ serves as hole doping, shedding light on the tunability of ${\mathrm{ZrP}}_{2-x}{\mathrm{Se}}_x$. These findings on the electronic structure establish an essential basis for understanding the superconductivity in the $A{\mathrm{P}}_{2-x}{X}_x$ system.

Strong spin-orbit coupling, the resulting large $g$ factor, and small effective mass make InAs an attractive material platform for inducing topological superconductivity. The surface Fermi level pinning in the conduction band enables highly transparent ohmic contact without excessive doping. We investigate electrostatically defined quantum point contacts (QPCs) in a deep-well InAs two-dimensional electron gas. Despite the 3.3% lattice mismatch between the InAs quantum well and the InP substrate, we report clean QPCs with up to eight pronounced quantized conductance plateaus at zero magnetic field. Source-drain dc bias spectroscopy reveals a harmonic confinement potential with a nearly 5 meV subband spacing. We find a many-body exchange interaction enhancement for the out-of-plane $g$ factor $|g_{\perp }^{*}|=27\pm 1$, whereas the in-plane $g$ factor is isotropic $|g_x^{*}|=|g_y^{*}|=12\pm 2$, close to the bulk value for InAs.