We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition for invalidating the TUR for general nonequilibrium (classical and quantum) systems. We find that the first nonzero contribution to the TUR beyond equilibrium, given in terms of nonlinear transport coefficients, can be positive or negative, thus affirming or violating the TUR depending on the details of the system. We exemplify our results for noninteracting quantum systems by expressing the thermodynamic uncertainty relation in the language of the transmission function. We demonstrate that quantum coherent systems that do not follow a population Markovian master equation, e.g., by supporting high-order tunneling processes or relying on coherences, violate the TUR.

We theoretically analyze the hybrid Mie-exciton optical modes arising from the strong coupling of excitons in organic dyes or transition-metal dichalcogenides with the Mie resonances of high-index dielectric nanoparticles. Detailed analytic calculations show that silicon core-exciton shell nanoparticles are characterized by a richness of optical modes, which can be tuned through nanoparticle dimensions to produce large anticrossings in the visible or near infrared, comparable to those obtained in plexcitonics. The complex magnetic-excitonic nature of these modes is understood through spectral decomposition into Mie-coefficient contributions, complemented by electric and magnetic near-field profiles. In the frequency range of interest, absorptive losses in silicon are sufficiently low to allow observation of several periods of Rabi oscillations in strongly coupled emitter-particle architectures, as confirmed here by discontinuous Galerkin time-domain calculations for the electromagnetic field beat patterns. These results suggest that Mie resonances in high-index dielectrics are promising alternatives for plasmons in strong-coupling applications in nanophotonics, with the coupling of magnetic and electric modes potentially providing additional freedom for external control, whilst offering new possibilities for tailoring artificial optical magnetism.

The issue on the effect of interactions in topological states concerns not only interacting topological phases but also novel symmetry-breaking phases and phase transitions. Here we study the interaction effect on Majorana zero modes (MZMs) bound to a square vortex lattice in two-dimensional topological superconductors. Under the neutrality condition, where single-body hybridization between MZMs is prohibited by an emergent symmetry, a minimal square-lattice model for MZMs can be faithfully mapped to a quantum spin model, which has no sign problem in the world-line quantum Monte Carlo simulation. Guided by an insight from a further duality mapping, we demonstrate that the interaction induces a Majorana stripe state, a gapped state spontaneously breaking lattice translational and rotational symmetries, as opposed to the previously conjectured topological quantum criticality. Away from neutrality, a mean-field theory suggests a quantum critical point induced by hybridization.

Negative nonlinear electron-phonon coupling involving an infrared-active phonon mode can lead to an instability towards the formation of a polar lattice distortion with ferrielectric (FE) moments accompanied by an electronic charge-density wave (CDW). Analyzing a small model system in and out of thermal equilibrium, we investigate the FE-CDW and its melting dynamics following an ultrashort laser pulse that drives the ionic dipoles. We observe nonequilibrium coherent phonon amplitude mode oscillations that soften towards the transition to the normal phase. Our case study serves as a first step towards a microscopic understanding of quantum nonlinear phononics as a basis for nonequilibrium control in quantum materials.

In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>\frac{1}{2}$, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin $\frac{1}{2}$. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively, corresponding to chiral and antichiral edge states. Here, for simplicity, we concentrate on the case $F=\frac{3}{2}$ (which is suitable for ${}^6\mathrm{Li}$ or ${}^2\mathrm{H}$ atoms) but extension to higher spins (such as ${}^{40}\mathrm{K}$ whose ground-state spin is $F=\frac{9}{2}$) is straightforward.

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U\left(1\right)$ gauge theories. These “higher rank” tensor models are particularly intriguing due to the presence of quasiparticles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional $U\left(1\right)$ spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.

An approach previously developed for the calculation of transport coefficients via the Mott relations is applied to the calculation of finite temperature transport properties of disordered alloys—electrical resistivity and the electronic part of thermal conductivity. The coherent-potential approximation is used to treat chemical disorder as well as other sources of electron scattering, i.e., temperature induced magnetic moment fluctuations and lattice vibrations via the alloy analogy model. This approach, which treats all forms of disorder on an equal first-principles footing, is applied to the calculation of transport properties of a series of fcc concentrated solid solutions of the $3d$-transition metals Ni, Fe, Co, and Cr. For the nonmagnetic alloys ${\mathrm{Ni}}_{0.8}{\mathrm{Cr}}_{0.2}$ and ${\mathrm{Ni}}_{0.33}{\mathrm{Co}}_{0.33}{\mathrm{Cr}}_{0.3}$, the combined effects of chemical disorder and electron-lattice vibrations scattering result in a monotonic increase in the resistivity as a function of temperature from an already large, $T=0$, residual resistivity. For magnetic ${\mathrm{Ni}}_{0.5}{\mathrm{Co}}_{0.5},{\mathrm{Ni}}_{0.5}{\mathrm{Fe}}_{0.5}$, and ${\mathrm{Ni}}_{0.33}{\mathrm{Fe}}_{0.33}{\mathrm{Co}}_{0.33}$, the residual resistivity of which is small, additional electron scattering from temperature induced magnetic moment fluctuations results in a further rapid increase of the resistivity as a function of temperature. The electronic part of the thermal conductivity in nonmagnetic ${\mathrm{Ni}}_{0.8}{\mathrm{Cr}}_{0.2}$ and ${\mathrm{Ni}}_{0.33}{\mathrm{Co}}_{0.33}{\mathrm{Cr}}_{0.33}$ monotonically increases with temperature. This behavior is a result of the competition between a reduction in the conductivity due to electron-lattice vibrations scattering and temperature induced increase in the number of carriers. In the magnetic alloys, electron scattering from magnetic fluctuations leads to an initial rapid decrease in thermal conductivity until this is overcome by an increasing number of carriers at temperatures slightly below the Curie temperature. Similar to the resistivity above $T_C$, the electronic parts of the thermal conductivities are close to each other in all alloys studied.

We study the percolative superconducting transition as the density of randomly placed attractive centers grows in a host metal. Employing the Hubbard-Stratanovich transformation for the interaction and allowing for spatial, thermal fluctuations of the pairing field, we obtain real-space features of the transition from weak to strong coupling. Spectral and transport properties are studied in detail. BCS-BEC crossover is discussed in the context of site dilution of attractive centers.

It is a generally accepted fact that the unique dielectric properties of relaxor ferroelectrics are related to the formation of polar nanoregion (PNRs). Less well recognized is the corollary that, because they are polar and therefore lack inversion symmetry, PNRs are also piezoelectric at the nanoscale and can therefore behave as nanoresonators. Using the particular relaxor ferroelectric ${\mathrm{K}}_{1-x}{\mathrm{Li}}_x{\mathrm{TaO}}_3$ (KLT), we show that, when electrically excited into oscillation, these piezoelectric nanoresonators can drive macroscopic electromechanical resonances. Unexpectedly, however, pairs of coupled resonances corresponding to a particular type of oscillation are observed, with one of the resonance exhibiting a characteristic Fano-like line shape. The complex resonance spectra can be described equally well by two alternative but complementary models both involving two resonances coupled through a relaxation: a purely classical one based on two coupled damped harmonic oscillators and a semiclassical based on two discrete excitations coupled to each other through a continuum. Together, they provide complementary perspectives on the underlying physics of the system. Both reproduce the rapid evolution of the resonance spectrum across three wide temperature ranges, including a phase transition range. In the high-temperature range, the coupling between modes is due to the collective $\pi$ relaxation of the lithium ions within PNRs and, in the phase transition range, to “heterophase relaxation” of the surrounding lattice between its high-temperature cubic and low-temperature tetragonal phases, both coherent effects. The coupling is suppressed in the intermediate range of the collective $\pi /2$ relaxation of the lithium ions. Incidentally, the measured dielectric spectra are shown to bear a surprising but justifiable resemblance to the optical spectra of certain atomic vapors exhibiting electromagnetically induced transparency.

Unconventional superconductivity (SC) often develops in magnetic metals on the cusp of static antiferromagnetic (AFM) order where spin fluctuations are strong. This association is so compelling that many SC materials are labeled as unconventional by proximity to an ordered AFM state. The Cr-Ru alloy system possesses such a phase diagram [see Fig. 1(a)]. Here we use inelastic neutron scattering to show that spin fluctuations are present in a SC ${\mathrm{Cr}}_{0.8}{\mathrm{Ru}}_{0.2}$ alloy ($T_{\mathrm{c}}=1.35$ K). However, the neutron spin resonance, a possible signature of unconventional SC, is not observed. Instead, data indicate a spin gap of order $2\mathrm{\Delta }$ (the superconducting gap) and a suppression of magnetic spectral weight at energies well above $2\mathrm{\Delta }$. The suppression decreases the magnetic exchange energy, suggesting that low energy spin fluctuations oppose the formation of SC. In conjunction with other experimental evidence, a possible scenario is that conventional SC sits on the cusp of AFM order in Cr-Ru alloys.

In a flat Bloch band, the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground-state energy of lattice models with completely flat band structure in a ring geometry in the presence of an attractive Hubbard interaction. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum ${\mathrm{\Phi }}_0/2=hc/\left(2e\right)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. For some one-dimensional lattice models, we show analytically that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover, for the same one-dimensional lattice models, we construct an extensive number of exact conserved quantities. These conserved quantities are associated to the occupation of localized single quasiparticle states and force the single-particle propagator to vanish beyond a finite range. Our results suggest that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.

The order-order magnetic phase transition “helical antiferromagnet–ferromagnet” in the ${\text{Gd}}_x{\text{Y}}_{1-x}$ system have been examined by means of the specific heat vs temperature. The observed anomaly in the specific heat does not follow the ordinary second-order transition scenario but resembles the exotic second-and-a-half–order behavior, according to the Ehrenfest's classification of the phase transitions. Such a behavior was first predicted for the Lifshitz electronic topological transition. We suggest that the observed anomaly is likely a product of the underlying Lifshitz transition associated with the magnetic phase transition.

Scanning tunneling experiments on single crystals of superconducting ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$ have recently provided evidence for discrete energy levels inside vortices. Although predicted long ago, such levels are seldom resolved due to extrinsic (temperature, instrumentation) and intrinsic (quasiparticle scattering) limitations. We study a microscopic multiband model with parameters appropriate for ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$. We confirm the existence of well-separated bound states and show that the chemical disorder due to random occupation of the chalcogen site does not affect significantly the vortex-core electronic structure. We further analyze the vortex bound states by projecting the local density of states on angular-momentum eigenstates. A rather complex pattern of bound states emerges from the multiband and mixed electron-hole nature of the normal-state carriers. The character of the vortex states changes from hole-like with negative angular momentum at low energy to electron-like with positive angular momentum at higher energy within the superconducting gap. We show that disorder in the arrangement of vortices most likely explains the differences found experimentally when comparing different vortices.

Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement spectrum can be obtained, describing the excitation spectrum of the critical point separating the topological phase from the trivial state with the same symmetry. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry-breaking phase transitions. Recently, the framework of matrix product states for topological phases with Majorana fermions/parafermions has been established. Here we first generalize these fixed-point matrix product states with the zero correlation length to the more generic ground-state wave functions with a finite correlation length for the general one-dimensional interacting Majorana fermion/parafermion systems. Then we employ the previous method to decode quantum criticality to the interacting Majorana fermion/parafermion matrix product states. The obtained quantum critical spectra are described by the conformal field theories with central charge $c\le 1$, characterizing the quantum critical theories separating the fermionic/parafermionic topological phase from the trivial phases with the same symmetry.

We introduce a quench of the geometry of Landau level orbitals as a probe of nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that such geometric quenches induce coherent many-body dynamics of neutral degrees of freedom of FQH fluids. The simplest case of mass anisotropy quench can be experimentally implemented as a sudden tilt of the magnetic field, and the resulting dynamics reduces to the harmonic motion of the spin-2 “graviton” mode, i.e., the long-wavelength limit of the Girvin-MacDonald-Platzman magnetoroton. We derive an analytical description of the graviton dynamics using the bimetric theory of FQH states and find agreement with exact numerical simulations at short times. We show that certain types of geometric quenches excite higher-spin collective modes, thus establishing their existence in a microscopic model and motivating an extension of geometric theories of FQH states.

Half-metals have fully spin-polarized charge carriers at the Fermi surface. Such polarization usually occurs due to strong electron-electron correlations. Recently [Phys. Rev. Lett. 119, 107601 (2017)] we have demonstrated theoretically that adding (or removing) electrons to systems with Fermi surface nesting also stabilizes the half-metallic states even in the weak-coupling regime. In the absence of doping, the ground state of the system is a spin or charge density wave, formed by four nested bands. Each of these bands is characterized by charge (electron/hole) and spin (up/down) labels. Only two of these bands accumulate charge carriers introduced by doping, forming a half-metallic two-valley Fermi surface. Analysis demonstrates that two types of such half-metallicity can be stabilized. The first type corresponds to the full spin polarization of the electrons and holes at the Fermi surface. The second type, with antiparallel spins in electronlike and holelike valleys, is referred to as a “spin-valley half-metal” and corresponds to the complete polarization with respect to the spin-valley operator. We analyze spin and spin-valley currents and possible superconductivity in these systems. We show that spin or spin-valley currents can flow in half-metallic phases.

We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely, the Creutz lattice, where we investigate the role of local attractive interactions in the $U<0$ Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.

Motivated by the appearance of a “reflection symmetry” in transport experiments and the absence of statistical periodicity in relativistic quantum field theories, we propose a series of relativistic composite fermion theories for the compressible states appearing at filling fractions $\nu =1/2n$ in quantum Hall systems. These theories consist of electrically neutral Dirac fermions attached to $2n$ flux quanta via an emergent Chern-Simons gauge field. While not possessing an explicit particle-hole symmetry, these theories reproduce the known Jain sequence states proximate to $\nu =1/2n$, and we show that such states can be related by the observed reflection symmetry, at least at mean-field level. We further argue that the lowest Landau-level limit requires that the Dirac fermions be tuned to criticality, whether or not this symmetry extends to the compressible states themselves.

We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is taking into account the scalar field associated with the redistribution of charge due to deformations on the same footing as the pseudomagnetic field. Working with the Born approximation approach, we show analytically that even when a relatively small scalar field is considered, strong backscattering and enhancement of the valley-splitting effect could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can reverse its sign as the incident energy is increased. These behaviors are totally absent if the scalar field is neglected or screened. Interestingly, we find that there is a further possibility of controlling the valley scattering polarization purely by electrical means through the presence of external scalar fields in combination with strain fields. These results are supported by quantum dynamical simulations of electron wave packets. Results for the average trajectories of wave packets in locally strained graphene clearly show focusing and beam-splitting effects enhanced by the presence of the scalar field that could be of interest in the implementation of valleytronic devices.