We derive an expression for the rate of change of the energy of an interacting many-body system connected to macroscopic leads. We show that the energy variation is the sum of contributions from each different lead. Unlike the charge current each of these contributions can differ from the rate of change of the energy of the lead. We demonstrate that the discrepancy between the two is due to the direct exchange of energy among the considered lead and all other leads. We conclude that the microscopic mechanism behind it is virtual processes via the interacting central region. We also speculate on what are the implications of our findings in the calculation of the thermal conductance of an interacting system.

Monolayer graphene contains two inequivalent local minimum valleys, located at $K$ and $K^{\prime }$ in the Brillouin zone. There has been considerable interest in the use of these two valleys as a doublet for information processing. Herein we propose a method to resolve valley currents spatially, using only a weak magnetic field. Due to the trigonal warping of the valleys, a spatial offset appears in the guiding center coordinate, and is strongly enhanced due to collimation. This can be exploited to spatially separate valley states. Based on current experimental devices, spatial separation is possible for densities well within current experimental limits. Using numerical simulations, we demonstrate the spatial separation of the valley states.

We study the spin-wave dynamics in nanoscale antidot lattices based on Co/Pd multilayers with perpendicular magnetic anisotropy. Using time-resolved magneto-optical Kerr effect measurements we demonstrate that the variation of the antidot shape introduces significant change in the spin-wave spectra, especially in the lower frequency range. By employing micromagnetic simulations we show that additional peaks observed in the measured spectra are related to narrow shell regions around the antidots, where in-plane domain structures are formed. This is because the magnetic anisotropy in these regions is reduced due to the $\mathrm{G}{\mathrm{a}}^{+}$ ion irradiation during the focused ion beam milling process of the antidot fabrication. The results point at possibilities for exploitation of localized spin waves in out-of-plane magnetized thin films, which are easily tunable and suitable for magnonic applications.

We have studied the spin-orbit torque (SOT) in Pt/Co/Ir multilayers with three repeats of the unit structure. As the system exhibits oscillatory interlayer exchange coupling with varying Ir layer thickness, we compare the SOT of films when the Co layers are coupled ferromagnetically and antiferromagnetically. SOT is evaluated using current-induced shift of the anomalous Hall resistance hysteresis loops. A relatively thick Pt layer, serving as a seed layer to the multilayer, is used to generate spin current via the spin Hall effect. In the absence of antiferromagnetic coupling, the SOT is constant against the applied current density and the corresponding spin torque efficiency (i.e., the effective spin Hall angle) is $\sim 0.09$, in agreement with previous reports. In contrast, for films with antiferromagnetic coupling, the SOT increases with the applied current density and eventually saturates. The SOT at saturation is a factor of $\sim 15$ larger than that without the antiferromagnetic coupling. The spin torque efficiency is approximately five times larger if we assume the net total magnetization is reduced by a factor of 3 due to the antiferromagnetic coupling. Model calculations based on the Landau-Lifshitz-Gilbert equation show that the presence of antiferromagnetic coupling can increase the SOT but the degree of enhancement is limited, in this case, to a factor of 1.2–1.4. We thus consider there are other sources of SOT, possibly at the interfaces, which may account for the highly efficient SOT in the uncompensated synthetic antiferromagnet multilayers.

The advances in topological condensed matter physics enable the manipulation of classic waves in different ways, such as unidirectional propagation featuring the suppression of backscattering and the robustness against impurities and disorder, making it possible to endow classical phenomena with topological properties. Fano resonance, a widely spread and basic kind of resonance, features an asymmetric line shape with an ultrahigh quality factor $Q$ that usually requires delicate designs and precise fabrication. In this work, we achieve a robust Fano mechanical resonance with topological protection by engineering band inversion of two different vibrating symmetries of a pillared beam that gives rise to dark and bright edge modes. The Fano resonance results from the constructive and destructive interferences between topological dark and bright modes. It is further demonstrated that the Fano asymmetric shape of the transmission peak and its frequency are robust against random perturbations in the pillars’ position as long as the symmetry is conserved. If random perturbations break the symmetry and only band inversion is involved, the asymmetric line shape of the Fano resonance weakens until disappearing before the closure of the bulk band gap, since the excitation will couple all fundamental modes of the beam. The analysis of the robustness of Fano resonance originating from band inversion and symmetry protection reveals the nature of topological protection which can be applied to design topological high-$Q$ resonance in sensing application.

Based on first-principles calculations, we predict that the superconductor ${\mathrm{MgB}}_2$ with an ${\mathrm{AlB}}_2$-type centrosymmetric lattice hosts the so-called phononic topological Weyl nodal lines (PTWNLs) in its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the $-H–K–H$ direction within the three-dimensional Brillouin zone (BZ) and are always paired with opposite Berry phase. Their topologically nontrivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are unique, because they are located exactly at the high-symmetry boundary of the BZ protected by the mirror symmetry and, simultaneously, are straightly transverse to the whole BZ, differently from known classifications, including nodal rings, nodal chains or nets, and nodal loops. On the $\left(10\overline{1}0\right)$ crystal surface, the PTWNL-induced drumhead-like nontrivial surface states appear within the rectangular area confined by the projected lines of the PTWNLs. Moreover, when the mirror symmetry is broken, the double-degenerate PTWNLs are further lifted to form a pair of WPs with opposite chirality. Our results pave the way for future experimental study of topological phonons on ${\mathrm{MgB}}_2$ and highlight similar results in a series of isostructural ${\mathrm{AlB}}_2$-type metallic diborides.

Amperean pairing states, which represent a special case of pair-density-wave (PDW) states with members of the Cooper pair carrying equal momenta, offer a promising description of the pseudogap phase of the cuprates. It has been suggested that such states may develop in systems with current-current interactions; here we check this proposal by a fully self-consistent mean-field analysis. We find that previous non-self-consistent theories have correctly identified the essential physical properties of the Amperean states. However, we find that Amperean pairing states are not optimal within the class of PDW states and our lowest-energy solutions do not fit the pseudogap phenomenology. A model-independent interpretation of the Fermi arcs is presented as well.

Centrosymmetric (CS) nonmagnetic materials with hidden spin polarization induced by non-CS site symmetries and spin-orbit coupling are promising candidates for spintronic applications, in light of the zero net spin polarization and modulatable spin effects hidden in the local structures. There is, however, an open issue regarding the possible spin splitting induced by broken inversion symmetry at the sample surface. Here, we performed combinatorial experimental and theoretical studies on the potentially hidden spin polarization in $2H\text{−}\mathrm{MoT}{\mathrm{e}}_2$ and its mechanism. A large spin splitting of 236 meV and opposite spin polarizations up to 80% along out-of-plane direction ($z$ axis) in $K$ and $K^{\prime }$ valleys were observed from both spin- and angle-resolved photoemission spectroscopy (spin-ARPES) and density functional theory (DFT). We further found from the DFT calculations that a medium dipole field mimicked the surface symmetry breaking in ARPES measurements induces negligible variation of spin polarization. Our study demonstrates the existence of the intrinsic hidden spin effects in $2H\text{−}\mathrm{MoT}{\mathrm{e}}_2$ and opens a way of utilizing these effects in spintronic devices.

We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy in both the presence and absence of a quantizing magnetic field. We show that the anisotropy leads to doping dependences of thermopower and thermal conductivities which are different from those in isotropic Dirac materials. Additionally, we find that a quantizing magnetic field in such systems leads to an interesting magnetic field dependence of the longitudinal thermopower, resulting in unsaturated thermoelectric coefficients. Thus, the results presented here will serve as a guide to achieving high thermopower and a thermoelectric figure of merit in graphene-based materials, as well as organic conductors such as $\alpha$-BEDT-${\mathrm{TTF}}_2{\mathrm{I}}_3$.

We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux ${\mathrm{\Phi }}_B$ along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out phonon-induced $2k_F$-backscattering processes. We determine the zero-temperature phase diagram and identify a regime dominated by superconducting pairing of surface states. As an example, we consider the phase diagram of HgTe nanowires. We also determine the phonon-induced electrical resistivity, where we find a quadratic dependence on the flux deviation $\delta {\mathrm{\Phi }}_B$ from the nearest half-integer value.

Strong light-matter interaction realized by an individual nanoparticle with large coupling energy has attracted much interest due to its great importance in both fundamental quantum science research and potential applications in quantum information devices. We theoretically investigate the strong coupling between a plasmon-induced magnetic resonance supported by a single nanorod and excitons in a two-dimensional atomic crystal. We demonstrate a record of Rabi splitting over $220\mathrm{meV}$ at ambient condition with the involvement of only a few excitons. Importantly, a full quantum model is established to quantitatively describe the coherent and incoherent coupling dynamics of the hybrid modes. We reveal that the extra repopulation/depopulation of high-energy/low-energy polariton states induced by the incoherent coupling process is the microscopic origin of the subradiance/superradiance of the hybrid modes. In particular, large incoherent coupling strength can lead to not only the drastic population accumulation, but also the great enhancement of the scattering intensity in a high-energy polariton state, which is expected to hold promise for realizing polariton lasing without population inversion, as well as for other quantum optics applications.

The notion of spin accumulation and spin relaxation in the diffusive regime was introduced by Valet and Fert in 1993 to describe the current-perpendicular-to-plane (CPP) diffusive transport in metallic magnetic multilayers. This theory has been quite successful in explaining the giant magnetoresistance of magnetic multilayers in CPP geometry in the frequency range from DC to a few gigahertz. In this paper, we investigate the dynamic aspect of spin accumulation from the theoretical point of view when reaching the terahertz (THz) frequency range. The characteristic relaxation time of electron elastic scattering is typically in the femtosecond range. However, since spin accumulation results from a diffusion process involving a very large number of individual scattering events, the characteristic time of spin accumulation variation when the current and/or the magnetic configuration are varied can be significantly longer than that of the input signal, eventually reaching the picosecond range. In spintronic devices operating in the THz range such as those based on ferrimagnetic or antiferromagnetic materials, the spin accumulation amplitude and, correlatively, the device magnetoresistance can therefore depend on the actual device operating frequency. We investigate this question by extending the Valet and Fert theory in the time domain.

The amorphous iron-germanium system ($a-{\mathrm{Fe}}_x{\mathrm{Ge}}_{1-x}$) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of $a-{\mathrm{Fe}}_x{\mathrm{Ge}}_{1-x}$ is well explained by the Stoner model for Fe concentrations $x$ above the onset of magnetic order around $x=0.4$, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-$3d$ states sufficiently to polarize the electronic structure despite $\mathbf{k}$ being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity ${\rho }_{xy}^{\mathrm{AH}}$ relative to crystalline FeGe; this ${\rho }_{xy}^{\mathrm{AH}}$ is compared to density-functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied $\mathbf{k}$ states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of $a-{\mathrm{Fe}}_x{\mathrm{Ge}}_{1-x}$ ($0.38\le x\le 0.61$). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to $\mathbf{k}$ space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.

Topological phases of matter, sound, light, and vibrations have enabled brand new routes to direct and control signals at high fidelity. Chern insulators are known for outcompeting other reciprocal systems in terms of their robustness against crystal imperfections and defects. For sound waves we present the combination of a Chern insulator and a valley-Hall-based configuration and explore novel valley-Chern phases that enable both nonreciprocal band inversion processes and bandwidth broadening of valley-polarized one-way interface states. Interestingly, we find that a valley-Chern system made of two adjacent insulators of which one only breaks the time-reversal symmetry, enables entirely robust waveguiding appearing quantitatively equivalent to the classical Chern insulator. Beyond the rich physics presented, we foresee that our findings may stimulate new research in terms of acoustic waveguiding and control.

The quantum phase-coherent behavior of superconducting weak links (WLs) is often quenched in the finite voltage state, due to the heat dissipation and related thermal hysteresis. The latter can be reduced by improving heat evacuation and/or by lowering the critical current so a phase-dynamic regime is obtained, albeit over a narrow bias-current and temperature range. Here we demonstrate that an inductive shunt with well-chosen parameters introduces unexpected nonlinear dynamics that destabilize an otherwise stable fixed point in the dissipative branch. This leads to a nonhysteretic behavior with large voltage oscillations in intrinsically hysteretic WL-based micron-size superconducting quantum interference devices. A dynamic thermal model quantitatively describes our observations and further allows us to elaborate on the optimal shunting conditions.

Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have low energies. The low-energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry-protected topological order. This motivates us, as a simplest example, to study a lattice model of ${\mathbb{Z}}_n$-1 symmetry-protected topological (1-SPT) states in $3+1$ dimensions for even $n$. We write an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial self-statistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double-semion topological order for $m=1$ and toric code for $m=2$. The bulk ground-state wave-function amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry.

We present here results of an atomistic theory of electrons confined by metallic gates in a single layer of transition metal dichalcogenides. The electronic states are described by the tight-binding model and computed using a computational box with periodic boundary conditions including up to millions of atoms. The confinement is modelled with a parabolic confining potential over the computational box. With this methodology applied to ${\mathrm{MoS}}_{\text{2}}$, we find a twofold degenerate energy spectrum of electrons confined in the two nonequivalent $K$ valleys by the metallic gates as well as sixfold degenerate spectrum associated with $Q$ valleys. We compare the electron spectrum with the energy levels of electrons confined in GaAs/GaAlAs and in self-assembled quantum dots. We discuss the role of spin splitting and topological moments on the $K$ and $Q$ valley electronic states in quantum dots with sizes comparable to experiment.

Fundamental properties of the spin-noise signal formation in a quantum-dot microcavity are studied by measuring the angular characteristics of the scattered light intensity. A distributed Bragg reflector microcavity was used to enhance the light-matter interaction with an ensemble of $n$-doped (In,Ga)As/GaAs quantum dots, which allowed us to study subtle effects of coherent scattering at the quantum dot ensemble. Detecting the scattered light outside of the aperture of the transmitted light, we measured the basic electron spin properties, such as $g$ factor and spin dephasing time. Further, we investigated the influence of the microcavity on the scattering distribution and possibilities of signal amplification by additional resonant excitation.