First-principles calculations show that electric fields applied to ferromagnets generate spin currents flowing perpendicularly to the electric field. Reduced symmetry in these ferromagnets enables a wide variety of such spin currents. However, the total spin current is approximately the sum of a magnetization-independent spin Hall current and an anisotropic spin anomalous Hall current. Intrinsic spin currents are not subject to dephasing, enabling their spin polarizations to be misaligned with the magnetization and allowing for the magnetization-independent spin Hall effect. The spin Hall conductivity and spin anomalous Hall conductivities of transition-metal ferromagnets are comparable to those found in heavy metals, opening different avenues for efficient spin current generation in spintronic devices.

Density functional theory is used to explore the possibility of inducing impurity band ferromagnetism in monolayers of semiconducting ${\mathrm{MoS}}_2$ by introducing holes into the narrow Mo $4d$ band that forms the top of the valence band. A large out-of-plane anisotropy is found for unpaired spins bound to the substitutional acceptor impurities V, Nb, and Ta that couple ferromagnetically for all but the shortest separations. Using the separation-dependent exchange interactions as the input to Monte Carlo calculations, we estimate ordering temperatures as a function of the impurity concentration. For about 9% of V impurities, Curie temperatures in excess of 160 K are predicted. The singlet formation at short separations that limits the ordering temperature is explained and we suggest how it can be circumvented.

Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low, i.e., area-law, entanglement, in contrast with the volume-law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area-law entanglement for any measurement rate, as seen in certain noninteracting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law, and critical “fixed points.” We also discuss a Floquet random unitary circuit, where the answers depend on the order of limits—one order of limits yields area-law entanglement for any nonzero measurement rate, whereas a different order of limits allows for an arealaw–volumelaw transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume-law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase.

A charge flow through a magnetic tunnel junction (MTJ) leads to the generation of a spin-polarized current which exerts a spin-transfer torque (STT) on the magnetization. When the density of applied direct current exceeds some critical value, the STT excites high-frequency magnetization precession in the “free” electrode of MTJ. Such precession gives rise to microwave output voltage and, furthermore, can be employed for spin pumping into adjacent normal metal or semiconductor. Here we describe theoretically the spin dynamics and charge transport in the CoFeB/MgO/CoFeB/Au tunneling heterostructure connected to a constant-current source. The magnetization dynamics in the free CoFeB layer with weak perpendicular anisotropy is calculated by numerical integration of the Landau-Lifshitz-Gilbert-Slonczewski equation accounting for both STT and voltage-controlled magnetic anisotropy (VCMA) associated with the CoFeB|MgO interface. It is shown that a large-angle magnetization precession can be generated in a certain range of relatively low current densities. Remarkably, it results from a dynamic spin reorientation transition caused by the joint impact of STT and VCMA. An oscillating spin current, which is pumped into the Au overlayer owing to the magnetization precession, is then evaluated together with the injected spin current. Considering both the driving spin-polarized charge current and the pumped spin current, we also describe the charge transport in the CoFeB/Au bilayer with the account of anomalous Hall effect and inverse spin Hall effect. An electric potential difference between the lateral sides of the CoFeB/Au bilayer is calculated as a function of distance from the CoFeB|MgO interface. It is found that this transverse voltage signal in Au is large enough for experimental detection, which indicates significant efficiency of the proposed current-driven spin injector.

Impressive advances in the field of molecular spintronics allow one to study electron transport through individual magnetic molecules embedded between metallic leads in the purely quantum regime of single electron tunneling. Besides fundamental interest, this experimental setup, in which a single molecule is manipulated by electronic means, provides the elementary units of possible forthcoming technological applications, ranging from spin valves to transistors and qubits for quantum information processing. Theoretically, while for weakly correlated molecular junctions established first-principles techniques do enable the system-specific description of transport phenomena, methods of similar power and flexibility are still lacking for junctions involving strongly correlated molecular nanomagnets. Here we propose an efficient scheme based on the ab initio construction of material-specific Hubbard models and on the master-equation formalism. We apply this approach to a representative case, the {${\mathrm{Ni}}_2$} molecular spin dimer, in the regime of weak molecule-electrode coupling, the one relevant for quantum-information applications. Our approach allows us to study in a realistic setting many-body effects such as current suppression and negative differential conductance. We think that this method has the potential for becoming a very useful tool for describing transport phenomena in strongly correlated molecules.

The widely studied hidden-order phase in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ exemplifies a broad class of emergent macroscopic states originating from $d$- and $f$-electron orbitals and their collective modes. This naturally has resulted in a focus on the associated elements (i.e., U and Ru), but recently it was discovered that electronic tuning on the more passive $s$ and $p$ orbitals fundamentally alters the electronic behavior and thus opens opportunities to disentangle the hidden-order conundrum. Here we present a detailed magnetoresistivity study of ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$, which focuses on two important aspects of this topic. First, we show that the anisotropy of the high field ordered states is preserved after hidden order is destroyed by Si $\to$ P chemical substitution, suggesting that this feature is mainly associated with the Kondo lattice, i.e., not hidden order itself. Second, Shubnikov–de Haas oscillations reveal that the observable parts of the Fermi surface topography are robust upon approaching the hidden-order phase boundary and the associated quasiparticle masses remain roughly constant. These observations place constraints on theories and prepare a path towards a resolution to the hidden-order problem.

We discuss the results of ${}^{75}\mathrm{As}$ nuclear quadrupole resonance (NQR) and muon spin relaxation measurements in $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A$ = Cs, Rb) iron-based superconductors. We point out that the crossover detected in the nuclear spin-lattice relaxation rate $1/T_1$ (around 150 K in ${\mathrm{RbFe}}_2{\mathrm{As}}_2$ and around 75 K in ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ ), from a high temperature nearly localized to a low temperature delocalized behavior, is associated with the onset of an inhomogeneous local charge distribution causing the broadening or even the splitting of the NQR spectra as well as an increase in the muon spin relaxation rate. We argue that this crossover, occurring at temperatures well above the phase transition to the nematic long-range order, is due to a charge disproportionation at the Fe sites induced by competing Hund's and Coulomb couplings. In ${\mathrm{RbFe}}_2{\mathrm{As}}_2$ around 35 K, far below that crossover temperature, we observe a peak in the NQR $1/T_1$ which is possibly associated with the critical slowing down of electronic nematic fluctuations on approaching the transition to the nematic long-range order.

In this paper we propose a special type of a tree tensor network that has the geometry of a comb—a one-dimensional (1D) backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher-dimensional objects with special limited interactions or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave function as a comb tensor network and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge.

We investigate the topological properties of a regular B-form single-stranded DNA (ssDNA) proximity-coupled by an $s$-wave superconductor, where the spin-orbit coupling and a Zeeman energy along with the helix axis are considered. It is found that a topological nontrivial superconductor phase can be formed under open boundary condition, in which the ssDNA molecule hosts a pair of Majorana zero modes. In addition both the magnitude and direction of the gate voltage on the topological superconducting ssDNA can adjust the Majorana zero modes. We also study the transport properties of the topological superconducting ssDNA, and find that the differential conductance shows a distinct peak structure at zero-bias voltage, which can be used to probe the existence of the Majorana zero modes in ssDNA in experiment.

The extended Falicov-Kimball model is analyzed exactly for finite temperatures in the limit of large dimensions. The onsite, as well as the intersite, density-density interactions represented by the coupling constants $U$ and $V$, respectively, are included in the model. Using the dynamical mean field theory formalism on the Bethe lattice we find rigorously the temperature-dependent density of states (DOS) at half-filling. At zero temperature ($T=0$), the system is ordered to form the checkerboard pattern and the DOS has the gap $\mathrm{\Delta }\left({\varepsilon }_F\right)>0$ at the Fermi level, if only $U\ne 0$ or $V\ne 0$. With an increase of $T$, the DOS evolves in various ways that depend both on $U$ and $V$. If $U<0$ or $U>2V$, two additional subbands develop inside the principal energy gap. They become wider with increasing $T$ and at a certain $U$- and $V$-dependent temperature $T_{\text{MI}}$ they join with each other at ${\varepsilon }_F$. Since above $T_{\text{MI}}$ the DOS is positive at ${\varepsilon }_F$, we interpret $T_{\text{MI}}$ as the transformation temperature from insulator to metal. It appears that $T_{\text{MI}}$ approaches the order-disorder phase transition temperature $T_{\text{OD}}$ for $\left|U\right|=2$ and $0<U\lesssim 2V$, but otherwise $T_{\text{MI}}$ is substantially lower than $T_{\text{OD}}$. Moreover, we show that if $V\lesssim 0.54$, then $T_{\text{MI}}=0$ at two quasi-quantum-critical points $U_{cr}^{\pm }$ (one positive and the other negative), whereas for $V\gtrsim 0.54$ there is only one negative $U_{cr}^{-}$. Having calculated the temperature-dependent DOS, we study thermodynamic properties of the system starting from its free energy $F$ and then we construct the phase diagrams in the variables $T$ and $U$ for a few values of $V$. Our calculations give that inclusion of the intersite coupling $V$ causes the finite-temperature phase diagrams to become asymmetric with respect to a change of sign of $U$. On these phase diagrams we detected stability regions of eight different kinds of ordered phases, where both charge order and antiferromagnetism coexist (five of them are insulating and three are conducting) and three different nonordered phases (two of them are insulating and one is conducting). Moreover, both continuous and discontinuous transitions between various phases were found.

Damage formation is investigated in GaAs implanted with 1 MeV Si ions to ion fluences from $3\times {10}^{12}$ to $5\times {10}^{15}{\mathrm{cm}}^{-2}$ at room temperature. Under the conditions applied, amorphization of the implanted layers does not occur. The weakly damaged layers are studied by applying different experimental techniques including Rutherford backscattering spectrometry in channeling configuration, x-ray diffraction, in situ curvature measurement, optical subgap spectroscopy, and transmission electron microscopy. The results are evaluated and quantitatively connected with each other. Damage formation is described as a function of the ion fluence using a common defect evolution model. Point defects and defect clusters have to be taken into account in the ion fluence range of main interest up to $2\times {10}^{15}{\mathrm{cm}}^{-2}$. Point defects contribute by a factor of about 8 more to both perpendicular strain and in-plane stress than defect clusters. When the concentration of point defects or the induced strain reaches a critical value, defect clusters form, which ensures that no further increase of perpendicular strain occurs. This reveals a clear driving force for cluster formation. The microstructure of the defect clusters cannot be determined from the results. ${\mathrm{As}}_3{\mathrm{Ga}}_2$ interstitial clusters are supposed. A remarkable decrease of the shear modulus of the implanted layers below the value of pristine GaAs by $\approx -35\%$ is observed. Surprisingly, the change of shear modulus already sets in at a very low damage level of a few percent.

The shot noise of the current $I$ through junctions to single trioxatriangulenium cations $\left({\mathrm{TOTA}}^{+}\right)$ on Au(111) is measured with a low-temperature scanning tunneling microscope using Au tips. The noise is significantly reduced compared to the Poisson noise power of $2eI$ and varies linearly with the junction conductance. The data are consistent with electron transmission through a single spin-degenerate transport channel and show that ${\mathrm{TOTA}}^{+}$ in a Au contact does not acquire an unpaired electron. Ab initio calculations reproduce the observations and show that the current involves the lowest unoccupied orbital of the molecule and tip states close to the Fermi level.

Recent microwave reflection measurements of Josephson junction chains have suggested the presence of nearly coherent collective charge oscillations deep in the insulating phase. Here we develop a qualitative understanding of such coherent charge modes by studying the local dynamical polarizability of the insulating phase of a finite length sine-Gordon model. By considering parameters near the noninteracting fermion limit where the charge operator dominantly couples to soliton-antisoliton pairs of the sine-Gordon model, we find that the local dynamical polarizability shows an array of sharp peaks in frequency representing coherent phase oscillations on top of an incoherent background. The strength of the coherent peaks relative to the incoherent background increases as a power law in frequency as well as exponentially as the Luttinger parameter approaches a critical value. The dynamical polarizability also clearly shows the insulating gap. We then compare the results in the high frequency limit to a perturbative estimate of phase-slip-induced decay of plasmons in the Josephson junction chain.

Complex oxides exhibit a variety of unusual physical properties, which can be used for designing novel electronic devices. Here we fabricate and study experimentally nanoscale superconductor/ferromagnet/ superconductor junctions with the high-$T_c$ cuprate superconductors ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ and the colossal magnetoresistive (CMR) manganite ferromagnets ${\mathrm{La}}_{2/3}{X}_{1/3}{\mathrm{MnO}}_{3+\delta }(X=\mathrm{Ca}\text{or}\mathrm{Sr})$. We demonstrate that in a broad temperature range the magnetization of a manganite nanoparticle, forming the junction interface, switches abruptly in a monodomain manner. The CMR phenomenon translates the magnetization loop into a hysteretic magnetoresistance loop. The latter facilitates a memory functionality of such a junction with just a single CMR ferromagnetic layer. The orientation of the magnetization (stored information) can be read out by simply measuring the junction resistance in a finite magnetic field. The CMR facilitates a large readout signal in a small applied field. We argue that such a simple single-layer CMR junction can operate as a memory cell both in the superconducting state at cryogenic temperatures and in the normal state up to room temperature.

Employing elastic and inelastic neutron scattering (INS) techniques, we report on the microscopic properties of the ferromagnetism in the dilute magnetic topological insulator ${\left({\mathrm{Bi}}_{0.95}{\mathrm{Mn}}_{0.05}\right)}_2{\mathrm{Te}}_3$. Neutron diffraction of polycrystalline samples shows the ferromagnetic (FM) ordering is long range within the basal plane, and mainly two dimensional (2D) in character with short-range correlations between layers below $T_{\mathrm{C}}\approx 13$ K. Remarkably, we observe gapped and collective magnetic excitations in this dilute magnetic system. The excitations appear typical of quasi-2D FM systems despite the severe broadening of short-wavelength magnons which is expected from the random spatial distribution of Mn atoms in the Bi planes. A detailed analysis of the INS provides the average values for exchange couplings which are consistent with reports of carrier-mediated interactions.

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang et al. [Phys. Rev. B 93, 224201 (2016)] and Goremykina et al. [Phys. Rev. Lett. 122, 040601 (2019)], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length and an internal decay length $\zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $\tilde{\zeta }$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $\tilde{\zeta }$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.

Refrigerators use a thermodynamic cycle to move thermal energy from a cold reservoir to a hot one. Implementing this operation principle with mesoscopic components has recently emerged as a promising strategy to control heat currents in micro and nanosystems for quantum technological applications. Here we combine concepts from stochastic and quantum thermodynamics with advanced methods of optimal control theory to develop a universal optimization scheme for such small-scale refrigerators. Covering both the classical and the quantum regime, our theoretical framework provides a rigorous procedure to determine the periodic driving protocols that maximize either cooling power or efficiency. As a main technical tool, we decompose the cooling cycle into two strokes, which can be optimized one by one. In the regimes of slow or fast driving, we show how this procedure can be simplified significantly by invoking suitable approximations. To demonstrate the practical viability of our scheme, we determine the exact optimal driving protocols for a quantum microcooler, which can be realized experimentally with current technology. Our work provides a powerful tool to develop optimal design strategies for engineered cooling devices and it creates a versatile framework for theoretical investigations exploring the fundamental performance limits of mesoscopic thermal machines.

We review the parity anomaly of the massless Dirac fermion in $2+1$ dimensions from the Hamiltonian, as opposed to the path integral, point of view. We have two main goals for this paper. First, we hope to make the parity anomaly more accessible to condensed matter physicists, who generally prefer to work within the Hamiltonian formalism. The parity anomaly plays an important role in modern condensed matter physics, as the massless Dirac fermion is the surface theory of the time-reversal invariant topological insulator (TI) in $3+1$ dimensions. Our second goal is to clarify the relation between the time-reversal symmetry of the massless Dirac fermion and the fractional charge of $\pm \frac{1}{2}$ (in units of $e$) that appears on the surface of the TI when a magnetic monopole is present in the bulk. To accomplish these goals we study the Dirac fermion in the Hamiltonian formalism using two different regularization schemes. One scheme is consistent with the time-reversal symmetry of the massless Dirac fermion, but leads to the aforementioned fractional charge. The second scheme does not lead to any fractionalization, but it does break time-reversal symmetry. For both regularization schemes we also compute the effective action $S_{\text{eff}}\left[A\right]$ that encodes the response of the Dirac fermion to a background electromagnetic field $A$. We find that the two effective actions differ by a Chern-Simons counterterm with fractional level equal to $\frac{1}{2}$, as is expected from path-integral treatments of the parity anomaly. Finally, we propose the study of a bosonic analog of the parity anomaly as a topic for future work.

We investigate the dynamics of Gaussian wave packets in multilayer black phosphorus (BP). Time-dependent average position and velocity are calculated analytically and numerically by using a continuum model and a method based on the split-operator technique, respectively. By analyzing the wave-packet trajectories with nonvanishing initial momentum along $y$ direction, we observed transient spatial oscillations due to the effect known as zitterbewegung (ZBW). We also demonstrated, based on the Heisenberg picture and by the calculation of the velocity operators, that the trembling motion along the $y$ direction at small times is unavoidable even for null initial momentum. We verified that the ZBW is directly related to the splitting of the wave packet into two parts moving with opposite velocities, as similar to graphene, and the linear dependence on $k_y$ in out-of-diagonal terms in the Hamiltonian. In addition for phosphorene systems, the two portions of the propagated wave packets have an asymmetric shape for unbalanced $\left({[1,0]}^T\right)$ and phased different $\left({[1,i]}^T\right)$ initial pseudospin components, playing an important role in the amplitude, frequency and duration time of the transient oscillations. Electrons in the vicinity of the Fermi energy traveling in $N$-layer phosphorene also exhibit qualitatively similar trembling motion and transient character as found in the monolayer case, except by the oscillation phase difference and final group velocity achieved after the transient behavior. As a consequence of the anisotropy on the $N$-layer BP energy bands, effective masses and group velocities along the $x$ and $y$ directions, the wave packet propagates nonuniformly along the different directions and deforms into an elliptical shape. By comparing our analytical results with those ones obtained by the split-operator technique, we verified a good qualitative and quantitative agreement between them, except for very larger values of wave vector and after long time steps.