The electronic circulator and its close relative the gyrator are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative nonreciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an Ohmically contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90°. In this limit, we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the ac wavelength. An experiment is proposed to achieve GHz-band gyration in millimeter (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realizing a Hall gyrator is also analyzed.

The study of non-Abelian Majorana zero modes advances our understanding of the fundamental physics in quantum matter and pushes the potential applications of such exotic states to topological quantum computation. It has been shown that in two-dimensional (2D) and 1D chiral superconductors, the isolated Majorana fermions obey non-Abelian statistics. However, Majorana modes in a $Z_2$ time-reversal-invariant (TRI) topological superconductor come in pairs due to Kramers’s theorem. Therefore, braiding operations in TRI superconductors always exchange two pairs of Majoranas. In this work, we show interestingly that, due to the protection of time-reversal symmetry, non-Abelian statistics can be obtained in 1D TRI topological superconductors and may have advantages in applications to topological quantum computation. Furthermore, we unveil an intriguing phenomenon in the Josephson effect, that the periodicity of Josephson currents depends on the fermion parity of the superconducting state. This effect provides direct measurements of the topological qubit states in such 1D TRI superconductors.

We study the nature of superfluid pairing in imbalanced Fermi mixtures in two spatial dimensions. We present evidence that the combined effect of Fermi surface mismatch and order parameter fluctuations of the superfluid condensate can lead to continuous quantum phase transitions from a normal Fermi mixture to an intermediate Sarma-Liu-Wilczek superfluid with two gapless Fermi surfaces—even when mean-field theory (incorrectly) predicts a first-order transition to a phase-separated “Bardeen-Cooper-Schrieffer plus excess fermions” ground state. We propose a mechanism for non-Fermi-liquid behavior from repeated scattering processes between the two Fermi surfaces and fluctuating Cooper pairs. Prospects for experimental observation with ultracold atoms are discussed.

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes that occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.

The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional $\epsilon$ expansion about the upper critical dimension $d_c=4$ and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (sub)diffusive model B with complex coefficients.

Recently, a programmable quantum annealing machine has been built that minimizes the cost function of hard optimization problems by, in principle, adiabatically quenching quantum fluctuations. Tests performed by different research teams have shown that, indeed, the machine seems to exploit quantum effects. However, experiments on a class of random-bond instances have not yet demonstrated an advantage over classical optimization algorithms on traditional computer hardware. Here, we present evidence as to why this might be the case. These engineered quantum annealing machines effectively operate coupled to a decohering thermal bath. Therefore, we study the finite-temperature critical behavior of the standard benchmark problem used to assess the computational capabilities of these complex machines. We simulate both random-bond Ising models and spin glasses with bimodal and Gaussian disorder on the D-Wave Chimera topology. Our results show that while the worst-case complexity of finding a ground state of an Ising spin glass on the Chimera graph is not polynomial, the finite-temperature phase space is likely rather simple because spin glasses on Chimera have only a zero-temperature transition. This means that benchmarking optimization methods using spin glasses on the Chimera graph might not be the best benchmark problems to test quantum speedup. We propose alternative benchmarks by embedding potentially harder problems on the Chimera topology. Finally, we also study the (reentrant) disorder-temperature phase diagram of the random-bond Ising model on the Chimera graph and show that a finite-temperature ferromagnetic phase is stable up to 19.85(15)% antiferromagnetic bonds. Beyond this threshold, the system only displays a zero-temperature spin-glass phase. Our results therefore show that a careful design of the hardware architecture and benchmark problems is key when building quantum annealing machines.

We calculate the dynamical conductivity $\sigma (\omega )$ and the bosonic (pair) spectral function $P(\omega )$ from quantum Monte Carlo simulations across clean and disorder-driven superconductor-insulator transitions (SITs). We identify characteristic energy scales in the superconducting and insulating phases that vanish at the transition due to enhanced quantum fluctuations, despite the persistence of a robust fermionic gap across the SIT. Disorder leads to enhanced absorption in $\sigma (\omega )$ at low frequencies compared to the SIT in a clean system. Disorder also expands the quantum critical region, due to a change in the universality class, with an underlying $T=0$ critical point with a universal low-frequency conductivity ${\sigma }^{*}\simeq 0.5(4e^2/h)$.

Using ultrafast optical spectroscopy, we show that polaronic behavior associated with interfacial antiferromagnetic order is likely the origin of tunable magnetotransport upon switching the ferroelectric polarity in a ${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{MnO}}_3/{\mathrm{BiFeO}}_3$ (LCMO/BFO) heterostructure. This is revealed through the difference in dynamic spectral weight transfer between LCMO and LCMO/BFO at low temperatures, which indicates that transport in LCMO/BFO is polaronic in nature. This polaronic feature in LCMO/BFO decreases in relatively high magnetic fields due to the increased spin alignment, while no discernible change is found in the LCMO film at low temperatures. These results thus shed new light on the intrinsic mechanisms governing magnetoelectric coupling in this heterostructure, potentially offering a new route to enhancing multiferroic functionality.

We study a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. One example of such a transition is the recently proposed many-body localization-delocalization transition, in which transport coefficients vanish at a critical temperature with no singularities in thermodynamic observables. Describing this purely dynamical quantum criticality is technically challenging as understanding the finite-temperature dynamics necessarily requires averaging over a large number of matrix elements between many-body eigenstates. Here, we develop a real-space renormalization group method for excited states that allows us to overcome this challenge in a large class of models. We characterize a specific example: the 1 D disordered transverse-field Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the real-space renormalization group method for excited states we find a finite-temperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the low-frequency heat conductivity and in the long-time (dynamic) spin correlation function. The latter is a consequence of an up-down spin symmetry that results in the appearance of an Edwards-Anderson-like order parameter in one of the localized phases.

We use femtosecond optical spectroscopy to systematically measure the primary energy relaxation rate ${\Gamma }_1$ of photoexcited carriers in cuprate and pnictide superconductors. We find that ${\Gamma }_1$ increases monotonically with increased negative strain in the crystallographic $a$ axis. Generally, the Bardeen-Shockley deformation potential theorem and, specifically, pressure-induced Raman shifts reported in the literature suggest that increased negative strain enhances electron-phonon coupling, which implies that the observed direct correspondence between $a$ and ${\Gamma }_1$ is consistent with the canonical assignment of ${\Gamma }_1$ to the electron-phonon interaction. The well-known nonmonotonic dependence of the superconducting critical temperature $T_c$ on the $a$-axis strain is also reflected in a systematic dependence $T_c$ on ${\Gamma }_1$, with a distinct maximum at intermediate values ($\sim 16{\mathrm{ps}}^{-1}$ at room temperature). The empirical nonmonotonic systematic variation of $T_c$ with the strength of the electron-phonon interaction provides us with unique insight into the role of electron-phonon interaction in relation to the mechanism of high-$T_c$ superconductivity as a crossover phenomenon.

The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of $D(S_3)$. This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.

Disordered packings of soft grains are fragile mechanical systems that lose rigidity upon lowering the external pressure toward zero. At zero pressure, we find that any infinitesimal strain impulse propagates initially as a nonlinear solitary wave progressively attenuated by disorder. We demonstrate that the particle fluctuations generated by the solitary-wave decay can be viewed as a granular analogue of temperature. Their presence is manifested by two emergent macroscopic properties absent in the unperturbed granular packing: a finite pressure that scales with the injected energy (akin to a granular temperature) and an anomalous viscosity that arises even when the microscopic mechanisms of energy dissipation are negligible. Consistent with the interpretation of this state as a fluidlike thermalized state, the shear modulus remains zero. Further, we follow in detail the attenuation of the initial solitary wave, identifying two distinct regimes—an initial exponential decay, followed by a longer power-law decay—and suggest simple models to explain these two regimes.

The electron transport properties of atomically thin semiconductors such as ${\mathrm{MoS}}_2$ have attracted significant recent scrutiny and controversy. In this work, the scattering mechanisms responsible for limiting the mobility of single-layer semiconductors are evaluated. The roles of individual scattering rates are tracked as the two-dimensional electron gas density is varied over orders of magnitude at various temperatures. From a comparative study of the individual scattering mechanisms, we conclude that all current reported values of mobilities in atomically thin transition-metal dichalcogenide semiconductors are limited by ionized impurity scattering. When the charged impurity densities are reduced, remote optical phonon scattering will determine the ceiling of the highest mobilities attainable in these ultrathin materials at room temperature. The intrinsic mobilities will be accessible only in clean suspended layers, as is also the case for graphene. Based on the study, we identify the best choices for surrounding dielectrics that will help attain the highest mobilities.

Magnetite, ${\mathrm{Fe}}_3{\mathrm{O}}_4$, is the first magnetic material discovered and utilized by mankind in Ancient Greece, yet it still attracts attention due to its puzzling properties. This is largely due to the quest for a full and coherent understanding of the Verwey transition that occurs at $T_V=124\mathrm{K}$ and is associated with a drop of electric conductivity and a complex structural phase transition. A recent detailed analysis of the structure, based on single crystal diffraction, suggests that the electron localization pattern contains linear three-Fe-site units, the so-called trimerons. Here, we show that whatever the electron localization pattern is, it partially survives up to room temperature as short-range correlations in the high-temperature cubic phase, easily discernible by diffuse scattering. Additionally, ab initio electronic structure calculations reveal that characteristic features in these diffuse scattering patterns can be correlated with the Fermi surface topology.

The topologically protected conducting state is expected to exist on the entire surface of three-dimensional topological insulators (TIs). Using concurrent measurements of the local and nonlocal conduction, we provide experimental evidence for the topological robustness of the surface-conducting states of bulk-insulating ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ crystalline flakes. The detailed investigation of local and nonlocal charge conductance on the top surfaces, combining with the comprehensive numerical simulation, reveals that the charge current is widely distributed over the entire surface of a TI. Our findings show evidence of the presence of the topologically protected conducting state at the side wall with irregularly stacked edges between the top and bottom surfaces. This study provides a reliable means of accurately characterizing the topological surface states with inherent nonlocal surface-dominant conducting channels in a TI.

We report results of the magnetization and ac susceptibility measurements down to very low fields on a single crystal of the perovskite manganite, $\mathrm{La}{}_{0.82}\mathrm{Ca}{}_{0.18}\mathrm{MnO}{}_3$. This composition falls in the intriguing ferromagnetic insulator region of the manganite phase diagram. In contrast to earlier beliefs, our investigations reveal that magnetically (and in every other sense), this is a single-phase system with a ferromagnetic ordering temperature of around 170 K. However, this ferromagnetic state is magnetically frustrated, and the system exhibits pronounced glassy dynamics below 90 K. Based on measured dynamical properties, we propose that this quasi-long-ranged ferromagnetic phase, and the associated superspin glass behavior, is the true magnetic state of the system, rather than being a macroscopic mixture of ferromagnetic and antiferromagnetic phases, as often suggested. Our results provide an understanding of the quantum phase transition from an antiferromagnetic insulator to a ferromagnetic metal via this ferromagnetic insulating state as a function of $x$ in $\mathrm{La}{}_{1-x}\mathrm{Ca}{}_x\mathrm{MnO}{}_3$, in terms of the possible formation of magnetic polarons.

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green’s observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional $p+ip$ superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the ${\mathbb{Z}}_3$ Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-$2e$ Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane’s construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a $p+ip$ superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.

On the basis of first-principles calculations, we show that the M-type hexaferrite ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$ exhibits frustrated antiferroelectricity associated with its trigonal bipyramidal ${\mathrm{Fe}}^{3+}$ sites. The ferroelectric state of ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$, reachable by applying an external electric field to the antiferroelectric state, can be made stable at room temperature by appropriate element substitution or strain engineering. Thus, M-type hexaferrite, as a new type of multiferoic with coexistence of antiferroelectricity and ferrimagnetism, provides a basis for studying the phenomenon of frustrated antiferroelectricity and realizing multiple-state memory devices.

We derive an effective Hamiltonian that describes the dynamics of electrons in the conduction band of monolayer transition metal dichalcogenides (TMDC) in the presence of perpendicular electric and magnetic fields. We discuss in detail both the intrinsic and the Bychkov-Rashba spin-orbit coupling induced by an external electric field. We point out interesting differences in the spin-split conduction band between different TMDC compounds. An important consequence of the strong intrinsic spin-orbit coupling is an effective out-of-plane $g$ factor for the electrons that differs from the free-electron $g$ factor $g\simeq 2$. We identify a new term in the Hamiltonian of the Bychkov-Rashba spin-orbit coupling that does not exist in III-V semiconductors. Using first-principles calculations, we give estimates of the various parameters appearing in the theory. Finally, we consider quantum dots formed in TMDC materials and derive an effective Hamiltonian that allows us to calculate the magnetic field dependence of the bound states in the quantum dots. We find that all states are both valley and spin split, which suggests that these quantum dots could be used as valley-spin filters. We explore the possibility of using spin and valley states in TMDCs as quantum bits, and conclude that, due to the relatively strong intrinsic spin-orbit splitting in the conduction band, the most realistic option appears to be a combined spin-valley (Kramers) qubit at low magnetic fields.

We present a combined experimental and theoretical study of the proximity effect in an atomic-scale controlled junction between two different superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb nanocrystal with an energy gap ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$, connected to a crystalline atomic monolayer of lead with ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$. Using in situ scanning tunneling spectroscopy, we probe the local density of states of this hybrid system both in space and in energy, at temperatures below and above the critical temperature of the superconducting monolayer. Direct and inverse proximity effects are revealed with high resolution. Our observations are precisely explained with the help of a self-consistent solution of the Usadel equations. In particular, our results demonstrate that in the vicinity of the Pb islands, the Pb monolayer locally develops a finite proximity-induced superconducting order parameter, well above its own bulk critical temperature. This leads to a giant proximity effect where the superconducting correlations penetrate inside the monolayer a distance much larger than in a nonsuperconducting metal.