Design and Simulation of Tunneling Diodes with 2D Insulators for Rectenna Switches.

Rectenna is the key component in radio-frequency circuits for receiving and converting electromagnetic waves into direct current. However, it is very challenging for the conventional semiconductor diode switches to rectify high-frequency signals for 6G telecommunication (>100 GHz), medical detection (>THz), and rectenna solar cells (optical frequencies). Such a major challenge can be resolved by replacing the conventional semiconductor diodes with tunneling diodes as the rectenna switches. In this work, metal-insulator-metal (MIM) tunneling diodes based on 2D insulating materials were designed, and their performance was evaluated using a comprehensive simulation approach which includes a density-function theory simulation of 2D insulator materials, the modeling of the electrical characteristics of tunneling diodes, and circuit simulation for rectifiers. It is found that novel 2D insulators such as monolayer TiO2 can be obtained by oxidizing sulfur-metal layered materials. The MIM diodes based on such insulators exhibit fast tunneling and excellent current rectifying properties. Such tunneling diodes effectively convert the received high-frequency electromagnetic waves into direct current.

Learning a compass spin model with neural network quantum states.

Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its capacity to describe complex magnetic orders with large unit cells has not been demonstrated, and its performance in a rugged energy landscape has been questioned. Here we apply restricted Boltzmann machines (RBMs) and stochastic gradient descent to seek the ground states of a compass spin model on the honeycomb lattice, which unifies the Kitaev model, Ising model and the quantum 120° model with a single tuning parameter. We report calculation results on the variational energy, order parameters and correlation functions. The phase diagram obtained is in good agreement with the predictions of tensor network ansatz, demonstrating the capacity of RBMs in learning the ground states of frustrated quantum spin Hamiltonians. The limitations of the calculation are discussed. A few strategies are outlined to address some of the challenges in machine learning frustrated quantum magnets.

Knots and Non-Hermitian Bloch Bands.

Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian (NH) Hamiltonians with separable bands. A Z_{2} knot invariant, the global biorthogonal Berry phase Q as the sum of the Wilson loop eigenphases, is proved to be equal to the permutation parity of the NH bands. We show the transition between two phases characterized by distinct knots occur through exceptional points and come in two types. We further develop an algorithm to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and propose a scheme to probe the knot structure via quantum quench. The theory and algorithm are demonstrated by model Hamiltonians that feature, for example, the Hopf link, the trefoil knot, the figure-8 knot, and the Whitehead link.

Topological Invariants for Quantum Quench Dynamics from Unitary Evolution.

Recent experiments began to explore the topological properties of quench dynamics, i.e., the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well-established theory for static band insulators or periodically driven systems, at present it is not clear whether, and how, topological invariants can be defined for a general quench of band insulators. Previous work solved a special case of this problem beautifully using Hopf mapping of two-band Hamiltonians in two dimensions. However, it only works for a topologically trivial initial state and is hard to generalize to multiband systems or other dimensions. Here we introduce the concept of loop unitary constructed from the unitary time-evolution operator and show its homotopy invariant fully characterizes the dynamical topology. For two-band systems in two dimensions, we prove that the invariant is precisely equal to the change in the Chern number across the quench, regardless of the initial state. We further show that the nontrivial dynamical topology manifests as hedgehog defects in the loop unitary and also as winding and linking of its eigenvectors along a curve where dynamical quantum phase transition occurs. This opens up a systematic route to classify and characterize quantum quench dynamics.

Dynamical Singularities of Floquet Higher-Order Topological Insulators.

We propose a versatile framework to dynamically generate Floquet higher-order topological insulators by multistep driving of topologically trivial Hamiltonians. Two analytically solvable examples are used to illustrate this procedure to yield Floquet quadrupole and octupole insulators with zero- and/or π-corner modes protected by mirror symmetries. Furthermore, we introduce dynamical topological invariants from the full unitary return map and show its phase bands contain Weyl singularities whose topological charges form dynamical multipole moments in the Brillouin zone. Combining them with the topological index of a Floquet Hamiltonian gives a pair of Z_{2} invariant ν_{0} and ν_{π} which fully characterize the higher-order topology and predict the appearance of zero- and π-corner modes. Our work establishes a systematic route to construct and characterize Floquet higher-order topological phases.

Exactly Solvable Points and Symmetry Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice.

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases, respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.

Weyl nodes in periodic structures of superconductors and spin-active materials.

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), in this paper we show that certain periodic structures of S and M can behave effectively as superconductors with pairs of point nodes, near which the low-energy excitations are Weyl fermions. A simple model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero-energy surface states in the form of open Fermi lines (Fermi arcs). As a second example, a lattice model with alternating layers of S and magnetic Z2 topological insulators is solved. The calculated spectrum confirms previous predictions of Weyl nodes based on the tunnelling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.This article is part of the theme issue 'Andreev bound states'.

Absence of Long-Range Order in a Triangular Spin System with Dipolar Interactions.

The antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that the next nearest neighbor interaction J_{2} enhances the frustration, and it leads to a spin liquid for J_{2}/J_{1}∈(0.08,0.15). In addition, a DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at a small dipole tilting angle θ∈[0,10°). In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, θ∈[0,54°), for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG), which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules.

Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State.

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J_{1}-J_{2} model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.

Spin-orbital exchange of strongly interacting fermions in the p band of a two-dimensional optical lattice.

Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here, we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the p band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the p band when the density fluctuations are suppressed, and show that it frustrates the development of long-range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the s band.

Counter-propagating edge modes and topological phases of a kicked quantum Hall system.

A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands.

Topological insulators are classified according to their symmetries. Discovery of them in electronic solids is thus restricted by orbital and crystalline symmetries available in nature. Synthetic quantum matter, such as the recent double-well optical lattices loaded with s and p orbital ultracold atoms, can exploit symmetries and interaction beyond natural conditions. Here we unveil a topological phase of interacting fermionic atoms on a two-leg ladder derived from the above experimental optical lattice by dimension reduction. The topological band structure originates from the staggered phases of sp orbital tunnelling, requiring neither spin-orbit coupling nor other known mechanisms like p-wave pairing, artificial gauge field or rotation. Upon crossing over to two-dimensional coupled ladders, the edge modes from individual ladder form a parity-protected flat band at zero energy. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators.

Quantum phases of quadrupolar Fermi gases in optical lattices.

We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

Bond order solid of two-dimensional dipolar fermions.

The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.

Topological phases of dipolar particles in elongated Wannier orbitals.

We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Because of the dipolar interaction and lattice confinement, a quantum dimer model emerges naturally as the effective theory describing the low-energy behaviors of these systems under well-controlled approximations. The desired hierarchy of interaction energy scales is achieved by controlling the anisotropy of the orbital dimers and the dipole moments of particles. Experimental realization and detection of various phases are discussed, as well as the possible relevance for quantum computation.

Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases.

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

Orbital order in Mott insulators of spinless p-band fermions.

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.

Dynamics of spin transport in voltage-biased Josephson junctions.

We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage characteristics of the spin current (IS) for superconductor-ferromagnet-superconductor Josephson junctions. The subharmonic gap structure of IS(V) is shown to be sensitive to the degree of spin mixing generated by the ferromagnetic interface, and exhibits a pronounced even-odd effect associated with spin transport during multiple Andreev reflection processes. For strong spin mixing both the magnitude and the direction of the dc spin current can be sensitively controlled by the bias voltage.

Excitations in correlated superfluids near a continuous transition into a supersolid.

We study a superfluid on a lattice close to a transition into a supersolid phase and show that a uniform superflow in the homogeneous superfluid can drive the roton gap to zero. This leads to supersolid order around the vortex core in the superfluid, with the size of the modulated pattern around the core being related to the bulk superfluid density and roton gap. We also study the electronic tunneling density of states for a uniform superconductor near a phase transition into a supersolid phase. Implications are considered for strongly correlated superconductors.

BCS-BEC crossover on the two-dimensional honeycomb lattice.

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.