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Superconducting diode effects have recently attracted much attention for their potential applications in superconducting logic circuits. Several mechanisms such as magneto-chiral effects, finite momentum Cooper pairing, asymmetric edge currents have been proposed to give rise to a supercurrent diode effect in different materials. In this work, we establish the presence of a large intrinsic Josephson diode effect in a type-II Dirac semimetal $1T-PtTe_2$ facilitated by its helical spin-momentum locking and distinguish it from other extrinsic effects. The magnitude of the Josephson diode effect is shown to be directly correlated to the large second-harmonic component of the supercurrent that is induced by the significant contribution of the topological spin-momentum locked states that promote coherent Andreev processes in the junction. We denote such junctions, where the relative phase between the two harmonics corresponding to charge transfers of $2e$ and $4e$ can be tuned by a magnetic field, as second order ${\phi}_0$-junctions. The direct correspondence between the second harmonic supercurrent component and the diode effect in $1T-PtTe_2$ junctions makes topological semimetals with high transparency an ideal platform to study and implement the Josephson diode effect, while also enabling further research on higher order supercurrent transport in Josephson junctions.

The confluence between high-energy physics and condensed matter has produced groundbreaking results via unexpected connections between the two traditionally disparate areas. In this work, we elucidate additional connectivity between high-energy and condensed matter physics by examining the interplay between spin-orbit interactions and local symmetry-breaking magnetic order in the magnetotransport of thin-film magnetic semimetal FeRh. We show that the change in sign of the normalized longitudinal magnetoresistance observed as a function of increasing in-plane magnetic field results from changes in the Fermi surface morphology. We demonstrate that the geometric distortions in the Fermi surface morphology are more clearly understood via the presence of pseudogravitational fields in the low-energy theory. The pseudogravitational connection provides additional insights into the origins of a ubiquitous phenomenon observed in many common magnetic materials and points to an alternative methodology for understanding phenomena in locally-ordered materials with strong spin-orbit interactions., Comment: accepted version. 34+22pgs, 4+7 figures

Nonreciprocal superconducting devices have attracted growing interest in recent years as they potentially enable directional charge transport for applications in superconducting quantum circuits. Specifically, the superconducting diode effect has been explored in two-terminal devices that exhibit superconducting transport in one current direction while showing dissipative transport in the opposite direction. Here, we exploit multi-terminal Josephson junctions (MTJJs) to engineer magnetic-field-free nonreciprocity in multi-port networks. We show that when treated as a two-port electrical network, a three-terminal Josephson junction (JJ) with an asymmetric graphene region exhibits reconfigurable two-port nonreciprocity. We observe nonreciprocal (reciprocal) transport between superconducting terminals with broken (preserved) spatial mirror symmetry. We explain our observations by considering a circuit-network of JJs with different critical currents.

There is growing interest in using multi-terminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate complex superconducting mechanisms such as quartet and multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of coupled two-terminal resistively and capacitively shunted junctions (RCSJs). Under appropriate bias current, the model predicts that a current flowing between two diagonal terminals in a four-terminal geometry may be represented as a sinusoidal function of a weighted sum of the superconducting phases. We show that starting from a semi-classical model with diffusive current-phase relations, the MTJJ effectively emulates a general form of the expected current-phase relation for multiplet Cooper pairings. Our study therefore suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semi-classical circuit-network effects., Comment: 9 pages, 8 figures

Artificially engineered topological superconductivity has emerged as a viable route to create Majorana modes, exotic quasiparticles which have raised great expectations for storing and manipulating information in topological quantum computational schemes. The essential ingredients for their realization are spin non-degenerate metallic states proximitized to an s-wave superconductor. In this context, proximity-induced superconductivity in materials with a sizable spin-orbit coupling has been heavily investigated in recent years. Although there is convincing evidence that superconductivity may indeed be induced, it has been difficult to elucidate its topological nature. In this work, we systematically engineer an artificial topological superconductor by progressively introducing superconductivity (Nb) into metals with strong spin-orbital coupling (Pt) and 3D topological surface states (Bi2Te3). Through a longitudinal study of the character of superconducting vortices within s-wave superconducting Nb and proximity-coupled Nb/Pt and Nb/Bi2Te3, we detect the emergence of a zero-bias peak that is directly linked to the presence of topological surface states. Supported by a detailed theoretical model, our results are rationalized in terms of competing energy trends which are found to impose an upper limit to the size of the minigap separating Majorana and trivial modes, its size being ultimately linked to fundamental materials properties.

Antiferromagnet materials have recently gained renewed interest due to their possible use in spintronics technologies, where spin transport is the foundation of their functionalities. In that respect metallic antiferromagnets are of particular interest, since they enable complex interplays between electronic charge transport, spin, optical, and magnetization dynamics. Here we review phenomena where the metallic conductivity provides unique perspectives for the practical use and fundamental properties of antiferromagnetic materials., Comment: 18 pages, 10 figures

In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe$_{(1-x)}$Se$_x$., Comment: 16 pages including the supplementary materials. 4 figures

Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the winding number necessitates an augmentation of the winding number formulation to account for each intersection. In addition, we show that imposing additional mirror symmetries globally protect the nodal line-arc intersections and the corresponding Majorana cones.

Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain and loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. The recent generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is so far no established connection between a non-Hermitian topological invariant and the quantization of an observable. In this work, we show that no such relationship exists between the Chern number of non-Hermitian bands and the quantization of the Hall conductivity. Using field theoretical techniques, we calculate the longitudinal and Hall conductivities of a non-Hermitian Hamiltonian with a finite Chern number to explicitly demonstrate the physics of a non-quantized Hall conductivity despite an invariable Chern number. These results demonstrate that the Chern number does not provide a physically meaningful classification of non-Hermitian Hamiltonians.

Topological nodal superconductors possess gapless low energy excitations that are characterized by point or line nodal Fermi surfaces. In this work, using a coupled wire construction, we study topological nodal superconductors that have protected Dirac nodal points. In this construction, the low-energy electronic degrees of freedom are confined in a three dimensional array of wires, which emerge as pairing vortices of a microscopic superconducting system. The vortex array harbors an antiferromagnetic time-reversal and a mirror glide symmetry that protect the massless Dirac fermion in the single-body non-interacting limit. Within this model, we demonstrate exact-solvable many-body interactions that preserve the underlying symmetries and introduce a finite excitation energy gap. These gapping interactions support fractionalization and generically lead to non-trivial topological order. We also construct a special case of $N=16$ Dirac fermions where corresponding the gapping interaction leads to a trivial $E_8$ topological order that is closely related to the cancellation of the large gravitational anomaly., Comment: 25 pages, 9 figures

Recent demonstrations on manipulating antiferromagnetic (AF) order have triggered a growing interest in antiferromagnetic metal (AFM), and potential high-density spintronic applications demand further improvements in the anisotropic magnetoresistance (AMR). The antiferromagnetic semimetals (AFS) are newly discovered materials that possess massless Dirac fermions that are protected by the crystalline symmetries. In this material, a reorientation of the AF order may break the underlying symmetries and induce a finite energy gap. As such, the possible phase transition from the semimetallic to insulating phase gives us a choice for a wide range of resistance ensuring a large AMR. To further understand the robustness of the phase transition, we study thermal fluctuations of the AF order in AFS at a finite temperature. For macroscopic samples, we find that the thermal fluctuations effectively decrease the magnitude of the AF order by renormalizing the effective Hamiltonian. Our finding suggests that the insulating phase exhibits a gap narrowing at elevated temperatures, which leads to a substantial decrease in AMR. We also examine spatially correlated thermal fluctuations for microscopic samples by solving the microscopic Landau-Lifshitz-Gilbert equation finding a qualitative difference of the gap narrowing in the insulating phase. For both cases, the semimetallic phase shows a minimal change in its transmission spectrum illustrating the robustness of the symmetry protected states in AFS. Our finding may serve as a guideline for estimating and maximizing AMR of the AFS samples at elevated temperatures., Comment: 19 pages, 7 figures

Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the quantum anomalous Hall effect (QAHE) generated in the Dirac surface states of a 3D time-reversal-invariant topological insulator (TI) that is proximity-coupled to a metallic ferromagnet. By constructing a contact self-energy for the ferromagnet, we show that in addition to generating a mass gap in the surface spectrum, the ferromagnet can introduce a non-Hermitian broadening term, which can obscure the mass gap in the spectral function. We calculate the Hall conductivity for the effective non-Hermitian Hamiltonian describing the heterostructure and show that it is no longer quantized despite being classified as a Chern insulator based on non-Hermitian topological band theory. Our results indicate that the QAHE will be challenging to experimentally observe in ferromagnet-TI heterostructures due to the finite lifetime of quasi-particles at the interface., Comment: 7 pages, 3 figures. Supplement with 7 pages and 2 figures

With the continued scaling of microelectronic devices along with the growing demand of high-speed wireless telecommunications technologies, there is increasing need for high-frequency device modeling techniques that accurately capture the quantum mechanical nature of charge transport in nanoscale devices along with the dynamic fields that are generated. In an effort to fill this gap, we develop a simulation methodology that self-consistently couples AC non-equilibrium Green functions (NEGF) with the full solution of Maxwell's equations in the frequency domain. We apply this technique to simulate radiation from a quantum-confined, quarter-wave, monopole antenna where the length $L$ is equal to one quarter of the wavelength, $\lambda_0$. Classically, such an antenna would have a narrower, more directed radiation pattern compared to one with $L \ll \lambda_0$, but we find that a quantum quarter-wave antenna has no directivity gain compared to the classical solution. We observe that the quantized wave function within the antenna significantly alter the charge and current density distribution along the length of the wire, which in turn modifies the far-field radiation pattern from the antenna. These results show that high-frequency radiation from quantum systems can be markedly different from classical expectations. Our method, therefore, will enable accurate modeling of the next generation of high-speed nanoscale electronic devices., Comment: 12 pages, 6 figures

Unconventional superconductivity arising from the interplay between strong spin-orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the 3D topological insulator Bi2Se3. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi2Se3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov-Bohm flux.

An antiferromagnetic semimetal has been recently identified as a new member of topological semimetals that may host three-dimensional symmetry-protected Dirac fermions. A reorientation of the N\'{e}el vector may break the underlying symmetry and open a gap in the quasi-particle spectrum, inducing the (semi)metal-insulator transition. Here, we predict that such transition may be controlled by manipulating the chemical potential location of the material. We perform both analytical and numerical analysis on the thermodynamic potential of the model Hamiltonian and find that the gapped spectrum is preferred when the chemical potential is located at the Dirac point. As the chemical potential deviates from the Dirac point, the system shows a possible transition from the gapped to the gapless phase and switches the corresponding N\'{e}el vector configuration. We perform density functional theory calculations to verify our analysis using a realistic material and discuss a two terminal transport measurement as a possible route to identify the voltage induced switching of the N\'{e}el vector., Comment: 16 pages, 9 figures, the density functional theory calculation analysis (Section IV.D) has been modified

The realization of high-performance, small-footprint, on-chip inductors remains a challenge in radio-frequency and power microelectronics, where they perform vital energy transduction in filters and power converters. Modern planar inductors consist of metallic spirals that consume significant chip area, resulting in low inductance densities. We present a novel method for magnetic energy transduction that utilizes ferromagnetic islands (FIs) on the surface of a 3D time-reversal-invariant topological insulator (TI) to produce paradigmatically different inductors. Depending on the chemical potential, the FIs induce either an anomalous or quantum anomalous Hall effect in the topological surface states. These Hall effects direct current around the FIs, concentrating magnetic flux and producing a highly inductive device. Using a novel self-consistent simulation that couples AC non-equilibrium Green functions to fully electrodynamic solutions of Maxwell's equations, we demonstrate excellent inductance densities up to terahertz frequencies, thus harnessing the unique properties of topological materials for practical device applications., Comment: 13 pages, 3 figures, 1 table

A computational framework integrating optimization algorithms, parallel computing and plant physiology was developed to explore crop ideotype design. The backbone of the framework is a plant physiology model that accurately tracks water use (i.e. a plant hydraulic model) coupled with mass transport (CO2 exchange and transport), energy conversion (leaf temperature due to radiation, convection and mass transfer) and photosynthetic biochemistry of an adult maize plant. For a given trait configuration, soil parameters and hourly weather data, the model computes water use and photosynthetic output over the life of an adult maize plant. We coupled this validated model with a parallel, meta-heuristic optimization algorithm, specifically a genetic algorithm (GA), to identify trait sets (ideotypes) that resulted in desired water use behavior of the adult maize plant. We detail features of the model as well as the implementation details of the coupling with the optimization framework and deployment on high performance computing platforms. We illustrate a representative result of this framework by identifying maize ideotypes with optimized photosynthetic yields using weather and soil conditions corresponding to Davis, CA. Finally, we show how the framework can be used to identify broad ideotype trends that can inform breeding efforts. The developed presented tool has the potential to inform the development of future climate-resilient crops.

Nanoscience offers a unique opportunity to design modern materials from the bottom up, via low-cost, solution processed assembly of nanoscale building blocks. These systems promise electronic band structure engineering using not only the nanoscale structural modulation, but also the mesoscale spatial patterning, although experimental realization of the latter has been challenging. Here we design and fabricate a new type of artificial solid by stacking graphene on a self-assembled, nearly periodic array of nanospheres, and experimentally observe superlattice miniband effects. We find conductance dips at commensurate fillings of charge carriers per superlattice unit cell, which are key features of minibands that are induced by the quasi-periodic deformation of the graphene lattice. These dips become stronger when the lattice strain is larger. Using a tight-binding model, we simulate the effect of lattice deformation as a parameter affecting the inter-atomic hopping integral, and confirm the superlattice transport behavior. This 2D material-nanoparticle heterostructure enables facile band structure engineering via self-assembly, promising for large area electronics and optoelectronics applications.

We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped topological insulator(TI). Using the mean field theory, we show that Fulde-Ferrell(FF) pairing can be induced in the conventional superconductor by having inverse proximity effect(IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal band of the superconductor possesses a proximity induced spin-orbit coupling and magnetization. We find that the energetics of the different pairings are dependent on the coupling strength between the TI and the BCS superconductor and the thickness of the superconductor film. As the thickness of the superconductor film is increased, we find a crossover from the FF pairing to the BCS pairing phase. This is a consequence of the increased number of the superconducting bands, which favor the BCS pairing, implying that the FF phase can only be observed in the thin-film limit. In addition, we also propose transport experiments that show distinct signatures of the FF phase.

We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the Bogoliubov-de Gennes (BdG) symmetry classes of the Altland-Zimbauer classification of random matrices in $1$D, $2$D, and $3$D in the presence of discrete rotational invariance. Our analysis emphasizes the important role played by the angular momentum of the Cooper pairs in the system: for pairings of nonzero angular momentum, the rotation symmetry may be represented projectively, and a projective representation of rotation symmetry may have anomalous properties, including the anti-commutation with the time-reversal symmetry. In 1D and 3D, we show how an $n$-fold axis enhances the topological classification and give additional topological numbers; in 2D, we establish a relation between the Chern number (in class D and CI) and the eigenvalues of rotation symmetry at high-symmetry points. For each nontrivial class in 3D, we write down a minimal effective theory for the surface Majorana states., Comment: 21 pages, 5 figures

As a promising candidate system to realize topological superconductivity, the system of a 3D topological insulator (TI) grown on top of the s-wave superconductor has been extensively studied. To access the topological superconductivity experimentally, the 3D TI sample must be thin enough to allow for Cooper pair tunneling to the exposed surface of TI. The use of magnetically ordered dopants to break time-reversal symmetry may allow the surface of a TI to host Majorana fermion, which are believed to be a signature of topological superconductivity. In this work, we study a magnetically-doped thin film TI-superconductor hybrid systems. Considering the proximity induced order parameter in thin film of TI, we analyze the gap closing points of the Hamiltonian and draw the phase diagram as a function of relevant parameters: the hybridization gap, Zeeman energy, and chemical potential of the TI system. Our findings provide a useful guide in choosing relevant parameters to facilitate the observation of topological superconductivity in thin film TI-superconductor hybrid systems. In addition, we further perform numerical analysis on a TI proximity coupled to a s-wave superconductor and find that, due to the spin-momentum locked nature of the surface states in TI, the induced s-wave order parameter of the surface states persists even at large magnitude of the Zeeman energy.

Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.

The poor performance of copper interconnects at the nanometer scale calls for new material solutions for continued scaling of integrated circuits. We propose the use of three dimensional time-reversal-invariant topological insulators (TIs), which host backscattering-protected surface states, for this purpose. Using semiclassical methods, we demonstrate that nanoscale TI interconnects have a resistance 1-3 orders of magnitude lower than copper interconnects and graphene nanoribbons at the nanometer scale. We use the nonequilibrium Green function (NEGF) formalism to measure the change in conductance of nanoscale TI and metal interconnects caused by the presence of impurity disorder. We show that metal interconnects suffer a resistance increase, relative to the clean limit, in excess of 500% due to disorder while the TI's surface states increase less than 35% in the same regime., Comment: 4 pages, 3 figures

Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an s-wave superconductor in which we show that the application of a transverse uniform current in s-wave superconductor effectively cancels the momentum carried by FFLO states in doped WSM. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in s-wave superconductor that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSM. We analyze the topological phase transitions induced by nodal pair annihilation in non-equilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSM., Comment: 8 pages, 4 figures (5 pages, 2 figures for supplementary material)

The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an anomalous phase arising in the edge theory of a D-dimensional system under modular transformation, or modular anomaly, signals the presence of a (D+1)-D non-trivial bulk. In this work, we discuss the modular transformations of conformal field theories along a (2+1)-D and a (3+1)-D edge. Using both analytical and numerical methods, we show that chiral complex free fermions in (2+1)-D and (3+1)-D are modular invariant. However, we show in (3+1)-D that when the edge theory is coupled to a background U(1) gauge field this results in the presence of a modular anomaly that is the manifestation of a quantum Hall effect in a (4+1)-D bulk. Using the modular anomaly, we find that the edge theory of (4+1)-D insulator with spacetime inversion symmetry(P*T) and fermion number parity symmetry for each spin becomes modular invariant when 8 copies of the edges exist.