Helical Topological Superconducting Pairing at Finite Excitation Energies.

We propose helical topological superconductivity away from the Fermi surface in three-dimensional time-reversal-symmetric odd-parity multiband superconductors. In these systems, pairing between electrons originating from different bands is responsible for the corresponding topological phase transition. Consequently, a pair of helical topological Dirac surface states emerges at finite excitation energies. These helical Dirac surface states are tunable in energy by chemical potential and strength of band splitting. They are protected by time-reversal symmetry combined with crystalline twofold rotation symmetry. We suggest concrete materials in which this phenomenon could be observed.

Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials.

Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.

Nonequilibrium Fractional Josephson Effect.

Josephson tunnel junctions exhibit a supercurrent typically proportional to the sine of the superconducting phase difference ϕ. In general, a term proportional to cos(ϕ) is also present, alongside microscopic electronic retardation effects. We show that voltage pulses sharply varying in time prompt a significant impact of the cos(ϕ) term. Its interplay with the sin(ϕ) term results in a nonequilibrium fractional Josephson effect (NFJE) ∼sin(ϕ/2) in the presence of bound states close to zero frequency. Our microscopic analysis reveals that the interference of nonequilibrium virtual quasiparticle excitations is responsible for this phenomenon. We also analyze this phenomenon for topological Josephson junctions with Majorana bound states. Remarkably, the NFJE is independent of the ground state fermion parity unlike its equilibrium counterpart.

Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields.

The non-Hermitian skin effect is a unique phenomenon in which an extensive number of eigenstates are localized at the boundaries of a non-Hermitian system. Recent studies show that the non-Hermitian skin effect is significantly suppressed by magnetic fields. In contrast, we demonstrate that the second-order skin effect (SOSE) is robust and can even be enhanced by magnetic fields. Remarkably, SOSE can also be induced by magnetic fields from a trivial non-Hermitian system that does not experience any skin effect at zero field. These properties are intimately related to to the persistence and emergence of topological line gaps in the complex energy spectrum in the presence of magnetic fields. Moreover, we show that a magnetic field can drive a non-Hermitian system from a hybrid skin effect, where the first-order skin effect and SOSE coexist, to pure SOSE. Our results describe a qualitatively new magnetic field behavior of the non-Hermitian skin effect.

Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading.

We propose a novel spatially inhomogeneous setup for revealing quench-induced fractionalized excitations in entanglement dynamics. In this quench-probe setting, the region undergoing a quantum quench is tunnel coupled to a static region, the probe. Subsequently, the time-dependent entanglement signatures of a tunable subset of excitations propagating to the probe are monitored by energy selectivity. We exemplify the power of this generic approach by identifying a unique dynamical signature associated with the presence of an isolated Majorana zero mode in the postquench Hamiltonian. In this case excitations emitted from the topological part of the system give rise to a fractionalized jump of log(2)/2 in the entanglement entropy of the probe. This dynamical effect is highly sensitive to the localized nature of the Majorana zero mode, but does not require the preparation of a topological initial state.

Microscopic Theory of the Current-Voltage Characteristics of Josephson Tunnel Junctions.

Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.

Electron-Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator.

We have experimentally investigated the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We have found that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a nonmonotonic differential resistance of narrow channels. We have shown that the observed initial increase in resistance can be attributed to electron-hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron-hole scattering in the transport properties of topological insulators.

Higher-Order Fabry-Pérot Interferometer from Topological Hinge States.

We propose an intrinsic three-dimensional Fabry-Pérot type interferometer, coined "higher-order interferometer," that is based on the chiral hinge states of second-order topological insulators and cannot be mapped to an equivalent two-dimensional setting because of higher-order topological obstructions. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple frequencies depending on the field strength and direction in a unique fashion. Our novel interferometer thus provides feasible and robust magnetotransport signatures for hinge states of higher-order topological insulators.

Resistivity Exponents in 3D Dirac Semimetals From Electron-Electron Interaction.

We study the resistivity of three-dimensional semimetals with linear dispersion in the presence of on-site electron-electron interaction. The well-known quadratic temperature dependence of the resistivity of conventional metals is turned into an unusual T^{6} behavior. An analogous change affects the thermal transport, preserving the linearity in T of the ratio between thermal and electrical conductivities. These results hold from weak coupling up to the nonperturbative region of the Mott transition. Our findings yield a natural explanation for the hitherto not understood large exponents characterizing the temperature dependence of transport experiments on various topological semimetals.

Super-Resonant Transport of Topological Surface States Subjected to In-Plane Magnetic Fields.

Magnetic oscillations of Dirac surface states of topological insulators are typically expected to be associated with the formation of Landau levels or the Aharonov-Bohm effect. We instead study the conductance of Dirac surface states subjected to an in-plane magnetic field in the presence of a barrier potential. Strikingly, we find that, in the case of large barrier potentials, the surface states exhibit pronounced oscillations in the conductance when varying the magnetic field, in the absence of Landau levels or the Aharonov-Bohm effect. These novel magnetic oscillations are attributed to the emergence of super-resonant transport by tuning the magnetic field, in which many propagating modes cross the barrier with perfect transmission. In the case of small and moderate barrier potentials, we identify a positive magnetoconductance due to the increase of the Fermi surface by tilting the surface Dirac cone. Moreover, we show that for weak magnetic fields, the conductance displays a shifted sinusoidal dependence on the field direction with period π and phase shift determined by the tilting direction with respect to the field direction. Our predictions can be applied to various topological insulators, such as HgTe and Bi_{2}Se_{3}, and provide important insights into exploring and understanding exotic magnetotransport properties of topological surface states.

Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime.

Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting, which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultrastrong magnetic fields. We develop a scattering approach to study quantum-Hall-superconductor-quantum-Hall junctions formed by a two-dimensional time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit, where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, the junction width, the length, and the doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.

Semiclassical Conservation of Spin and Large Transverse Spin Current in Dirac Systems.

In Dirac materials, the low-energy excitations obey the relativistic Dirac equation. This dependence implies that electrons are exposed to strong spin-orbit coupling. Hence, real spin conservation is believed to be violated in Dirac materials. We show that this point of view needs to be refined in the semiclassical picture which applies to the case of doped Dirac materials (away from the nodal point in the spectrum). We derive a novel type of Boltzmann equation for these systems if they are brought slightly out of equilibrium. Remarkably, spin-momentum locking is softened and a generalized spin conservation law can be formulated. The most striking observable consequence of our theory is a large transverse spin current in a nearly ballistic transport regime.

Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering.

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.

Chirality Josephson Current Due to a Novel Quantum Anomaly in Inversion-Asymmetric Weyl Semimetals.

We study Josephson junctions based on inversion-asymmetric but time-reversal symmetric Weyl semimetals under the influence of Zeeman fields. We find that, due to distinct spin textures, the Weyl nodes of opposite chirality respond differently to an external magnetic field. Remarkably, a Zeeman field perpendicular to the junction direction results in a phase shift of opposite sign in the current-phase relations of opposite chirality. This leads to a finite chirality Josephson current (CJC) even in the absence of a phase difference across the junction. This feature could allow for applications in chiralitytronics. In the long junction and zero temperature limit, the CJC embodies a novel quantum anomaly of Goldstone bosons at π phase difference which is associated with a Z_{2} symmetry at low energies. It can be detected experimentally via an anomalous Fraunhofer pattern.

Coexisting edge states and gapless bulk in topological states of matter.

We consider two-dimensional systems in which edge states coexist with a gapless bulk. Such systems may be constructed, for example, by coupling a gapped two-dimensional state of matter that carries edge states to a gapless two-dimensional system in which the spectrum is composed of a number of Dirac cones. We find that, in the absence of disorder, the edge states could be protected even when the two systems are coupled, due to momentum and energy conservation. We distinguish between weak and strong edge states by the level of their mixing with the bulk. In the presence of disorder, the edge states may be stabilized when the bulk is localized or destabilized when the bulk is metallic. We analyze the conditions under which these two cases occur. Finally, we propose a concrete physical realization for one of our models based on bilayer Hg(Cd)Te quantum wells.

Parity measurement in topological Josephson junctions.

We study the properties of a topological Josephson junction made of both edges of a two-dimensional topological insulator. We show that, due to fermion parity pumping across the bulk, the global parity of the junction has a clear signature in the periodicity and critical value of the Josephson current. In particular, we find that the periodicity with the flux changes from 4π in a junction with an even number of quasiparticles to 2π in the odd sector. In the case of long junctions, we exhibit a rigorous mathematical connection between the spectrum of Andreev bound states and the fermion parity anomaly, through bosonization. Additionally, we discuss the rather quantitative effects of Coulomb interactions on the Josephson current.

Plasmons due to the interplay of Dirac and Schrödinger fermions.

We study the interplay between Dirac and Schrödinger fermions in the polarization properties of a two-dimensional electron gas (2DEG). Specifically, we analyze the low-energy sector of narrow-gap semiconductors described by a two-band Kane model. In the context of quantum spin Hall insulators, particularly, in Hg(Cd)Te quantum wells, this model is named the Bernevig-Hughes-Zhang model. Interestingly, it describes electrons with intermediate properties between Dirac and Schrödinger fermions. We calculate the dynamical dielectric function of such a model at zero temperature within random phase approximation. Surprisingly, plasmon resonances are found in the intrinsic (undoped) limit, whereas they are absent-in that limit-in graphene as well as ordinary 2DEGs. Additionally, we demonstrate that the optical conductivity offers a quantitative way to identify the topological phase of Hg(Cd)Te quantum wells from a bulk measurement.

Time reversal symmetric topological exciton condensate in bilayer HgTe quantum wells.

We investigate a bilayer system of critical HgTe quantum wells, each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic interlayer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological Z2 invariant of the resulting mean-field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state, coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, due to its multiband nature, the present bilayer model exhibits a nontrivial interplay between spontaneous symmetry breaking and topology: Depending on which symmetry the condensate order parameter spontaneously picks in combined orbital and spin space, stable minima in the free energy corresponding to both trivial and nontrivial gapped states can be found.

Majorana bound states and nonlocal spin correlations in a quantum wire on an unconventional superconductor.

We study theoretically the proximity effect of a one-dimensional metallic quantum wire (in the absence of spin-orbit interaction) lying on top of an unconventional superconductor. Three different material classes are considered as a substrate: (i) a chiral superconductor in class D with broken time-reversal symmetry and a class DIII superconductor (ii) with and (iii) without a nontrivial Z(2) number. Interestingly, we find degenerate zero energy Majorana bound states at both ends of the wire for all three cases. They are unstable against spin-orbit interaction in case (i), while they are topologically protected by time-reversal symmetry in cases (ii) and (iii). Remarkably, we show that nonlocal spin correlations between the two ends of the wire can be simply controlled by a gate potential in our setup.

Exact results for the Kondo screening cloud of two helical liquids.

We analyze the screening of a magnetic quantum dot with spin 1/2 coupled to two helical liquids. Interestingly, we find two qualitatively different sets of Toulouse points, i.e., nontrivial parameters for which we can solve the two channel Kondo model exactly. This enables us to calculate the temperature and voltage dependent Kondo screening cloud, which develops oscillations for an applied spin voltage µ(s). Such a spin voltage can be conveniently applied by a charge bias in a four-terminal helical liquid setup.