Constrained Motions and Slow Dynamics in One-Dimensional Bosons with Double-Well Dispersion.

We demonstrate slow dynamics and constrained motion of domain walls in one-dimensional (1D) interacting bosons with double-well dispersion. In the symmetry-broken regime, the domain-wall motion is "fractonlike"-a single domain wall cannot move freely, while two nearby domain walls can move collectively. Consequently, we find an Ohmic-like linear response and a vanishing superfluid stiffness, which are atypical for a Bose condensate in a 1D translation invariant closed quantum system. Near Lifshitz quantum critical point, we obtain superfluid stiffness ρ_{s}∼T and sound velocity v_{s}∼T^{1/2}, showing similar unconventional low-temperature slow dynamics to the symmetry-broken regime. Particularly, the superfluid stiffness suggests an order by disorder effect as ρ_{s} increases with temperature. Our results pave the way for studying fractons in ultracold atom experiments.

Machine Learning the Disorder Landscape of Majorana Nanowires.

We develop a practical machine learning approach to determine the disorder landscape of Majorana nanowires by using training of the conductance matrix and inverting the conductance data in order to obtain the disorder details in the system. The inversion carried out through machine learning using different disorder parametrizations turns out to be unique in the sense that any input tunnel conductance as a function of chemical potential and Zeeman energy can indeed be inverted to provide the correct disorder landscape. Our work opens up a qualitatively new direction of directly determining the topological invariant and the Majorana wave-function structure corresponding to a transport profile of a device using simulations that quantitatively match the specific conductance profile. In addition, this also opens up the possibility for optimizing Majorana systems by figuring out the (generally unknown) underlying disorder only through the conductance data. An accurate estimate of the applicable spin-orbit coupling in the system can also be obtained within the same scheme.

Eliashberg Theory for Dynamical Screening in Bilayer Exciton Condensation.

We study the effect of dynamical screening of interactions on the transition temperatures (T_{c}) of exciton condensation in a symmetric bilayer of quadratically dispersing electrons and holes by solving the linearized Eliashberg equations for the anomalous interlayer Green's functions. We find that T_{c} is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. T_{c} is suppressed well below that predicted by a Hartree Fock mean field theory with unscreened Coulomb interaction, but is above the estimates from the statically screened Coulomb interaction. Furthermore, using a diagrammatic framework, we show that the system is always an exciton condensate at zero temperature but T_{c} is exponentially small for large interlayer separation.

Correlation-Induced Triplet Pairing Superconductivity in Graphene-Based Moiré Systems.

Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model of Dirac fermions with spin, valley, and sublattice degrees of freedom. We find that the f-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and nontopological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively to Dirac fermions for the triplet-pairing superconductivity in graphene-based moiré systems, which is fundamentally distinct from triplet superconductivity in ^{3}He and ferromagnetic superconductors.

Acoustic-Phonon-Mediated Superconductivity in Rhombohedral Trilayer Graphene.

Motivated by the observation of two distinct superconducting phases in the moiréless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest T_{c}∼3 K near the Van Hove singularity. Away from the Van Hove singularity, T_{c} remains finite in a wide range of doping. In our model, the s-wave spin-singlet and f-wave spin-triplet pairings yield the same T_{c}, while other pairing states have negligible T_{c}. Our theory provides a simple explanation for the two distinct superconducting phases in the experiment and suggests that superconductivity and other interaction-driven phases (e.g., ferromagnetism) can have different origins.

Inversion-Protected Higher-Order Topological Superconductivity in Monolayer WTe_{2}.

Monolayer WTe_{2}, a centrosymmetric transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topological nature of superconducting WTe_{2} with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate in-plane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring "higher-order topology" from the boundary perspective. Generally, a superconducting inversion-symmetric quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe_{2}, hosts Majorana corner modes if the superconductivity is parity-odd. We further point out that this higher-order phase is an inversion-protected topological crystalline superconductor and study the bulk-boundary correspondence. Finally, we discuss possible experiments for probing the Majorana corner modes. Our findings suggest superconducting monolayer WTe_{2} is a playground for higher-order topological superconductivity and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.

Proposal for Measuring the Parity Anomaly in a Topological Superconductor Ring.

A topological superconductor ring is uniquely characterized by a switch in the ground state fermion number parity upon insertion of one superconducting flux quantum-a direct consequence of the topological "parity anomaly." Despite the many other tantalizing signatures and applications of topological superconductors, this fundamental, defining property remains to be observed experimentally. Here we propose definitive detection of the fermion parity switch from the charging energy, temperature, and tunnel barrier dependence of the flux periodicity of two-terminal conductance of a floating superconductor ring. We extend the Ambegaokar-Eckern-Schön formalism for superconductors with a Coulomb charging energy to establish new explicit relationships between thermodynamic and transport properties of such a ring and the topological invariant of the superconductor. Crucially, we show that the topological contribution to the conductance oscillations can be isolated from Aharonov-Bohm oscillations of nontopological origin by their different dependence on the charging energy or barrier transparency.

Global Phase Diagram of a Three-Dimensional Dirty Topological Superconductor.

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random s-wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as Cu_{x}Bi_{2}Se_{3}, is discussed.

Z_{3} Parafermionic Zero Modes without Andreev Backscattering from the 2/3 Fractional Quantum Hall State.

Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized 2/3 fractional quantum edge, even an array size of order 10 should allow one to systematically tune into a parafermionic degeneracy.

Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems.

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

Bound States of a Ferromagnetic Wire in a Superconductor.

We consider the problem of bound states in strongly anisotropic ferromagnetic impurities in a superconductor, motivated by recent experiments that claim to observe Majorana modes at the ends of ferromagnetic wires on a superconducting substrate [S. Nadj-Perge et al., Science 346, 602 (2014)]. Generalizing the successful theory of bound states of spherically symmetric impurities, we consider a wirelike potential using both analytical and numerical approaches. We find that away from the ends of the wire the bound states form bands with pronounced van Hove singularities, giving rise to subgap peaks in the local density of states. For sufficiently strong magnetization of the wire, we show that this process generically produces a sharp peak at zero energy in the local density of states near the ends of the wire. This zero-energy peak has qualitative similarities to the claimed signature of a Majorana mode observed in the aforementioned experiment.

Transport in two-dimensional disordered semimetals.

We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the electron-hole liquid subject to zero and finite perpendicular magnetic fields using an effective medium approximation and a complementary mapping on resistor networks. In the presence of smooth disorder and in the limit of a weak electron-hole recombination rate, we find for small but finite overlap of the electron and hole bands an abrupt upturn in resistivity when lowering the temperature but no divergence at zero temperature. We discuss how this behavior is relevant for several experimental realizations and introduce a simple physical explanation for this effect.

Topological invariants for spin-orbit coupled superconductor nanowires.

We show that the Hamiltonian of a multiband spin-orbit coupled semiconductor nanowire with Zeeman splitting and s-wave superconductivity is approximately chiral symmetric. The chiral symmetry becomes exact when only one pair of confinement bands is occupied and the Zeeman splitting is parallel to the nanowire. In this idealized case the Hamiltonian is in the BDI symmetry class of the topological classification of band Hamiltonians, allowing an arbitrary integer number of zero-energy Majorana fermion modes at each end. In the realistic case of multiband wires (Zeeman splitting still parallel to the length) the chiral symmetry is approximate and results in multiple near-zero-energy end states with increasing Zeeman splitting. The existence of such low energy end states implies the vanishing of the minigap with increased Zeeman splitting which can only be restored by breaking the approximate chiral symmetry by a second Zeeman field.

To close or not to close: the fate of the superconducting gap across the topological quantum phase transition in Majorana-carrying semiconductor nanowires.

We investigate theoretically the low-energy physics of semiconductor Majorana wires in the vicinity of a magnetic field-driven topological quantum phase transition (TQPT). The local density of states at the end of the wire, which is directly related to the differential conductance in the limit of point-contact tunneling, is calculated numerically. We find that the dependence of the end-of-wire local density of states on the magnetic field is nonuniversal and that the signatures associated with the closing of the superconducting gap at the Majorana TQPT are essentially invisible within a significant range of experimentally relevant parameters. Our results provide a possible explanation for the recent observation of the apparent nonclosure of the gap at the Majorana TQPT in semiconductor nanowires.

Avoidance of Majorana resonances in periodic topological superconductor-nanowire structures.

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermion in these semiconductor-superconductor-nanowire structures is tuning the semiconductor chemical potential in close proximity to the metallic superconductor. We show that presently realizable structures in experiments with tunable chemical potential lead to Majorana resonances, which are interesting in their own right, but do not manifest non-Abelian statistics. To resolve this crucial barrier to the solid state realization of Majorana fermions, we propose a new topological superconducting array structure where introducing the superconducting proximity effect from adjacent nanowires generates Majorana fermions with non-Abelian statistics.

Diamagnetic susceptibility obtained from the six-vertex model and its implications for the high-temperature diamagnetic state of cuprate superconductors.

We study the diamagnetism of the six-vertex model with the arrows as directed bond currents. To our knowledge, this is the first study of the diamagnetism of this model. A special version of this model, called the F model, describes the thermal disordering transition of an orbital antiferromagnet, known as d-density wave, a proposed state for the pseudogap phase of the high-T(c) cuprates. We find that the F model is strongly diamagnetic and the susceptibility may diverge in the high-temperature critical phase with power-law arrow correlations. These results may explain the surprising recent observation of a diverging low-field diamagnetic susceptibility seen in some optimally doped cuprates within the d-density wave model of the pseudogap phase.

Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures.

We propose and analyze theoretically an experimental setup for detecting the elusive Majorana particle in semiconductor-superconductor heterostructures. The experimental system consists of one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded into a superconducting quantum interference device. We show that the energy spectra of the Andreev bound states at the junction are qualitatively different in topologically trivial (i.e., not containing any Majorana) and nontrivial phases having an even and odd number of crossings at zero energy, respectively. The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage. The observation of this phase transition will be a direct demonstration of the existence of Majorana particles.

Generic new platform for topological quantum computation using semiconductor heterostructures.

We show that a film of a semiconductor in which s-wave superconductivity and Zeeman splitting are induced by the proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. Since time-reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose-a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator-is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.

Emergent gauge field and the Lifshitz transition of spin-orbit coupled bosons in one dimension.

In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z2 inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z ≃ 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.

Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled s-wave superconductors.

Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a platform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled s-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, n, can be either one or two, and should be revealed by a robust zero-bias peak (ZBP) of height 2 ne(2)/h in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.