The non-trivial topology in the layered $text{FeTe}_{0.55}text{Se}_{0.45}$ (FTS) superconductor has been suggested by both theory and experiment to be strongly dependent on the Te concentration. Motivated by this together with the Te fluctuations exp
ected from alloy disorder, we develop a simple layered model for a strong topological insulator that allows us to describe a scenario where topologically trivial domains permeate the sample. We refer to such a phase as topological domain disordered and study the local density (LDOS) of the topological surface states that can be measured using scanning tunneling spectroscopy (STS) in this phase. We find that topologically trivial domains on the surface, where one would expect the topological surface state to be absent, appear as regions of suppressed LDOS surrounded by domain walls with enhanced LDOS. Furthermore, we show that studying the energy dependence of the STS should allow us to distinguish the topologically trivial parts of the surface from other forms of disorder. Finally, we discuss implications of such local disappearance of the topological surface states for the observation of Majorana modes in vortices.
Motivated by the observation of two distinct superconducting phases in the moireless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superco
nductivity with the highest $T_csim 3$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.
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 on a honeycomb lattice. W
e 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 non-topological. 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 for the triplet-pairing superconductivity in graphene-based moire systems, which is fundamentally distinct from triplet superconductivity in $^3$He and ferromagnetic superconductors.
We study phenomena driven by electron-electron interactions in the minimally twisted bilayer graphene (mTBLG) with a perpendicular electric field. The low-energy degrees of freedom in mTBLG are governed by a network of one-dimensional domain-wall sta
tes, described by two channels of one-dimensional linearly dispersing spin-1/2 fermions. We show that the interaction can realize a spin-gapped inter-channel charge density wave (CDW) state at low temperatures, forming a Coulomb drag between the channels and leaving only one charge conducting mode. For sufficiently high temperatures, power-law-in-temperature resistivity emerges from the charge umklapp scatterings within a domain wall. Remarkably, the presence of the CDW states can strengthen the charge umklapp scattering and induce a resistivity minimum at an intermediate temperature corresponding to the CDW correlation energy. We further discuss the conditions that resistivity of the network is dominated by the domain walls. In particular, the power-law-in-temperature resistivity results can apply to other systems that manifest topological domain-wall structures.
Coulomb blockaded transport of topological superconducting nanowires provides an opportunity to probe the localization of states at both ends of the system in a two-terminal geometry. In addition, it provides a way for checking for subgap states away
from the leads. At the same time, Coulomb blockade transport is difficult to analyze because of the interacting nature of the problem arising from the nonperturbative Coulomb interaction inherent in the phenomenon. Here we show that the Coulomb blockade transport can be modeled at the same level of complexity as quantum point contact tunneling that has routinely been used in mesoscopic physics to understand nanowire experiments provided we consider the regime where the tunneling rate is below the equilibration rate of the nanowire. This assumption leads us to a generalized Meir-Wingreen formula for the tunnel conductance which we use to study various features of the nanowire such as Andreev bound states, self-energy, and soft gap. We anticipate that our theory will provide a route to interpret Coulomb blockade transport in hybrid Majorana systems as resulting from features of the nanowire, such as Andreev bound states and soft gaps.
We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key q
uestion addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias conductance peaks), the nanowire in the presence of quantum dots and inhomogeneous potential (bad zero-bias conductance peaks), and the nanowire in the presence of large disorder (ugly zero-bias conductance peaks). The local conductance by itself is incapable of distinguishing the trivial states from the topological states since zero-bias conductance peaks are generic in the presence of disorder and inhomogeneous potential. The nonlocal conductance, which in principle is capable of providing the bulk gap closing and reopening information at the topological quantum phase transition, is found to be far too weak in magnitude to be particularly useful in the presence of disorder and inhomogeneous potential. Therefore, we focus on the question of whether the combination of the local, nonlocal electrical, and thermal conductance can separate the good, bad, and ugly zero-bias conductance peaks in finite-length wires. Our paper aims to provide a guide to future experiments, and we conclude that a combination of all three measurements would be necessary for a decisive demonstration of topological Majorana zero modes in nanowires -- positive signals corresponding to just one kind of measurements are likely to be false positives arising from disorder and inhomogeneous potential.
Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e
., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.
We propose a general theoretical framework for both constructing and diagnosing symmetry-protected higher-order topological superconductors using Kitaev building blocks, a higher-dimensional generalization of Kitaevs one-dimensional Majorana model. F
or a given crystalline symmetry, the Kitaev building blocks serve as a complete basis to construct all possible Kitaev superconductors that satisfy the symmetry requirements. Based on this Kitaev construction, we identify a simple but powerful bulk Majorana counting rule that can unambiguously diagnose the existence of higher-order topology for all Kitaev superconductors. For a systematic construction, we propose two inequivalent stacking strategies using the Kitaev building blocks and provide minimal tight-binding models to explicitly demonstrate each stacking approach. Notably, some of our Kitaev superconductors host higher-order topology that cannot be captured by the existing symmetry indicators in the literature. Nevertheless, our Majorana counting rule does enable a correct diagnosis for these beyond-indicator models. We conjecture that all Wannierizable superconductors should yield a decomposition in terms of our Kitaev building blocks, up to adiabatic deformations. Based on this conjecture, we propose a universal diagnosis of higher-order topology that possibly works for all Wannierizable superconductors. We also present a realistic example of higher-order topological superconductors with fragile Wannier obstruction to verify our conjectured universal diagnosis. Our work paves the way for a complete topological theory for superconductors.
The bulk photovoltaic effect is an example of a non-linear optical response that leads to a DC current that is relevant for photo-voltaic applications. In this work, we theoretically study this effect in the presence of electron-phonon interactions.
Using the response function formalism we find that the non-linear optical response, in general, contains three operator correlation functions, one of which is not ordered in time. This latter correlator cannot be computed from equilibrium field theory. Using a semiclassical approach instead, we show that the bulk photovoltaic effect can be attributed to the dipole moment of the generated excitons. We then confirm the validity of the semiclassical result (which agrees with the non-interacting result) for non-linear DC response from a quantum master equation approach. From this formalism we find that, in contrast to usual linear response, the scattering rate has a strong implicit effect on the non-linear DC response. Most interestingly, the semiclassical treatment shows that the non-linear DC response for spatially inhomogeneous excitation profiles is strongly non-local and must involve the aforementioned out-of-time-ordered correlators that cannot be computed by equilibrium field theory.
We propose a scheme for the use of magnetic force microscopy to manipulate Majorana zero modes emergent in vortex cores of topological superconductors in the Fe(Se,Te) family. We calculate the pinning forces necessary to drag two vortices together an
d the resulting change in current and charge density of the composite fermion. A possible algorithm for measuring and altering Majorana pair parity is demonstrated.
