Twisted bilayers of high-$T_c$ cuprate superconductors have been argued to form topological phases with spontaneously broken time reversal symmetry ${cal T}$ for certain twist angles. With the goal of helping to identify unambiguous signatures of the
se topological phases in transport experiments, we theoretically investigate a suite of Josephson phenomena between twisted layers. We find an unusual non-monotonic temperature dependence of the critical current at intermediate twist angles which we attribute to the unconventional sign structure of the $d$-wave order parameter. The onset of the ${cal T}$-broken phase near $45^circ$ twist is marked by a crossover from the conventional $2pi$-periodic Josephson relation $J(varphi)simeq J_csin{varphi}$ to a $pi$-periodic function as the single-pair tunneling becomes dominated by a second order process that involves two Cooper pairs. Despite this fundamental change, the critical current remains a smooth function of the twist angle $theta$ and temperature $T$ implying that a measurement of $J_c$ alone will not be a litmus test for the ${cal T}$-broken phase. To obtain clear signatures of the ${cal T}$-broken phase one must measure $J_c$ in the presence of an applied magnetic field or radio-frequency drive, where the resulting Fraunhofer patterns and Shapiro steps are altered in a characteristic manner. We discuss these results in light of recent experiments on twisted bilayers of the high-$T_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$.
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $pm K$ valleys can give rise to moir{e} flat bands with nonzero Chern numbers in each valley. The nontrivial b
and topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $mathcal{S} = pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1/2$-filling into a valley-polarized state, which realizes a correlated quantum anomalous Hall state with Chern number $mathcal{C} = pm 2$. Effects of displacement fields are discussed with comparison to nontrivial topology from layer-pseudospin magnetic fields.
We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time reversal symmetry, which can be solved exactly in the limit of a large number $N$ of degrees of freedom. At low temperature, its phase diagram includes a compressibl
e non-Fermi liquid and a strongly-correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a non-zero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction, and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.
Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor F
eTe$_{0.55}$Se$_{0.45}$ that combines bulk $s$-wave pairing with spin helical Dirac surface states, and which thus comprises the ingredients for Majorana modes in absence of an additional proximitizing superconductor. In this work, we investigate the emergence of Majorana vortex modes and lattices in such materials depending on parameters like the magnetic field strength and vortex lattice disorder. A simple 2D square lattice model here allows us to capture the basic physics of the underlying materials system. To address the problem of disordered vortex lattice, which occurs in real systems, we adopt the technique of the singular gauge transformation which we modify such that it can be used in a system with periodic boundary conditions. This approach allows us to go to larger vortex lattices than otherwise accessible, and is successful in replicating several experimental observations of Majorana vortex bound states in the FeTe$_{0.55}$Se$_{0.45}$ platform. Finally it can be related to a simple disordered Majorana lattice model that should be useful for further investigations on the role of interactions, and towards topological quantum computation.
A superconductor with $p_x+ip_y$ order has long fascinated the physics community because vortex defects in such a system host Majorana zero modes. Here we propose a simple construction of a chiral superconductor using proximitized quantum wires and t
wist angle engineering as basic ingredients. We show that a weakly coupled parallel array of such wires forms a gapless $p$-wave superconductor. Two such arrays, stacked on top of one another with a twist angle close to $90^circ$, spontaneously break time reversal symmetry and form a robust, fully gapped $p_x+ip_y$ superconductor. We map out topological phases of the proposed system, demonstrate existence of Majorana zero modes in vortices, and discuss prospects for experimental realization.
Quantum effects can stabilize wormhole solutions in general relativity, allowing information and matter to be transported between two connected spacetimes. Here we study the revival dynamics of signals sent between two weakly coupled quantum chaotic
systems, represented as identical Sachdev-Ye-Kitaev models, that realize holographically a traversable wormhole in anti-de Sitter spacetime AdS$_2$ for large number $N$ of particles. In this limit we find clear signatures of wormhole behavior: an excitation created in one system is quickly scrambled under its unitary dynamics, and is reassembled in the other system after a characteristic time consistent with holography predictions. This leads to revival oscillations that at low but finite temperature decay as a power-law in time. For small $N$ we also observe revivals and show that they arise from a different, non-gravitational mechanism.
Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian (nH) quantum systems. We propose here a circuit realization of nH Dirac and Weyl Hamiltonians subject to time-rever
sal invariant pseudo-magnetic field, enabling the exploration of novel nH physics. We identify the low-energy physics with a generic real energy spectrum from the nH Landau quantization of exceptional points and rings, which can avoid the nH skin effect and provides a physical example of a quasiparticle moving in the complex plane. Realistic detection schemes are designed to probe the flat energy bands, sublattice polarization, edge states protected by a nH energy-reflection symmetry, and a characteristic nodeless probability distribution.
We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single specie
s of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number $N$ of fermions are obtained and show a characteristic scale-invariant $sim |omega|^{-1/2}$ behavior of the spectral function below the transition which is replaced by a $sim |omega|^{-1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle point equations and discussed in the broader context of the field.
Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in s
uch networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral edge modes that traverse the gap and are robust to perturbations. The requisite time reversal symmetry breaking is achieved by including a class of weakly dissipative Hall resistor elements whose physical implementation we describe in detail.
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly-shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi liquid sta
te of such a quantum dot coupled to non-interacting leads. The properties of this setup depend essentially on the ratio $p$ between the number of transverse modes in the lead $M$ and the number of the fermion degrees of freedom $N$ on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the non-trivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear response conductance acquires distinct $sqrt{p}$ and $1/sqrt{p}$ dependencies for the two phases respectively in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak tunneling regime we find differential conductance proportional to the inverse square root of the applied voltage bias $U$. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to $1/sqrt{T}$ for bias energy $eU$ smaller than temperature scale $k_BT$. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
