arXiv subjects

Daniel Shaffer

Publications and source records attributed to Daniel Shaffer.

24 records · Page 2Linked to original sources

arXiv2022

Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides

The possibility of realizing pair density wave (PDW) phases, in which Cooper pairs have a finite momentum, presents an interesting challenge that has been studied in a wide variety of systems. In conventional superconductors, this is only possible when external fields lift the spin degeneracy of the Fermi surface, leading to pair formation at an incommensurate momentum. Here, we study a second possibility, potentially relevant to transition metal dichalcogenides, in which the Fermi surface consists of a pair of pockets centered at the $\pm K$ points of the Brillouin zone as well as a central pocket at the $Γ$ point. In the limit where these three pockets are identical, the pairing susceptibility has a logarithmic divergence at the non-zero wave-vectors $\pm \mathbf{K}$, allowing for a weak-coupling analysis of the PDW instability. We find that repulsive electronic interactions combine to yield effective attractive interactions in the singlet and triplet PDW channels, as long as the $Γ$ pocket is present. Because these PDW channels decouple from the uniform superconducting channel, they can become the leading unconventional pairing instability of the system. Upon solving the linearized gap equations, we find that the PDW instability is robust against small trigonal warping of the $\pm K$ pockets and small detuning between the $Γ$ and $\pm K$ pockets, which affect the PDW transition in a similar way as the Zeeman magnetic field affects the uniform superconducting transition. We also derive the Ginzburg-Landau free energy for the PDW gaps with momenta $\pm \mathbf{K}$, analyzing the conditions for and consequences of the emergence of FF-type and LO-type PDW ground states. Our classification of the induced orders in each ground state reveals unusual phases, including an odd-frequency charge-$2e$ superconductor in the LO-type PDW.

cond-mat.supr-con↗

arXiv2022

Chiral Superconductivity in UTe$_2$ via Emergent $C_4$ Symmetry and Spin Orbit Coupling

A lot of attention has been drawn to superconductivity in UTe$_2$, with suggestions of time-reversal symmetry breaking triplet chiral superconducting order parameter. The chirality of the order parameter has been attributed to an accidental near degeneracy of two superconducting components belonging to 1D irreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it has been argued that the chiral $B_{2u}+iB_{3u}$ combination is selected by ferromagnetic fluctuations. In this work we present a possible explanation of the near-degeneracy as a result of an accidental $C_4$ symmetry of the band structure, with the superconducting order parameter belonging the 2D $E_u$ irrep of $D_{4h}$ that uniquely descends to the sought after $B_{2u}+iB_{3u}$ combination. We show that the $C_4$ symmetry is emergent at the level of the interactions using a renormalization group calculation and argue that the chiral combination of the order parameter is favored when spin-orbit coupling is added to the model.

cond-mat.supr-con↗

arXiv2021

Theory of Hofstadter Superconductors

We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $Φ= (p/q)Φ_0$ comparable to the flux quantum $Φ_0 = h/e$. It is established that the dimension and degeneracy of the irreducible representations of the magnetic translation group (MTG) furnished by the charge 2e pairing fields have different properties from those furnished by single particle Bloch states, and in particular are shown to depend on the parity of the denominator $q$. We explore this symmetry analysis to formulate a Ginzburg-Landau theory describing the thermodynamic properties of Hofstadter superconductors at arbitrary rational flux $Φ= (p/q)Φ_0$ in terms of a multicomponent order parameter that describes the finite momentum pairing of electrons across different Fermi surface patches. This phenomenological theory leads to a rich phase diagram characterized by different symmetry breaking patterns of the MTG, which can be interpreted as distinct classes of vortex lattices. A class of $\mathbb{Z}_q$-symmetric Hofstadter SCs is identified, in which the MTG breaks down to a $\mathbb{Z}_q$ subgroup. We study the topological properties of such $\mathbb{Z}_q$-symmetric Hofstadter SCs and show that the parity of the Chern numbers is fixed by the parity of $q$. We identify the conditions for the realization of Bogoliubov Fermi surfaces in the presence of parity and MTG symmetries, establishing a novel topological invariant capturing the existence of such charge-neutral gapless excitations. Our findings, which could bear relevance to the description of re-entrant superconductivity in moiré systems in the Hofstadter regime, establish Hofstadter SC as a fertile setting to explore symmetry broken and topological orders.

cond-mat.supr-con↗

arXiv2020

Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe$_2$

We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_{2}$ in presence of both in-plane magnetic field and Rashba spin-orbit coupling (SOC). Repulsive interactions lead to two distinct instabilities, in singlet- and triplet- interaction channels. While we recover the previously predicted nodal topological superconducting state in the absence of Rashba SOC at large magnetic field with six pairs of nodes along $Γ$-$M$ lines, a finite Rashba SOC breaks the symmetry that protects these nodes and therefore generally lifts them, resulting in a topologically trivial phase. There is an exception when the field is applied along one of the three $Γ$-$K$ lines, however. In that case, a single mirror symmetry remains that can protect two pairs of nodes out of the original six, resulting in a \emph{crystalline} topological superconducting phase. Depending on the Cooper pairs' center-of-mass momentum, this superconducting state displays either Bogolyubov Fermi surfaces or point nodes. Moreover, a chiral topological superconducting phase with Chern number of 6 is realized in the regime of large Rashba SOC and dominant triplet interactions, spontaneously breaking time-reversal symmetry.

cond-mat.str-el↗

arXiv2020

Unexpected two-fold symmetric superconductivity in few-layer NbSe$_2$

Two-dimensional transition metal dichalcogenides (TMDs) have been attracting significant interest due to a range of properties, such as layer-dependent inversion symmetry, valley-contrasted Berry curvatures, and strong spin-orbit coupling (SOC). Of particular interest is niobium diselenide (NbSe2), whose superconducting state in few-layer samples is profoundly affected by an unusual type of SOC called Ising SOC. Combined with the reduced dimensionality, the latter stabilizes the superconducting state against magnetic fields up to ~35 T and could lead to other exotic properties such as nodal and crystalline topological superconductivity. Here, we report transport measurements of few-layer NbSe$_2$ under in-plane external magnetic fields, revealing an unexpected two-fold rotational symmetry of the superconducting state. In contrast to the three-fold symmetry of the lattice, we observe that the magnetoresistance and critical field exhibit a two-fold oscillation with respect to an applied in-plane magnetic field. We find similar two-fold oscillations deep inside the superconducting state in differential conductance measurements on NbSe$_2$/CrBr$_3$ superconductor-magnet junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behavior to the mixing between two closely competing pairing instabilities, namely, the conventional s-wave instability typical of bulk NbSe$_2$ and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results thus demonstrate the unconventional character of the pairing interaction in a few-layer TMD, opening a new avenue to search for exotic superconductivity in this family of 2D materials.

cond-mat.supr-con↗

arXiv2014

Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

quant-ph↗