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A heavy-fermion superconductor UPt$_3$ is a unique spin-triplet superconductor with multiple superconducting phases. Here we provide the first report on the first-principles analysis of the microscopic superconducting gap structure. We find…
We present our investigations on the superconducting properties of monolayers of FeSe$_{0.5}$Te$_{0.5}$ grown on the 3D topological insulator Bi$_{2}$Se$_{1.2}$Te$_{1.8}$ using low temperature scanning tunneling spectroscopy (STS). While…
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five…
Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum…
The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of…
We systematically investigate the topological properties of spin polarized Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through tuning the Rydberg coupling strength and the inter-layer tunneling amplitude, we…
Three-dimensional topological insulators are characterized by the presence of a bandgap in their bulk and gapless Dirac fermions at their surfaces. New physical phenomena originating from the presence of the Dirac fermions are predicted to…
Conventional topological insulators and superconductors have topologically protected nodal points on their boundaries, and the recent interests in nodal-line semimetals only concerned bulk band structures. Here, we present a novel…
We study the properties of $s$-wave superconductivity induced around a nematic quantum critical point in two-dimensional metals. The strong Landau damping and the Cooper pairing between incoherent fermions have dramatic mutual influence on…
Pairing symmetry plays a central role in the study of superconductivity. It is usually characterized by integer partial-waves, for example, $s$-, $p$-, $d$-waves. In this article, we investigate a new class of topological superconductivity…
We present a general framework for analyzing inhomogeneous (color-) superconducting phases in mean-field approximation without restriction to the Ginzburg-Landau approach. As a first application, we calculate real gap functions with general…
I study cross dimensionality of $p$-orbital atomic fermions loaded in an optical square lattice with repulsive interactions. The cross-dimensionality emerges when the transverse tunneling of $p$-orbital fermions is negligible. With…
For two-dimensional single-valley quadratic band crossing systems with weak repulsive electron-electron interactions, we show that upon introducing a chemical potential, particle-hole order is suppressed and superconductivity becomes the…
Photonic platforms invariant under parity ($\mathcal{P}$), time-reversal ($\mathcal{T}$), and duality ($\mathcal{D}$) can support topological phases analogous to those found in time-reversal invariant ${\mathbb{Z}_2}$ electronic systems…
We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS)…
Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped,…
While the experimental progress on three dimensional topological insulators is rapid, the development of their two dimensional counterparts has been comparatively slow, despite their technological promise. The main reason is materials…
We compute the topological phase diagram of 2D tetragonal superconductors for the only possible nodeless pairing channels compatible with that crystal symmetry. Subject to a Zeeman field and spin-orbit coupling, we demonstrate that these…
The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered…
Intrinsic rhombohedral graphene hosts an unusual low-energy electronic wavefunction, predominantly localized at its outer crystal faces with negligible presence in the bulk. Increasing the number of graphene layers amplifies the density of…