Erhai Zhao

Nonequilibrium superconductivity near spin-active interfaces

The Riccati formulation of the quasiclassical theory of nonequilibrium superconductors is developed for spin-dependent scattering near magnetic interfaces. We derive boundary conditions for the Riccati distribution functions at a spin-active interface that are applicable to a wide range of nonequilibrium transport properties of hybrid systems of superconducting and magnetic materials. We use these results to calculate spin, charge and heat transport for normal metal-ferromagnet-superconductor (NFS) and superconducting-ferromagnetic-superconducting (SFS) point contacts.

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands

Synthetic quantum orbital materials, such as the recent double-well optical lattices loaded with s and p orbital atoms [1, 2], open an avenue to exploit symmetries beyond natural crystals. Exotic superfluid states were reported for bosons. Here, we unveil a topological phase of interacting fermions on a two-leg ladder of unequal parity orbitals, derived from the experimentally realized double-well lattices by dimension reduction. Z2 topological invariant originates simply from the staggered phases of sp-orbital quantum tunneling, requiring none of the previously known mechanisms such as spin-orbit coupling or artificial gauge field. Another unique feature is that upon crossing over to two dimensions with coupled ladders, the edge modes from each ladder form a parity-protected flat band at zero energy, opening the route to strongly correlated states controlled by interactions. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators. The uneven double-well potential formed by laser light has been developed into a powerful tool for quantum gases by numerous groups [1–6]. For instance, controls of atoms on the sand p-orbitals of the checkerboard [1] and hexagonal [6] optical lattices have been demonstrated, and correlation between these orbitals tends to give exotic quantum states [6, 7]. Motivated by these developments, we consider a lattice of uneven double-wells where fermionic atoms are loaded up to the sand porbital levels of the shallow and deep wells respectively, as shown in Fig. 1. The spatial symmetry of the orbital wave function dictates the complex hopping amplitudes between nearby sites. Under certain circumstances, as for the uneven double wells, the orbital hopping pattern is sufficient for producing topologically nontrivial band structures [8]. We will first focus on a one-dimensional ladder system illustrated in Fig. 1b and 1c. This corresponds to the quasi-one dimensional limit of a standard double-well optical lattice, with the optical potential given byTopological insulators are classified according to their symmetries. Discovery of them in electronic solids is thus restricted by orbital and crystalline symmetries available in nature. Synthetic quantum matter, such as the recent double-well optical lattices loaded with s and p orbital ultracold atoms, can exploit symmetries and interaction beyond natural conditions. Here we unveil a topological phase of interacting fermionic atoms on a two-leg ladder derived from the above experimental optical lattice by dimension reduction. The topological band structure originates from the staggered phases of sp orbital tunnelling, requiring neither spin-orbit coupling nor other known mechanisms like p-wave pairing, artificial gauge field or rotation. Upon crossing over to two-dimensional coupled ladders, the edge modes from individual ladder form a parity-protected flat band at zero energy. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators.

Theory of quasi-one-dimensional imbalanced Fermi gases

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.

Phase modulated thermal conductance of Josephson weak links.

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference (phi) of the superconducting leads. Branch-conversion processes, low-energy Andreev bound states near the contact, and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature, and disorder, on the conductance, are reported. For high-transmission weak links, D-->1, the formation of an Andreev bound state leads to suppression of the density of states for the continuum excitations, and thus, to a reduction in the conductance for phi approximately pi. For low-transmission (D<<1) barriers resonant scattering leads to an increase in the thermal conductance as T drops below T(c) (for phase differences near phi=pi).

Current-phase relation for Josephson effect through helical metal

Josephson junctions fabricated on the surface of three-dimensional topological insulators (TI) show a few unusual properties distinct from conventional Josephson junctions. In these devices, the Josephson coupling and the supercurrent are mediated by helical metal, the two-dimensional surface state of the TI. A line junction of this kind is known to support Andreev bound states at zero energy for phase bias

Orbital order in Mott insulators of spinless p-band fermions.

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Heat Transport Through Josephson Point Contacts

and, consequently, the so-called fractional ac Josephson effect. Motivated by recent experiments on TI-based Josephson junctions, here we describe a convenient algorithm to compute the bound-state spectrum and the current-phase relation for junctions of finite length and width. We present analytical results for the bound-state spectrum, and discuss the dependence of the current-phase relation on the length and width of the junction, the chemical potential of the helical metal, and temperature. A thorough understanding of the current-phase relation may help in designing topological superconducting qubits and manipulating Majorana fermions.

Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases.

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.

Modulated pair condensate ofp-orbital ultracold fermions

We present a comprehensive study of heat transport through small superconducting point contacts. The heat current for a temperature-biased weak link is computed as a function of temperature and barrier transparency of thejunction. The transport of thermal energy is controlled by the quasiparticle transmission probability for the point contact that couples the superconducting leads. We derive this transmission probability and results for the heat current starting from nonequilibrium transport equations and interface boundary conditions for the Keldysh propagators in quasiclassical approximation. We discuss the thermal conductance for both clean and dirty superconducting leads, as well as aspects of the nonlinear current response. We show that the transmission probability for continuum quasiparticle states is both energy and phase dependent, and controlled by an interface Andreev bound state below the continuum. For high transparency barriers the formation of a low-energy bound state, when the phase is tuned to Φ=π, leads to a reduction of the heat current relative to that for Φ=0. For low-transparency barriers, a shallow Andreev bound state just below the continuum edge is connected with resonant transmission of quasiparticles for energies just above the gap edge, and leads to enhanced heat conductance as the temperature is lowered below the superconducting transition.

SnTe field effect transistors and the anomalous electrical response of structural phase transition

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.