Mutual Chern-Simons Theory of Spontaneous Vortex Phase

We apply the mutual Chern-Simons effective theory (Phys. Rev. B 71, 235102) of the doped Mott insulator to the study of the so-called spontaneous vortex phase in the low-temperature pseudogap region, which is characterized by strong unconventional superconducting fluctuations. An effective description for the spontaneous vortex phase is derived from the general mutual Chern-Simons Lagrangian, based on which the physical properties including the diamagnetism, spin paramagnetism, magneto-resistance, and the Nernst coefficient, have been quantitatively calculated. The phase boundaries of the spontaneous vortex phase which sits between the onset temperature $T_{v}$ and the superconducting transition temperature $T_{c}$, are also determined within the same framework. The results are consistent with the experimental measurements of the cuprates.Comment: 12 pages, 8 figure

Slopes for higher rank Artin-Schreier-Witt Towers

We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb{A}^1$, whose Galois group is canonically isomorphic to $\mathbb{Z}_{p^\ell}$, the degree $\ell$ unramified extension of $\mathbb{Z}_p$, which is abstractly isomorphic to $(\mathbb{Z}_p)^\ell$ as a topological group. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function asymptotically form a finite union of arithmetic progressions. As a corollary, we prove the spectral halo property of the spectral variety associated to the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower. This extends the main result in [DWX] from rank one case $\ell=1$ to the higher rank case $\ell\geq 1$.Comment: 20 page

Lower Pseudogap Phase: A Spin/Vortex Liquid State

The pseudogap phase is considered as a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin singlet pairing and the latter is characterized by the formation of the Cooper pair amplitude and described by a generalized Gingzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-1/2 and locking with a supercurrent vortex, known as spinon-vortex composite. Here thermally excited spinon-vortices destroy the phase coherence and are responsible for nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon-vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gapped S=1/2 excitations, where a resonancelike non-propagating spin mode emerges at the antiferromagnetic wavevector with a doping-dependent characteristic energy. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.Comment: 22 pages, 12 figure

An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection

We introduce a new expression for the Z2 topological invariant of band insulators using non- Abelian Berry's connection. Our expression can identify the topological nature of a general band insulator without any of the gauge fixing problems that plague the concrete implementation of previous invariants. The new expression can be derived from the "partner switching" of the Wannier function center during time reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele.Comment: 14 pages, 8 figure