arXiv subjects

Wenjie Ji

Publications and source records attributed to Wenjie Ji.

25 records · Page 2Linked to original sources

arXiv2020

Topological Transition on the Conformal Manifold

Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFT), a.k.a. the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point-by-point along the locus. At every point on the conformal manifold, the order and disorder operators have power-law two-point functions, but their critical exponents cross over with each other at the transition point, where stacking the IFTO leaves the fermionic CFT unchanged. We call this continuous transition on the fermionic conformal manifold a topological transition. By gauging the fermion parity, the IFTO stacking becomes a Kramers-Wannier duality between the corresponding bosonic CFTs. Both the IFTO stacking and the Kramers-Wannier duality are induced by the electromagnetic duality of the (2+1)$d$ $\mathbb{Z}_2$ topological order. We provide several examples of topological transitions, including the familiar Luttinger model of spinless fermions (i.e. the $c=1$ massless Dirac fermion with the Thirring interaction), and a new class of $c=2$ examples describing $U(1)\times SU(2)$-protected gapless phases.

cond-mat.str-el↗

arXiv2019

Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions

Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to study are invertible anomalies that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this paper, we introduce a notion of non-invertible anomaly, which describes the boundary of generic topological order. A key feature of non-invertible anomaly is that it has several partition functions. Under the mapping class group transformation of space-time, those partition functions transform in a certain way characterized by the data of the corresponding topological order in one higher dimension. In fact, the anomalous partition functions transform in the same way as the degenerate ground states of the corresponding topological order in one higher dimension. This general theory of non-invertible anomaly may have wide applications. As an example, we show that the irreducible gapless boundary of 2+1D double-semion (DS) topological order must have central charge $c=\bar c \geq \frac{25}{28}$.

cond-mat.str-el↗

arXiv2019

A continuous topological phase transition between two 1D anti-ferromagnetic spin-1 boson superfluids with the same symmetry

Spin-1 bosons on a 1-dimensional chain, at incommensurate filling with anti-ferromagnetic spin interaction between neighboring bosons, may form a spin-1 boson condensed state that contains both gapless charge and spin excitations. We argue that the spin-1 boson condensed state is unstable, and will become one of two superfluids by opening a spin gap. One superfluid must have a spin-1 ground state on a ring if it contains an odd number of bosons and has no degenerate states at the chain end. The other superfluid has a spin-0 ground state on a ring for any numbers of bosons and has a spin-$\frac{1}{2}$ degeneracy at the chain end. The two superfluids have the same symmetry and only differ by a spin-$SO(3)$ symmetry protected topological order. Although Landau theory forbids a continuous phase transition between two phases with the same symmetry, the phase transition between the two superfluids can be generically continuous, which is described by a conformal field theory (CFT) $su(2)_2\oplus u(1)_4 \oplus \overline{su(2)}_2\oplus \overline{u(1)}_4$. Such a CFT has a spin fractionalization: spin-1 excitation can decay into a spin-$\frac{1}{2}$ right mover and a spin-$\frac{1}{2}$ left mover. We determine the critical theory by solving the partition function based on emergent symmetries and modular invariance condition of CFTs.

cond-mat.str-el↗

arXiv2019

Realizing Majorana zero mode with a stripe of \emph{ionized} and \emph{isolated} magnetic atoms on a \emph{layered} superconductor

It has been proposed that a line junction between spiral magnet and superconductor or between ferromagnet and superconductor with Rashba spin-orbital coupling can produce Majorana zero mode (MZM) at the ends of the line. However, a strong magnetic exchange coupling between the magnetic atoms and the superconductor (about half of the bandwidth of the superconductor) is needed to obtain MZM. Here, we design devices to reduce the needed magnetic exchange coupling. In the first proposal, we cover a very narrow $s$-wave superconducting wire formed by a monolayer film or a layered material (such as FeSe or FeSe monolayer on SrTiO$_3$) with \emph{isolated} magnetic atoms. In our second proposal, we place a line of \emph{isolated} magnetic \emph{ions} on a monolayer superconductor or a \emph{layered} superconductor (such as FeSe). We show that, in the above devices, a spiral magnetic order will develop spontaneously to produce a 1D $p$-wave topological superconductor with a sizable gap (above 1/2 of the parent superconducting gap), even for a weak magnetic exchange coupling (less than 1/10 of the bandwidth). The topological superconductor has MZM at ends of the wire.

cond-mat.supr-con↗

arXiv2017

A mechanism of $\frac{e^2}{2h}$ conductance plateau without 1D chiral Majorana fermions

We address the question about the origin of the $\frac12 \frac{e^2}{h}$ conductance plateau observed in a recent experiment on an integer quantum Hall (IQH) film covered by a superconducting (SC) film. Since 1-dimensional (1D) chiral Majorana fermions on the edge of the above device can give rise to the half quantized plateau, such a plateau was regarded as a smoking-gun evidence for the chiral Majorana fermions. However, in this paper we give another mechanism for the $\frac12 \frac{e^2}{h}$ conductance plateau. We find the $\frac12 \frac{e^2}{h}$ conductance plateau to be a general feature of a good electric contact between the IQH film and SC film, and cannot distinguish the existence or the non-existence of 1D chiral Majorana fermions. We also find that the contact conductance between SC and an IQH edge channel has a non-Ohmic form $σ_\text{SC-Hall} \propto V^2$ in $k_BT \ll eV$ limit, if the SC and IQH bulks are fully gapped.

cond-mat.supr-con↗

arXiv2014

Motion of a Solitonic Vortex in the BEC-BCS Crossover

We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li atoms after phase-imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known equation of state in the BEC-BCS crossover.

cond-mat.quant-gas↗

arXiv2013

Heavy Solitons in a Fermionic Superfluid

Topological excitations are found throughout nature, in proteins and DNA, as dislocations in crystals, as vortices and solitons in superfluids and superconductors, and generally in the wake of symmetry-breaking phase transitions. In fermionic systems, topological defects may provide bound states for fermions that often play a crucial role for the system's transport properties. Famous examples are Andreev bound states inside vortex cores, fractionally charged solitons in relativistic quantum field theory, and the spinless charged solitons responsible for the high conductivity of polymers. However, the free motion of topological defects in electronic systems is hindered by pinning at impurities. Here we create long-lived solitons in a strongly interacting fermionic superfluid by imprinting a phase step into the superfluid wavefunction, and directly observe their oscillatory motion in the trapped superfluid. As the interactions are tuned from the regime of Bose-Einstein condensation (BEC) of tightly bound molecules towards the Bardeen-Cooper-Schrieffer (BCS) limit of long-range Cooper pairs, the effective mass of the solitons increases dramatically to more than 200 times their bare mass. This signals their filling with Andreev states and strong quantum fluctuations. For the unitary Fermi gas, the mass enhancement is more than fifty times larger than expectations from mean-field Bogoliubov-de Gennes theory. Our work paves the way towards the experimental study and control of Andreev bound states in ultracold atomic gases. In the presence of spin imbalance, the solitons created here represent one limit of the long sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of mobile Cooper pairs.

cond-mat.quant-gas↗