Coherent Transmutation of Electrons into Fractionalized Anyons

TL;DR

It is shown that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasi-particle, leaving its spin, charge, or statistics behind.

Abstract

Electrons have three quantized properties -- charge, spin, and Fermi statistics -- that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters certain exotic states of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to emergent gauge forces and fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasiparticle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.

Figures (1)

• Figure 1: Proposed geometries to observe geometric resonances (generalized Tomasch oscillations) in QSLs. $d_{qsl}$ and $d_{sc}$ are the widths of the QSL and superconducting regions, respectively. (A) An $e$ edge is created by coupling to a superconductor (SC), in which case an electron can coherently enter the $Z_{2}$ sRVB as a fermionic spinon $f$. (B) At the domain wall between $e$ and $m$ edges there is a Majorana fermion zero mode, allowing electrons to coherently pass into the QSL as a bosonic spinon $z$ by emitting a vison $v$ at the $m$ edge. (C) An $e$ edge is created by coupling a spin-rotationally invariant QSL to a noncolinear (N.C.) SDW, allowing an electron to coherently enter the QSL as a fermionic holon, $h$. (D) The Majorana fermion zero mode at the domain wall allows an electron to coherently enter the QSL as a bosonic holon, $b$. In (A) to (D), oscillations in $I(V)$ with a period determined by $d_{qsl}$ [without oscillations in the bulk current $I_{b}(V_{b})$] would provide a conclusive signature of fractionalization in the QSL.