Charge d -wave topological insulator
- PDF / 313,665 Bytes
- 10 Pages / 612 x 792 pts (letter) Page_size
- 70 Downloads / 222 Views
ONIC PROPERTIES OF SOLID
Charge dWave Topological Insulator Yu. V. Kopaev†, V. V. Kapaev, and V. I. Belyavskii Lebedev Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia email: [email protected] Received March 6, 2013
Abstract—Formation of a condensate of singlet electron–hole pairs in a twodimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the selfconsistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s and d wave channels of electron–hole pairing. Solutions with the pure orbital symmetry of s and dtype are found, as well as solutions with the mixed s + dsymmetry. It is shown that in a wide range of values of the s and d wave coupling constants, the twodimensional insulating order with the orbital symmetry d x2 –y2 can compete with pure ordered s and dxystates and mixed s + dstates. Time reversal symmetry breaking under an estab lished real order with d x2 –y2 wave symmetry may generate the imaginary component of the order parameter with symmetry dxy and cause a rise in topologically nontrivial d + idwave ordering similar to the quantum Hall state in the absence of external magnetic field. DOI: 10.1134/S1063776113120042 †
1. INTRODUCTION Time reversal (TR) symmetry breaking due to the internal magnetic ordering in a twodimensional (2D) crystal may give rise to a state in which excitations in the volume are separated from the ground state by a forbidden gap and, at the boundary, there exist topo logically protected (stable under scattering) edge cur rents as in the case of the quantum Hall effect, but without an external magnetic field [1]. In the case of the quantum spin Hall effect, TRsymmetry is unbro ken and, instead of the edge charge currents, topolog ically protected edge spin currents may occur [2, 3]. In contrast to such spin topological insulators (STIs), structures in which in the absence of an external mag netic field the conventional quantum Hall effect could be observed, are reasonably called charge topological insulators (CTIs). The forbidden gap in STIs may occur due to the excitonic effect as a result of condensation of elec tron–hole pairs (EHPs) in a metalinsulator phase transition [4]. Transition to the excitonic insulator state is possible yet in the weak coupling limit [4], pro vided that the electron spectrum of a singleband metal satisfies the nesting condition ε(p) = –ε(p + Q) on at least part of the Fermi surface. A similar condi tion in a twoband semimetal may hold as well for Q = 0 in the case where the extrema of the electron and the hole bands have the same location. In metals and semimetals with nesting of the Fermi surface, one may observe the occurrence of various ordered states in the form of charge density waves (CDWs) and spin density
† Deceased.
waves (SDWs), as well as charge current density waves and spin current density waves [5]. The nesting momentum Q determines the spatial modulation of the density wave
Data Loading...
