Symmetry of the charge density wave in cuprates

Abstract

We derive and analyze an effective Ginzburg-Landau (GL) functional for a charge density wave (CDW) for a model of electrons on a tight binding square lattice with density-density interactions. We show, using realistic electronic dispersions for the cuprates, that for the simplest GL theory, the preferred symmetry is typically uni-directional (stripe) type, but inclusion of third-order terms tends to destabilize this in favor of a checkerboard pattern depending on the strength and range of the interaction. This is of interest given the recent observation of such charge order in underdoped YBa2Cu3O6+x.

Charge order inNbSe2

“…(13) and which determines the value of Q CDW independent of the momentum dependence of the electron-phonon coupling. Conversely, in the presence of a band structure without any nesting, the bare electronic susceptibility will be an approximatelyflat function of momentum, and the predicted CDW wave vector Q CDW will be determined entirely by the shape of the electron-phonon coupling.…”

“…The apparent divergences in these expressions are canceled by the cyclic permutation over band indices, and can be removed analytically 35 .…”

“…In the layered cuprate superconductors, with a square lattice of copper atoms, the charge order may be either a 1Q or a 2Q CDW, with the latter consisting of 1Q CDWs along both in-plane lattice directions. These two phases can even compete with one another 13 . In comparison, the well-known 3Q CDW in the layered hexagonal material NbSe 2 , consisting of three superposed density waves at relative angles of 2π/3, has recently been shown to compete with 1Q order in locallystrained regions on the material's surface 14 .…”

Coexistence of Charge-Density-Wave and Pair-Density-Wave Orders in Underdoped Cuprates

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]) The two most frequently discussed candidates for electronic order are incommensurate charge density-wave (CDW) order (Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) and incommensurate pair-density-wave order (PDW), which is a SC order with a finite Cooper pair momentum Q (Refs. [33][34][35][36][37][38]).…”

“…[1-16]) The two most frequently discussed candidates for electronic order are incommensurate charge density-wave (CDW) order (Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) and incommensurate pair-density-wave order (PDW), which is a SC order with a finite Cooper pair momentum Q (Refs. [33][34][35][36][37][38] CDW order in underdoped cuprates has been proposed some time ago [17] and has been analyzed in detail by several groups in the last few years within the spinfluctuation formalism [19,20,[22][23][24][26][27][28] and within t − J model [18,21].…”