Charge order breaks time-reversal symmetry in CsV$_3$Sb$_5$

Abstract

The recently discovered vanadium-based kagome metals AV3Sb5 (A = K, Rb, Cs) exhibit superconductivity at low-temperatures and charge density wave (CDW) order at high-temperatures. A prominent feature of the charge ordered state in this family is that it breaks time-reversal symmetry (TRSB), which is connected to the underlying topological nature of the band structure. In this work, a powerful combination of zero-field and high-field muon-spin rotation/relaxation is used to study the signatures of TRSB of the charge order in CsV3Sb5, as well as its anisotropic character. By tracking the temperature evolution of the in-plane and out-of-plane components of the muonspin polarization, an enhancement of the internal field width sensed by the muon-spin ensemble was observed below TTRSB = TCDW 95 K. Additional increase of the internal field width, accompanied by a change of the local field direction at the muon site from the ab-plane to the c-axis, was detected below T * 30 K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8 T is applied along the crystallographic c−axis, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in CsV3Sb5 by charge order with an onset of 95 K, followed by an enhanced electronic response below 30 K. The observed two-step transition is discussed within the framework of different charge-order instabilities, which, in accordance with density functional theory calculations, are nearly degenerate in energy.

Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid

“…The most well known examples of these are skyrmion and meron crystals -creating and manipulating such topological textures has important spintronics and information storage applications [33][34][35][36][37][38]. More recently, chiral density-wave orders have been reported in the metallic kagomé mate-rials AV 3 Sb 5 [39][40][41][42][43], prompting a search for analogous chiral magnetic orders in kagomé magnets such as FeGe [44], and giving rise to the nascent field of "chiraltronics". How are the topologically ordered states such as CSLs related to chiral broken symmetry states with nontrivial real-space topology?…”

Loop currents in $A$V$_3$Sb$_5$ kagome metals: multipolar and toroidal magnetic orders

“…The nature of the SC state remains widely debated: while experiments have reported both nodeless [16][17][18][19][20] and nodal behavior [21,22], theoretical models have proposed unconventional chiral d-wave and f -wave states [23][24][25][26]. More exotic SC phenomena have also been discussed, motivated by intriguing data, including a time-reversal symmetry-breaking pairing state [21,[27][28][29], a pair density-wave [19], and charge-4e and charge-6e condensates [30].…”

“…Therefore, to achieve a complete description of the SC phase, much of the experimental and theoretical research has focused on elucidating the properties of the charge-ordered * mchriste@nbi.ku.dk state [8,19,27,28,. It is well-established that the CDW leads to a 2 × 2 increase of the unit cell in the (a, b) plane [37], whereas along the crystallographic c-axis the increase can be a factor of 1, 2 or 4 depending on the alkali atom, pressure, and temperature [31,41,44,48,61].…”

“…The most surprising property of the CDW state, which makes it stand out compared to other CDW phases like those seen in metallic chalcogenides [64][65][66][67], is that it appears to break time-reversal symmetry, as reported by scanning tunneling microscopy (STM), muon spin resonance (µSR), and magneto-optical Kerr effect (MOKE) measurements [21,27,28,37,49,63]. A time-reversal symmetry-broken charge order has a natural interpretation in terms of periodic patterns of loop currents [68,69], reminiscent of the Haldane model for the quantum Hall effect [70].…”