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Register a new userFermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
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We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom{e} lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the $x$-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.
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We investigate the impacts of combination of fermion-fermion interactions and impurity scatterings on the low-energy stabilities of two-dimensional asymmetric materials with a quadratic band crossing point by virtue of the renormalization group that allows us to treat distinct sorts of physical ingredients on the same footing. The coupled flow evolutions of all interaction parameters which carry the central physical information are derived by taking into account one-loop corrections. Several intriguing results are manifestly extracted from these entangled evolutions. At first, we realize that the quadratic band touching structure is particularly robust once the fermionic couplings flow toward the Gaussian fixed point. Otherwise, it can either be stable or broken down against the impurity scattering in the vicinity of nontrivial fixed points. In addition, we figure out two parameters $eta$ and $lambda$ that measure rotational and particle-hole asymmetries are closely energy-dependent and exhibit considerably abundant behaviors depending upon the fates of fermion-fermion couplings and different types of impurities. Incidentally, as both $eta$ and $lambda$ can be remarkably increased or heavily reduced in the low-energy regime, an asymmetric system under certain restricted conditions exhibits an interesting phenomenon in which transitions either from rotational or particle-hole asymmetry to symmetric situation would be activated.
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this context, we present a microscopic weak-coupling theory for the collective modes of a generic multi-component time-reversal symmetry breaking superconductor, and show that fluctuations in the relative amplitude and phase of the two order parameter components are well-defined underdamped collective modes, even in the presence of nodal quasiparticles. We then demonstrate that these generalized clapping modes can be detected using a number of experimental techniques including ac electronic compressibility measurements, electron energy loss spectroscopy, microwave spectroscopy, and ultrafast THz spectroscopy. Finally, we discuss the implications of our work as a new form of collective mode spectroscopy that drastically expands the number of experimental probes capable of detecting time-reversal symmetry breaking in unconventional superconductors such as Sr$_{text{2}}$RuO$_{text{4}}$, UTe$_{text{2}}$, and moire heterostructures.
We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in the topological superconducting state is result of spontaneous breaking of time-reversal symmetry in the superconducting state. The peculiarities in the chiral gapless edge modes behavior are studied, the Chern numbers are calculated.
The second law of thermodynamics points to the existence of an `arrow of time, along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators and the Haldane phase of quantum magnets. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility, but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics, and elucidate potential challenges in utilising topological systems for quantum technologies.
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