arXiv subjects

Heqiu Li

Publications and source records attributed to Heqiu Li.

25 records · Page 2Linked to original sources

arXiv2021

Classification of phase transitions and intertwined orders in crystallographic point groups

Symmetry provides important insight in understanding the nature of phase transitions. In the presence of crystalline symmetries, new phenomena in phase transition can emerge, such as intertwined orders and emergent symmetries. In this work, we present a group-theoretical diagnosis of these phenomena in 32 crystallographic point groups. For each group, we classify the possible combinations of intertwined order and analyze different symmetry-broken phases. We find that the symmetries before and after the phase transition uniquely determine the irreducible representation (irrep) of the order parameter and the allowed form of Ginzburg-Landau free energy, from which the nature of phase transition can be inferred, including the order of phase transition and the existence of intermediate phases and emergent symmetries. Our finding will be helpful for the experimental diagnosis of order parameters from symmetry breaking.

cond-mat.mes-hall↗

arXiv2021

Existence of Corner Modes in Elastic Twisted Kagome Lattices

This Letter investigates the emergence of corner modes in elastic twisted Kagome lattices at a critical twist angle, known as self-dual point. We show that a special type of corner modes exist and they are localized at a very specific type of corners independent of the overall shape of the finite lattice. Moreover, these modes appear even in the perturbed lattice at the corners with mirror planes. By exploring its counterpart in electronic system, we attribute such corner modes to charge accumulation at the boundary, which is confirmed by the plot of charge distribution in a finite lattice.

physics.app-ph↗

arXiv2020

Pfaffian formalism for higher-order topological insulators

We generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of four-fold rotational symmetry $C_4$ and the time-reversal symmetry $T$. This Pfaffian description reveals a deep and fundamental link between TIs and HOTIs, and allows important conclusions about TIs to be generalized to HOTIs. As examples, we demonstrate in the Letter how to generalize Fu-Kane's parity criterion for TIs to HOTIs, and also present a general method to efficiently compute the $Z_2$ index of 3D chiral HOTIs without a global gauge.

cond-mat.mes-hall↗

arXiv2020

Topological insulators and higher-order topological insulators from gauge-invariant 1D lines

In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a two-fold-rotational symmetry or a mirror symmetry, a gauge-invariant quantity can be defined for arbitrary 1D lines in the Brillouin zone. Such 1D quantities provide a new pathway to compute the $Z_2$ index of topological insulators. In contrast to the generic setup, where the $Z_2$ index generally involves 2D planes in the Brillouin zone with a globally-defined smooth gauge, this 1D approach only involves some 1D lines in the Brillouin zone without requiring a global gauge. Such a simplified approach can be used in any time-reversal invariant insulators with a two-fold crystalline symmetry, which can be found in 30 of the 32 point groups. In addition, this 1D quantity can be further generalized to higher-order topological insulators to compute the magnetoelectric polarization $P_3$.

cond-mat.mes-hall↗

arXiv2019

Diagnosis of topological nodal lines with nontrivial monopole charge in the presence of rotation symmetries

We discuss a general diagnosis scheme for topological nodal lines protected by time-reversal symmetry and space-inversion symmetry, in the absence of spin-orbit coupling. It is shown that when a shallow band inversion (with a small inverted gap) appears at the $Γ$-point in the Brillouin zone, nodal lines are generated along with the inversion. Much information on the types and numbers of these nodal lines can be related to the rotation eigenvalues and inversion eigenvalues of the inverted bands. In addition, we establish a $\mathbb{Z}$-type monopole charge for nodal lines with fourfold or sixfold rotation axis. We point out that the new monopole charge is only well-defined in a fragile sense, that is, when the orbitals near the Fermi energy are restricted to those having the same sign under a twofold rotation. The diagnosis scheme goes beyond the one discussed in Phys. Rev. X 8, 031069 (2018), particularly when there is a band crossing along some high-symmetry line, or when the nodal line has non-unity monopole charge.

cond-mat.str-el↗

arXiv2016

Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.

cond-mat.mes-hall↗

arXiv2015

Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box

Bose-Einstein condensation (BEC) of a noninteracting Bose gas of N particles in a two-dimensional box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite N at low temperatures T without the occurrence of a phase transition. The conventionally-defined transition temperature TE for an infinite 3D system is shown to correspond in a 2D system with finite N to a crossover temperature between a slow and rapid increase in the fractional boson occupation N0/N of the ground state with decreasing T. We further show that TE ~ 1/log(N) at fixed area per boson, so in the thermodynamic limit there is no significant BEC in 2D at finite T. Thus, paradoxically, BEC only occurs in 2D at finite N with no phase transition associated with it. Calculations of thermodynamic properties versus T and area A are presented, including Helmholtz free energy, entropy S , pressure p, ratio of p to the energy density U/A, heat capacity at constant volume (area) CV and at constant pressure Cp, isothermal compressibility kappa_T and thermal expansion coefficient alpha_p, obtained using both the grand canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE formalism gives acceptable predictions for S, p, p/(U/A), kappa_T and alpha_p at large N, T and A, but fails for smaller values of these three parameters for which BEC becomes significant, whereas the CE formalism gives accurate results for all thermodynamic properties of finite systems even at low T and/or A where BEC occurs.

cond-mat.stat-mech↗