[Paper Review] Hidden excitonic quantum states with broken time-reversal symmetry

G. Mazza, Marco Polini|arXiv (Cornell University)|Feb 1, 2023

Advanced Condensed Matter Physics4 citations

TL;DR

This paper proposes a mechanism to stabilize a hidden time-reversal symmetry broken (TRSB) excitonic quantum state in two-dimensional materials via engineered cylindrical geometry, which enables coupling between the excitonic order parameter and a self-generated vector potential. The transition from a charge-density wave state to a TRSB state with persistent orbital currents occurs at a critical cylinder radius, driven by topological constraints and self-generated flux, offering a route to disentangle excitonic from structural phase transitions.

ABSTRACT

The spontaneous breaking of time-reversal symmetry due to purely-orbital mechanisms (i.e.~not involving spin degrees of freedom) yields extremely exotic phases of matter such as Chern insulators and chiral superconductors. In this Letter, we show that excitonic insulators, by exploiting the transition from the excitonic ground state to a purely-orbital time reversal symmetry broken hidden state, can realize another notable example of this class. The transition to the hidden state is controlled by engineered geometrical constraints which enable the coupling between the excitonic order parameter and the free-space electromagnetic field. These results pave the way towards exotic orbital magnetic order in quantum materials and are also relevant for disentangling excitonic phase transitions from trivial structural ones.

Motivation & Objective

• To identify a mechanism for stabilizing a hidden time-reversal symmetry broken (TRSB) quantum state in excitonic insulators without spin degrees of freedom.
• To demonstrate that purely orbital TRSB states can emerge via topological constraints in 2D materials, avoiding reliance on magnetic fields or spin interactions.
• To provide a controlled pathway to distinguish excitonic phase transitions from trivial structural transitions by leveraging geometric confinement.
• To show that self-generated magnetic flux in a cylindrical geometry enables a stable TRSB excitonic state with persistent orbital currents.
• To establish a framework for experimentally probing and tuning excitonic transitions using external flux and geometric tuning.

Proposed method

• Model a 2D system with a square lattice potential and two atoms per unit cell, using Yukawa-type atomic potentials to engineer a band structure with overlapping s- and p±-orbital bands near the Fermi level.
• Use Wannier functions to map the single-particle Hamiltonian into a tight-binding form, ensuring vanishing local hybridization between s and p± orbitals due to symmetry.
• Introduce an excitonic instability in the spin-singlet channel, leading to a ground state that can be either charge-density wave (CDSB) or time-reversal symmetry broken (TRSB) depending on geometry.
• Apply cylindrical boundary conditions to the system, which enforce a self-generated magnetic flux that couples to the excitonic order parameter and stabilizes the TRSB state.
• Solve the coupled equations for the excitonic order parameter and the vector potential using a variational approach, showing that the TRSB state becomes energetically favorable above a critical radius.
• Use the Aharonov-Bohm effect and flux threading to control the transition between CDSB and TRSB states, demonstrating tunability via external flux.

Experimental results

Research questions

• RQ1 Can a purely orbital, time-reversal symmetry broken (TRSB) excitonic state be stabilized in a 2D material without spin-orbit coupling or external magnetic fields?
• RQ2 How do geometric constraints such as cylindrical confinement induce a transition from a charge-density wave (CDSB) state to a TRSB state with persistent orbital currents?
• RQ3 What is the role of self-generated magnetic flux in stabilizing the TRSB excitonic phase, and how does it differ from externally applied fields?
• RQ4 Can the TRSB state be experimentally distinguished from a structural phase transition, and what signatures does it leave in the charge density and current distribution?
• RQ5 How does the energy landscape of the excitonic state depend on the system’s topology and size, particularly in finite versus infinite 2D geometries?

Key findings

• A critical cylinder radius L* exists above which the ground state transitions from a charge-density wave (CDSB) state to a time-reversal symmetry broken (TRSB) state with persistent orbital currents.
• The TRSB state is stabilized by a self-generated magnetic flux that cannot be gauged away, lowering the system's energy relative to the CDSB state.
• The transition is tunable via an external magnetic flux, which controls the energy barrier between the CDSB and TRSB phases, enabling experimental access.
• In the limit of large cylinder radius (L/ℓ₀ → ∞), the diamagnetic and paramagnetic currents cancel, resulting in a TRSB state with vanishing surface current density.
• The cylindrical geometry is topologically distinct from an infinite 2D sheet, as the latter cannot support a finite, self-generated flux due to divergent vector potential and infinite magnetic energy.
• The TRSB excitonic state is charge-symmetric and thus expected to have no direct coupling to lattice distortions, offering a path to disentangle excitonic and structural phase transitions.