Spin-Selective Perfect Elliptic Dichroism

• The paper demonstrates that spin-selective perfect elliptic dichroism is an optical selection rule where elliptically polarized light excites one spin channel completely while the opposite channel remains inactive.
• It arises from anisotropic Dirac cones in d-wave altermagnets, with the optical transitions governed by a combination of the quantum metric and Berry curvature.
• Tuning the major-axis orientation and ellipticity of light enables precise control over spin-polarized photocurrents, offering promising applications in spin-optoelectronics and metrology.

Searching arXiv for the cited papers to ground the article in current literature. arXiv search query: (Ezawa, 8 Mar 2026) Spin-selective perfect elliptic dichroism is an optical-selection rule in which elliptically polarized light excites only one spin sector while the opposite spin-resolved absorption channel vanishes exactly. In the low-energy theory of a $d$-wave altermagnet, this effect arises from two inequivalent anisotropic Dirac cones carrying opposite spins, so that tuning the major-axis orientation and ellipticity of the incident field can isolate either the up-spin or the down-spin optical transition (Ezawa, 8 Mar 2026). The phenomenon belongs to a broader quantum-geometric optics program in which optical absorption under elliptical polarization is governed by the quantum metric and the Berry curvature, and it is closely related to perfect elliptic optical dichroism previously identified in $p$-wave magnets (Ezawa, 24 Apr 2025).

1. Definition and conceptual scope

In the altermagnetic setting, spin-selective perfect elliptic dichroism means that “only up-spin or down-spin electrons are excited by elliptically polarized light,” with the corresponding spin-resolved absorption rate of the opposite channel equal to zero (Ezawa, 8 Mar 2026). The defining feature is therefore stronger than ordinary polarization dependence: it is an exact extinction condition in one spin channel together with finite absorption in the other.

The mechanism is tied to anisotropic Dirac kinematics rather than to generic spin splitting alone. The abstract of the altermagnet study states that “nonzero photocurrent is induced only by the anisotropy of the Dirac cones,” and the detailed construction shows that the optical matrix elements depend on polarization in a spin-dependent way because the two cones exchange their anisotropy axes between the two spin sectors (Ezawa, 8 Mar 2026). This suggests that the operative control parameter is the joint structure of spin, valley-like cone location, and anisotropic band velocity.

The phenomenon should also be distinguished from broader crystal dichroism. In related first-principles work on circular dichroism of crystals, the central targets are chiral crystals and anisotropic circular-dichroic signals, with emphasis on orbital angular momentum, quadrupole matrix elements, and Wannier interpolation rather than spin-resolved perfect extinction (Multunas et al., 2023). A plausible implication is that spin-selective perfect elliptic dichroism occupies a narrower but more explicitly spin-optoelectronic niche.

2. $d$-wave altermagnet model and anisotropic Dirac structure

The starting point is a four-band model on the square lattice with two sublattices, represented by Pauli matrices $\tau_i$, and two spins, represented by Pauli matrices $\sigma_i$:

$$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$

Here $t,\lambda$ are nearest-neighbor hoppings, $A,B$ are isotropic and anisotropic next-nearest-neighbor hopping amplitudes, $C,D$ are the spin-dependent analogues of $A,B$, $p$0 is the sublattice-staggered exchange splitting, and $p$1 is the chemical potential (Ezawa, 8 Mar 2026).

Because $p$2, the Hamiltonian block-diagonalizes as $p$3. Around half filling, the up-spin sector has a Dirac cone at $p$4 while the down-spin sector has one at $p$5. The corresponding low-energy expansions are

$p$6

$p$7

with Dirac mass $p$8 (Ezawa, 8 Mar 2026).

The crucial feature is the anisotropy. For the up-spin cone at $p$9, the velocity along $d$0 is $d$1, whereas for the down-spin cone at $d$2 the velocity along $d$3 is $d$4; the corresponding roles are exchanged along $d$5 (Ezawa, 8 Mar 2026). This exchange of anisotropy axes is the kinematic origin of spin-selective optical addressing.

3. Elliptically polarized light, quantum geometry, and spin-resolved absorption

The applied monochromatic field has frequency $d$6 and complex amplitude

$d$7

where $d$8 sets the principal-axis orientation and $d$9 with $\tau_i$0 is the ellipticity, with $\tau_i$1 corresponding to circular polarization (Ezawa, 8 Mar 2026). In the dipole approximation, the interband optical transition matrix element is

$\tau_i$2

with $\tau_i$3.

For the anisotropic two-band Dirac model, the squared matrix element takes a compact quantum-geometric form:

$\tau_i$4

where $\tau_i$5 for up spin and $\tau_i$6 for down spin (Ezawa, 8 Mar 2026). The polarization dependence is therefore partitioned into a symmetric contribution from the quantum metric and an antisymmetric contribution from the Berry curvature.

For the Dirac cone with mass $\tau_i$7, the geometric objects are

$\tau_i$8

$\tau_i$9

$\sigma_i$0

The interband absorption rate for spin $\sigma_i$1 is

$\sigma_i$2

Near the band edge $\sigma_i$3, the dominant contribution comes from $\sigma_i$4, so $\sigma_i$5 may be approximated by $\sigma_i$6 (Ezawa, 8 Mar 2026).

This formulation places spin-selective perfect elliptic dichroism squarely within quantum geometry. The same structural decomposition into $\sigma_i$7 and $\sigma_i$8 also appears in the study of elliptic optical dichroism in $\sigma_i$9-wave magnets, where the optical conductivity under elliptical polarization is written as

$$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$0

with $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$1 determined by the Berry curvature (Ezawa, 24 Apr 2025).

4. Exact extinction condition and perfect dichroism

At the optical threshold, the spin-resolved absorption rates become

$$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$2

$$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$3

Perfect elliptic dichroism for spin $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$4 is defined by $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$5 with $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$6 (Ezawa, 8 Mar 2026).

For $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$7, the detailed derivation identifies the choice

$$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$8

as the condition under which $$\begin{aligned} H(k)=&[\mu + A(\cos k_x + \cos k_y)]\,\tau_0\otimes\sigma_0 + B(\cos k_x-\cos k_y)\,\tau_z\otimes\sigma_0 \ &+ t\cos(k_x/2)\cos(k_y/2)\,\tau_x\otimes\sigma_0 + \lambda\sin(k_x/2)\sin(k_y/2)\,\tau_y\otimes\sigma_z \ &+ C(\cos k_x-\cos k_y)\,\tau_0\otimes\sigma_z + [u + D(\cos k_x+\cos k_y)]\,\tau_z\otimes\sigma_z . \end{aligned}$$9 exactly, while

$t,\lambda$0

The complementary choice

$t,\lambda$1

kills $t,\lambda$2 and excites only the down-spin sector (Ezawa, 8 Mar 2026).

The exactness of the extinction condition is the distinctive content of the term “perfect.” In the companion $t,\lambda$3-wave-magnet setting, an analogous perfect elliptic optical dichroism appears at the band edge only for Néel vector $t,\lambda$4, where the conductivity factorizes as

$t,\lambda$5

so that $t,\lambda$6 and the dichroism ratio satisfies $t,\lambda$7 (Ezawa, 24 Apr 2025). By contrast, for $t,\lambda$8 or $t,\lambda$9, the optical conductivity remains strictly positive or has a nonzero minimum, so no perfect dichroism occurs (Ezawa, 24 Apr 2025). This comparison shows that perfect elliptic extinction is symmetry- and orientation-selective rather than generic.

5. Symmetry constraints and third-order nonlinear photocurrent

The altermagnet analysis attributes the optical response to a specific symmetry structure. Inversion symmetry forbids second-order photocurrents such as the shift current and the injection current because these are odd under inversion. The combined antiferromagnetic–fourfold rotational symmetry forces spin splitting without net magnetization, placing the up-spin Dirac cone at $A,B$0 and the down-spin cone at $A,B$1. Time-reversal $A,B$2 symmetry relates the two cones but with opposite spin and anisotropy axes (Ezawa, 8 Mar 2026).

Within this symmetry setting, applying both elliptically polarized light and a static electric field generates a third-order photocurrent whose formula is described in terms of the quantum metric and the Berry curvature. The abstract reports that “only up-spin polarized current is induced,” and that this third-order current is the leading nonzero photocurrent because the second-order photocurrent is prohibited by inversion symmetry inherent to altermagnets (Ezawa, 8 Mar 2026).

The same source emphasizes that the current is induced only by the anisotropy of the Dirac cones. This excludes a common oversimplification according to which any spin-split Dirac system under elliptical driving should show the same response. In the present framework, anisotropy is not a perturbative detail; it is the enabling condition for both the perfect spin-resolved dichroism and the leading third-order photocurrent.

6. Related optical-dichroic frameworks and experimental implications

The literature cited around this topic places spin-selective perfect elliptic dichroism alongside two adjacent lines of work. The first concerns elliptic optical dichroism in magnetic Dirac-type systems. The second concerns circular dichroism in crystalline materials computed from first principles. The three cited papers can be organized as follows.

System	Core optical result	Distinctive element
$A,B$3-wave altermagnet (Ezawa, 8 Mar 2026)	Spin-selective perfect elliptic dichroism; perfectly spin-polarized third-order nonlinear photocurrent	Opposite-spin anisotropic Dirac cones at $A,B$4 and $A,B$5
$A,B$6-wave magnet (Ezawa, 24 Apr 2025)	Perfect elliptic optical dichroism for $A,B$7	Optical response determined by quantum metric and Berry curvature
Chiral crystals (Multunas et al., 2023)	Efficient ab-initio calculation of circular dichroism in crystals	Orbital angular momentum, quadrupole matrix elements, DFT, Wannier interpolation

In the $A,B$8-wave-magnet work, the quantum geometric tensor is stated to be observable by optical absorption of elliptically polarized light, especially at zero momentum through optical absorption at the optical band edge. The same study further states that “It is possible to determine the Néel vector by measuring the ellipticity of the perfect elliptic dichroism,” and the detailed discussion specifies that a single optical-absorption experiment can fix both the magnitude and the sign of the in-plane Néel vector when it lies along the $A,B$9 axis (Ezawa, 24 Apr 2025). This suggests a general metrological role for perfect elliptic dichroism beyond simple spectroscopy.

In the broader crystal-optics context, the first-principles circular-dichroism study reports a computational framework that leverages direct calculations of orbital angular momentum and quadrupole matrix element calculations in density-functional theory and Wannier interpolation, removing the need for band convergence and accelerating Brillouin-zone convergence compared to prior approaches. It also shows the importance of the quadrupole contribution to anisotropic circular dichroism in crystals, and finds that spin-orbit coupling affects the circular dichroism of crystals with heavier atoms primarily through changes in the electronic energies rather than due to direct contributions from the spin matrix elements (Multunas et al., 2023). A plausible implication is that future quantitative treatments of spin-selective elliptic dichroism in realistic materials may likewise need to separate geometric, orbital, and symmetry-enforced contributions with comparable care.

For experimental access in altermagnets, the detailed account proposes spin-resolved optical spectroscopy or time-resolved ARPES with circular or elliptical polarization. One tunes the ellipticity to the predicted critical value and measures that only one spin species is lifted above the gap. In transport, one may further apply a small static in-plane bias and detect a perfectly spin-polarized photocurrent, identified in the detailed discussion as the “jerk” current, whose leading nonzero order is third order in the fields (Ezawa, 8 Mar 2026). Candidate materials are described there as recently identified $C,D$0-wave altermagnets such as strained RuO$C,D$1-type films or engineered oxide heterostructures, where next-nearest-neighbor spin-dependent hoppings produce the required velocity anisotropy $C,D$2 (Ezawa, 8 Mar 2026).

The resulting picture is technically specific. Perfect elliptic dichroism is neither a generic property of elliptical driving nor a synonym for ordinary dichroic contrast. In the altermagnetic realization, it is an exact spin-resolved cancellation phenomenon generated by the interplay of anisotropic Dirac cones, symmetry-protected spin texture, and the quantum-geometric structure of interband optical matrix elements (Ezawa, 8 Mar 2026).